# Publications

### 2024

There is now experimental evidence for Higgs boson decay into a pair of muons, and significant constraints on the Higgs boson decay into a charm quark-antiquark pair. The data on Higgs boson decays into second generation fermions probes various extensions of the Standard Model. We analyze the implications for the Standard Model effective field theory (SMEFT), without and with minimal flavor violation (MFV), for two Higgs doublet models (2HDM) with natural flavor conservation (NFC), for models with vector-like fermions, and for specific models that predict significant modifications of the Yukawa couplings to the light generations.

### 2023

The ATLAS Collaboration has recently reported a search for light-charged Higgs in t → H ^{+} b decay, with H^{+}→ cb¯ . An excess with a local significance of approximately 3σ is found at m_{H+} ≈ 130 GeV, with a best-fit value of BR(t → H ^{+} b) × BR(H^{+}→ cb¯) = (1.6 ± 0.6) × 10^{ −3}. We study the implications of such a hypothetical signal in multi-Higgs doublet models. We take into account constraints from searches for other charged Higgs decays and from flavor-changing neutral current processes. Two Higgs doublet models with flavor structure dictated by natural flavor conservation (NFC), minimal flavor violation (MFV), or the Froggatt-Nielsen (FN) mechanism cannot account for such excess. A three-Higgs doublet model with NFC can account for the signal. The Yukawa couplings of the neutral pseudoscalar A in the down sector, Ŷ_{A}^{D} , should be larger by a factor of 4 – 6 compared to the corresponding Yukawa couplings of the Higgs h, Ŷ_{h}^{D} . We further present two minimal scenarios, one in which a single Yukawa coupling in the down sector, (Ŷ_{A}^{D})_{bb} , gives the only significant contribution, and one in which two Yukawa couplings in the up sector, (Ŷ_{A}^{U})_{tt} and (Ŷ_{A}^{U})_{tc} , give the only significant contributions, and we discuss possible tests of these scenarios.

The Standard Model is an elegant and extremely successful theory that formulates the laws of fundamental interactions among elementary particles. This incisive textbook introduces students to the physics of the Standard Model while providing an essential overview of modern particle physics, with a unique emphasis on symmetry principles as the starting point for constructing models. The Standard Model equips students with an in-depth understanding of this impressively predictive theory and an appreciation of its beauty, and prepares them to interpret future experimental results.

Scalar ultralight dark matter (ULDM) interacting with neutrinos can induce, under certain conditions, time dependent modifications to neutrino oscillation probabilities. The limit in which the ULDM perturbation can be treated as constant throughout the neutrino propagation time has been addressed by several previous works. We complement these by systematically analyzing the opposite limit - accounting for the temporal variations of the ULDM field by solving time dependent Schrödinger equations. In particular, we study a novel two-generations-like CP violating (CPV) signature unique to rapidly oscillating ULDM. We derive the leading order, time dependent corrections to the oscillation probabilities, for both CP conserving and CPV couplings, and explain how they can be measured in current and future experiments.

If Ultra-light dark matter (ULDM) exists and couples to neutrinos, the neutrino oscillation probability might be significantly altered by a parametric resonance. This resonance can occur if the typical frequency of neutrino flavor-oscillations ∆m2/(2E), where ∆m2 is the mass-squared difference of the neutrinos and E is the neutrino energy, matches the oscillation frequency of the ULDM field, determined by its mass, mϕ. The resonance could lead to observable effects even if the ULDM coupling is very small, and even if its typical oscillation period, given by τϕ = 2π/mϕ, is much shorter than the experimental temporal resolution. Defining a small parameter ϵϕ to be the ratio between the contribution of the ULDM field to the neutrino mass and the vacuum value of the neutrino mass, the impact of the resonance is particularly significant if ϵϕmϕL ≳ 4, where L is the distance between the neutrino source and the detector. An outlier in the data collected by the KamLAND experiment which, until now, has been assumed to constitute a statistical fluctuation, or associated with the binning, can actually be explained by such narrow parametric resonance, without affecting the measurements of other current neutrino oscillation experiments. This scenario will be tested by the JUNO experiment.

The branching fraction of the B_{s}→ KK¯ decay has been recently measured by the LHCb and Belle experiments. We study the consistency of the measured value with three relations to other decay rates and CP asymmetries which follow from the Standard Model, and from the approximate flavor SU(3) symmetry of the strong interactions. We find that each of these relations is violated at a level of above 3σ. We argue that various subleading effects — rescattering, electroweak penguins and SU(3) breaking — if larger than theoretically expected, can account for some of these puzzles, but not for all of them simultaneously.

### 2022

The R(D(*)) puzzle stands for a ~ 3σ violation of lepton flavor universality between the decay rates of B → D(*)τν and B → D(*)ℓν, where ℓ = e, μ. If it is accounted for by new physics, there is no reason in general that the relevant neutrinos are, respectively, ντ and νℓ. We study whether the τ related rate could be enhanced by significant contributions to B → D(*)τνℓ from a class of operators in the Standard Model Effective Field Theory (SMEFT). We find the upper bounds from forbidden or rare meson decays imply that the contributions from the lepton flavor violating processes account for no more than about 4% of the required shift. Yet, no fine-tuned flavor alignment is required for the new physics. Searching for the related high-pT process pp → τ±μ∓ can at present put a lower bound on the scale of the lepton flavor violating new physics that is a factor of 2.2 weaker than the bound from meson decays. An exception to our conclusion arises from a specific combination of scalar and tensor SMEFT operators.

The LHCb experiment measured the time-dependent CP asymmetries CKK and SKK in Bs → K+K− decay. Combining with the corresponding CP asymmetries Cππ and Sππ in B → π+π− decay, we find that the size of U-spin breaking in this system is of order 20%. Moreover, the data suggest that these effects are dominated by factorizable contributions. We further study the constraints on new physics contributions to b → uu¯¯¯q (q = s, d). New physics that is minimally flavor violating (MFV) cannot be distinguished from the Standard Model (SM) in these decays. However, new physics that is not MFV can mimic large U-spin breaking. Requiring that the U-spin breaking parameters remain below the size implied by the data leads to a lower bound of 5 − 10 TeV on the scale of generic new physics. If the new physics is subject to the selection rules that follow from the Froggatt-Nielsen (FN) mechanism or from General Minimal Flavor Violation (GMFV), the bound is relaxed to 2 TeV.

If ultra-light dark matter (ULDM) exists and couples to neutrinos, it can be discovered via time-periodic variations in the neutrino mass and mixing parameters. We analyze the current bounds on such a scenario and establish the sensitivity expected for both time-averaged and time-resolved modulations in future neutrino oscillation experiments. We place a special emphasis in our analysis on time modulations of the CP violating mixing phase. We illustrate with a toy model the case where the leading modulation effect can be CP violating while the effect on CP conserving parameters is suppressed. We show a unique imprint that a time averaged CP violating modulation of ULDM can leave in neutrino oscillations, while direct CP asymmetries vanish.

### 2021

This research focuses on the absence of women among academic staff in physics. To explore the causes of this gender imbalance, we focus on the decision-making junction between obtaining a Ph.D. diploma and pursuing a postdoctoral position. We use the mixed-methods paradigm, combining a nationwide representative survey of Ph.D. students in Israel (n=267 respondents out of 404 questioned) and interviews with Ph.D. students and postdoctoral fellows (n=38). The theoretical novelty that we propose is to view such career decision making as a “deal” that involves contextual, organizational, and individual variables and their intersection. Young women are examining the components of this deal: what it offers them and what prices they will have to pay, but their decision is made within a gendered power structure. Studying both context factors and agency, we reveal the multiple hidden ways in which gender operates as a power structure, putting up barriers to women’s academic careers. This latent power structure influences women’s decision making and experiences in several ways. In the academic field, it produces unequal competition in a male-dominated playground. In the social sphere, choosing a demanding academic career is seen as disrupting gender order. Within the family, women carry a greater burden of family work and give precedence to their husband’s career and preferences. Within this social structure, women who decide to follow an academic career feel that they must excel, and this demand for “excellence” acts as a hidden mechanism within the gendered power structure that may prevent talented women from pursuing an academic career in physics.

Abstract We develop an efficient method for solving transport equations, particularly in the context of electroweak baryogenesis. It provides fully-analytical results under mild approximations and can also test semi-analytical results, which are applicable in more general cases. Key elements of our method include the reduction of the second-order differential equations to first order, representing the set of coupled equations as a block matrix of the particle densities and their derivatives, identification of zero modes, and block decomposition of the matrix. We apply our method to calculate the baryon asymmetry of the Universe (BAU) in a Standard Model effective field theory framework of complex Yukawa couplings to determine the sensitivity of the resulting BAU to modifications of various model parameters and rates, and to estimate the effect of the commonly-used thin-wall approximation.

### 2020

The ATLAS and CMS collaborations have not only discovered a new particle, argues Yosef Nir, but also laid bare the underpinnings of electroweak interactions and uncovered the first evidence for a new type of fundamental interaction – one not related to a known symmetry of nature.

We explore the implications of the Standard Model effective field theory (SMEFT) with dimension-six terms involving the Higgs boson and third-generation fermion fields on the rate of Higgs boson production and decay into fermions, on the electric dipole moments (EDMs) of the electron, and on the baryon asymmetry of the Universe. We study the consequences of allowing these additional terms for each flavor separately and for combinations of two flavors. We find that a complex tau Yukawa coupling can account for the observed baryon asymmetry YBobs within current LHC and EDM bounds. A complex b (t) Yukawa coupling can account for 4% (2%) of YBobs, whereas a combination of the two can reach 12%. Combining tau with either t or b enlarges the viable parameter space owing to cancellations in the EDM and in either Higgs production times decay or the total Higgs width, respectively. Interestingly, in such a scenario there exists a region in parameter space where the SMEFT contributions to the electron EDM cancel and collider signal strengths are precisely SM-like, while producing sufficient baryon asymmetry. Measuring C P violation in Higgs decays to tau leptons is the smoking gun for this scenario.

The upper bounds from the ATLAS and CMS experiments on the decay rate of the Higgs boson to two muons provide the strongest constraint on an imaginary part of the muon Yukawa coupling. This bound is more than an order of magnitude stronger than bounds from CP-violating observables, specifically the electric dipole moment of the electron. It excludes a scenario-which had been viable prior to these measurements-that a complex muon Yukawa coupling is the dominant source of the baryon asymmetry. Even with this bound, the muon source can still contribute O(16%) of the asymmetry.

The experimental study of CP violation in B decays has led to significant progress in our understanding of nature: (i) It demonstrated that the Kobayashi-Maskawa mechanism is the dominant source of CP violation in meson decays. (ii) It improved significantly the precision in the determination of the parameters of the Cabibbo–Kobayashi–Maskawa quark-mixing matrix. (iii) It proved that new physics that has order-one flavour-changing couplings to the b quark should be characterised by a mass scale higher than O(10^{3} TeV). Further progress is expected from the Belle II and LHC experiments during the next decade and beyond. Present status and perspectives are here discussed.

### 2019

The recent measurement of Delta A(CP) by the LHCb collaboration requires an O(10) enhancement coming from hadronic physics in order to be explained within the SM. We examine to what extent can NP models explain Delta A(CP) without such enhancements. We discuss the implications in terms of a low energy effective theory as well as in the context of several explicit NP models.

The Higgs program is relevant to many of the open fundamental questions in particle physics and cosmology. Thus, when discussing future collider experiments, one way of comparing them is by assessing their potential contributions to progress on these questions. We discuss in detail the capabilities of various proposed experiments in searching for singlet scalars, which are relevant to several of the open questions, and in measuring Higgs decays into fermion pairs, which are relevant to the flavor puzzles. With regard to other interesting questions, we list the most relevant observables within the Higgs program.

*Women in Physics*. Singh C., Cochran G. & Wilkin N.(eds.). (trueAIP Conference Proceedings). Abstract

This paper presents data on gender balance in physics in Israel, from the first encounter of young pupils with the subject, mainly at high school, through higher education, to the academic staff at Israeli institutions. The segregation by gender by field of study and, later, by occupation becomes very clear when the data on physics education and academic careers in Israel are analyzed. The percentage starts at about one-third girls who study physics at high school, drops to about 16% of female students at the first, second, and third university degrees, and then drops further down to about 7% of academic staff. During the last few years, universities in Israel have applied a series of initiatives to promote gender balance, but apart from preliminary evidence, it is still not possible to assess the success of these programs in improving gender balance.

### 2018

Searches for neutrino-less double-beta decay (0 nu 2 beta) place an important constraint on models where light fields beyond the Standard Model participate in the neutrino mass mechanism. While 0 nu 2 beta-experimental collaborations often consider various massless majoron models, including various forms of majoron couplings and multi-majoron final-state processes, none of these searches considered the scenario where the "majoron" phi is not massless, m(phi) similar to MeV, of the same order as the Q-value of the 0 nu 2 beta reaction. We consider this parameter region and estimate 0 nu 2 beta phi constraints for m(phi) of order MeV. The constraints are affected not only by kinematical phase space suppression but also by a change in the signal to background ratio charachterizing the search. As a result, 0 nu 2 beta phi constraints for m(phi) > 0 diminish significantly below the reaction threshold. This has phenomenological implications, which we illustrate focusing on high-energy neutrino telescopes. The spectral shape of high-energy astrophysical neutrinos could exhibit features due to resonant nu nu -> phi -> nu nu scattering. Such features fall within the sensitivity range of IceCube-like experiments, if m(phi) is of order MeV, making 0 nu 2 beta phi key complimentary laboratory constraint on the scenario. Our results motivate a dedicated analysis by 0 nu 2 beta collaborations, analogous to the dedicated analyses targeting massless majoron models.

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,873 new measurements from 758 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 118 reviews are many that are new or heavily revised, including a new review on Neutrinos in Cosmology.Starting with this edition, the Review is divided into two volumes. Volume 1 includes the Summary Tables and all review articles. Volume 2 consists of the Particle Listings. Review articles that were previously part of the Listings are now included in volume 1.The complete Review (both volumes) is published online on the website of the Particle Data Group (http://pdg.1b1.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is also available.

The present upper bound on κ _{e}, the ratio between the electron Yukawa coupling and its Standard Model value, is of O(600). We ask what would be the implications in case that κ _{e} is close to this upper bound. The simplest extension that allows for such enhancement is that of two Higgs doublet models (2HDM) without natural flavor conservation. In this framework, we find the following consequences: (i) Under certain conditions, measuring κ _{e} and κ _{V} would be enough to predict values of Yukawa couplings for other fermions and for the H and A scalars. (ii) In the case that the scalar potential has a softly broken Z _{2} symmetry, the second Higgs doublet must be light, but if there is hard breaking of the symmetry, the second Higgs doublet can be much heavier than the electroweak scale and still allow the electron Yukawa coupling to be very different from its SM value. (iii) CP must not be violated at a level higher than O(0.01 / κ _{e}) in both the scalar potential and the Yukawa sector. (iv) LHC searches for e ^{+}e ^{−} resonances constrain this scenario in a significant way. Finally, we study the implications for models where one of the scalar doublets couples only to the first generation, or only to the third generation.

### 2017

The R-K(*) anomaly can be explained by tree level exchange of leptoquarks. We study the consequences of subjecting these models to the principle of minimal flavor violation (MFV). We consider MFV in the linear regime, and take the charged lepton Yukawa matrix to be the only spurion that violates lepton flavor universality. We find that a combination of constraints from a variety of processes - b -> s mu mu, b -> s tau tau, b -> s nu nu, b (b) over bar -> tau tau and b -> c tau nu - excludes MFV in these models.

Experimental measurements of the ratios R(D(∗))≡Γ(B→D(*)τv)Γ(B→D(*)ℓv)(ℓ=e,μ) show a 3.9σ deviation from the Standard Model prediction. In the absence of light right-handed neutrinos, a new physics contribution to b → cτν decays necessarily modifies also bb¯ → τ^{+}τ^{−} and/or cc¯ → τ^{+}τ^{−} transitions. These contributions lead to violation of lepton flavor universality in, respectively, Y and ψ leptonic decays. We analyze the constraints resulting from measurements of the leptonic vector-meson decays on solutions to the R(D^{(*)}) puzzle. Available data from BaBar and Belle can already disfavor some of the new physics explanations of this anomaly. Further discrimination can be made by measuring Y(1S, 2S, 3S) → ττ in the upcoming Belle II experiment.

We embed Two Higgs Doublet Models (2HDMs) in the Froggatt Nielsen (FN) framework. We find that the approximate FN symmetry predicts i) approximate Natural Flavor Conservation (NFC) of Types II or IV in the Yukawa sector, and ii) approximate Peccei-Quinn (PQ) symmetry in the scalar sector. We discuss the phenomenological consequences of these features.

We study the phenomenology of exotic color-triplet scalar particles X with charge |Q| = 2/3, 4/3, 5/3, 7/3, 8/3 and 10/3. If X is an SU(2)_{W}-non-singlet, mass splitting within the multiplet allows for cascade decays of the members into the lightest state. We study examples where the lightest state, in turn, decays into a three-body W^{±}jj final state, and show that in such case the entire multiplet is compatible with indirect precision tests and with direct collider searches for continuum pair production of X down to m_{X} ∼ 250 GeV. However, bound states S, made of XX^{†} pairs at m_{S} ≈ 2m_{X}, form under rather generic conditions and their decay to diphoton can be the first discovery channel of the model. Furthermore, for SU(2)_{W}-non-singlets, the mode S → W^{+}W^{−} may be observable and the width of S → γγ and S → jj may appear large as a consequence of mass splittings within the X-multiplet. As an example we study in detail the case of an SU(2)_{W}-quartet, finding that m_{X} ≃ 450 GeV is allowed by all current searches.

### 2016

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,062 new measurements from 721 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Among the 117 reviews are many that are new or heavily revised, including new reviews on Pentaquarks and Inflation. The complete Review is published online in a journal and on the website of the Particle Data Group (http://pdg.lbl.gov). The printed PDG Book contains the Summary Tables and all review articles but no longer includes the detailed tables from the Particle Listings. A Booklet with the Summary Tables and abbreviated versions of some of the review articles is also available.

Abstract: The ATLAS and CMS experiments at the LHC have reported an excess of diphoton events with invariant mass around 750 GeV, with local significance of about 3.6 σ and 2.6 σ, respectively. We entertain the possibility that this excess is due to new physics, in which case the data suggest a new particle with 13 TeV LHC production cross section times diphoton branching ratio of about 5 fb. Interestingly, ATLAS reports a mild preference for a sizeable width for the signal of about 45 GeV; this result appears consistent with CMS, and is further supported by improving the compatibility of the 8 TeV and 13 TeV analyses. We focus on the possibility that the new state is a scalar. First, we show that, in addition to the new state that is needed directly to produce the diphoton bump, yet more new particles beyond the Standard Model are needed to induce diphoton decay rate of the right size. Second, we note that if the excess is attributed to the Breit-Wigner peak of a single new state, then the signal strength and width — taken together — suggest a total LHC production cross section of order 10^{5} fb. Restricting to perturbative models without ad-hoc introduction of many new states or exotic charges, we reach the following conclusions: (i) Gluon-fusion cannot explain the required large production cross section. (ii) Tree level production from initial state quarks cannot explain the required branching ratio to two photons. (iii) Tree level production is constrained by flavor data as well as LHC Run-I and Tevatron dijet analyses. Insisting on a large width we are led to suggest that more than one scalar states, nearly degenerate in mass, could conspire to produce an observed wide bump.

The diphoton excess around mS=750 GeV observed at ATLAS and CMS can be interpreted as coming from S=H and A, the neutral components of a second Higgs doublet. If so, then the consistency of the light Higgs decays with the Standard Model predictions provides upper bounds on the rates of Sto VV, hZ, hh decays. On the other hand, if h to tau mu decay is established, then a lower bound on the rate of S to tau mu decay arises. Requiring that Gamma_S less 45 GeV gives both an upper and a lower bound on the rotation angle from the Higgs basis (Phi_v,Phi_A) to the mass basis (Phi_h,Phi_H). The charged scalar, with mH± 750 GeV, is produced in association with a top quark, and can decay to μ±ν, τ±ν, tb and W±h.

We study how large the rate of the lepton-flavor violating Higgs decay h → τ μ can be in the (R-parity conserving) MSSM. We make no assumptions, such as universality or alignment, about the flavor structure of the MSSM. We only assume that all couplings and, in particular, the trilinear scalar ones, are perturbative. We take into account lower bounds on the bino and slepton masses from τ → μγ and h → γγ as well as upper bounds on the trilinear scalar couplings from the requirement that the global minimum is not charge breaking. We find that in highly fine-tuned regions of parameter space, the ratio BR(h → τ μ)/BR(h → τ τ) can be enhanced by about three orders of magnitude above the estimate from naive dimensional analysis, but still about two orders of magnitude below the present bound. Thus, if h → τ μ is experimentally established to be close to present bounds, the MSSM will be excluded.

### 2014

If t→hq (q=c,u) or h→τ (=μ,e) decays are observed, it will be a clear signal of new physics. We investigate whether natural and viable flavor models can saturate the present direct upper bounds without violating the indirect constraints from low energy loop processes. We carry out our analysis in two theoretical frameworks: minimal flavor violation (MFV) and Froggatt-Nielsen symmetry (FN). The simplest models in either framework predict flavor changing couplings that are too small to be directly observed. Yet, in the MFV framework, it is possible to have lepton flavor changing Higgs couplings close to the bound if spurions related to heavy singlet neutrinos play a role. In the FN framework, it is possible to have large flavor changing couplings in both the up and the charged lepton sectors if supersymmetry plays a role.

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,283 new measurements from 899 Japers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as heavy neutrinos, supersymmetric and technicolor particles, axions, dark photons, etc. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as Supersymmetry, Extra Dimensions, Particle Detectors, Probability, and Statistics. Among the 112 reviews are many that are new or heavily revised including those on: Dark Energy, Higgs Boson Physics, Electroweak Model, Neutrino Cross Section Measurements, Monte Carlo Neutrino Generators, Top Quark, Dark Matter, Dynamical Electroweak Symmetry Breaking, Accelerator Physics of Colliders, High-Energy Collider Parameters, Big Bang Nucleosynthesis, Astrophysical Constants and Cosmological Parameters.

A first measurement of time-reversal (T) asymmetries that are not also CP asymmetries has been recently achieved by the BaBar collaboration. We analyze the measured asymmetries in the presence of direct CP violation, CPTviolation, wrong strangeness decays and wrong sign semileptonic decays. We note that the commonly used SψK and CψK parameters are CP-odd, but have a T-odd CPT-even part and a T-even CPT-odd part. We introduce parameters that have well-defined transformation properties under CP, T and CPT. We identify contributions to the measured asymmetries that are T conserving. We explain why, in order that the measured asymmetries would be purely odd under time-reversal, there is no need to assume the absence of direct CP violation. Instead, one needs to assume (i) the absence of CPT violation in strangeness changing decays, and (ii) the absence of wrong sign decays.

### 2013

Within the four-generation standard model, the Higgs couplings to gluons and to photons deviate in a significant way from the predictions of the three-generation standard model. As a consequence, large departures in several Higgs production and decay channels are expected. Recent Higgs search results, presented by ATLAS, CMS, and CDF, hint on the existence of a Higgs boson with a mass around 125 GeV. Using these results and assuming such a Higgs boson, we derive exclusion limits on the four-generation standard model. For m _{H}=125 GeV, the model is excluded above 99.95% confidence level. For 124.5 GeV≤m_{H}≤127.5 GeV, an exclusion limit above 99% confidence level is found.

We clarify several subtleties concerning the implementation of minimal flavor violation (MFV) in two Higgs doublet models. We derive all the exact and approximate predictions of MFV for the neutral scalar (h, H, A) Yukawa couplings to fermions. We point out several possible tests of this framework at the LHC.

Measurements of the Yukawa couplings of the recently discovered boson h to fermion pairs will provide a new arena for studying flavor physics. We analyze the lessons that can be learned by measuring the h decay rates into the charged lepton pairs, τ ^{+}τ ^{-}, μ ^{+} μ ^{-} and τ ^{±} μ ^{±}. We demonstrate how this set of measurements can distinguish in principle between various classes of flavor models such as natural flavor conservation, minimal flavor violation, and Froggatt-Nielsen symmetry.

A phenomenon known as CP asymmetry, which explains our very existence, has been observed in the decays of Bs0 mesonic particles. The finding represents yet another triumph of the standard model of particle physics.

### 2012

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2658 new measurements from 644 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 112 reviews are many that are new or heavily revised including those on Heavy-Quark and Soft-Collinear Effective Theory, Neutrino Cross Section Measurements, Monte Carlo Event Generators, Lattice QCD, Heavy Quarkonium Spectroscopy, Top Quark, Dark Matter, V-cb & V-ub, Quantum Chromodynamics, High-Energy Collider Parameters, Astrophysical Constants, Cosmological Parameters, and Dark Matter.A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.lbl.gov.

In the supersymmetric framework, prior to the electroweak phase transition, the existence of a baryon asymmetry implies the existence of a Higgsino asymmetry. We investigate whether the Higgsino could be a viable asymmetric dark matter candidate. We find that this is indeed possible. Thus, supersymmetry can provide the observed dark matter abundance and, furthermore, relate it with the baryon asymmetry, in which case the puzzle of why the baryonic and dark matter mass densities are similar would be explained. To accomplish this task, two conditions are required. First, the gauginos, squarks, and sleptons must all be very heavy, such that the only electroweak-scale superpartners are the Higgsinos. With this spectrum, supersymmetry does not solve the fine-tuning problem. Second, the temperature of the electroweak phase transition must be low, in the (1-10)GeV range. This condition requires an extension of the minimal supersymmetric standard model.

There is experimental evidence for a direct CP asymmetry in singly Cabibbo suppressed D decays, ΔA _{CP}∼0.006. Naive expectations are that the standard model contribution to ΔA _{CP} is an order of magnitude smaller. We explore the possibility that a major part of the asymmetry comes from supersymmetric contributions. The leading candidates are models where the flavor structure of the trilinear scalar couplings is related to the structure of the Yukawa couplings via approximate flavor symmetries, particularly U(1), [U(1)]2 and U(2). The recent hints for a lightest neutral Higgs boson with mass around 125 GeV support the requisite order one trilinear terms. The typical value of the supersymmetric contribution to the asymmetry is ΔACPSUSY∼0.001, but it could be accidentally enhanced by order one coefficients.

The CDF and LHCb experiments have recently provided two intriguing hints for new physics: a large forward-backward asymmetry in tt̄ production and a direct CP asymmetry in D decays of order of a percent. In both cases, flavor nonuniversal interactions are required in the up sector, raising the possibility that the two effects come from one and the same new physics source. We show that a minimal model, with an extra scalar doublet, previously suggested to explain the top data, gives-without any modifications or additions-a contribution to CP violation in charm decays that is of the right size.

The new MEG bound on BR(μ→eγ) provides the strongest upper bound on the scale of gauge mediation of supersymmetry breaking. If, in the future, this decay is observed by MEG, the mediation scale will become known to within 1 order of magnitude, and the seesaw scale will be constrained. In such a case, contributions from Planck mediated supersymmetry breaking are likely to be non-negligible, and an interpretation in terms of purely seesaw parameters will be impossible. The recent evidence for |U _{e3}|∼0.15 further sharpens the predictions of gauge-mediated supersymmetry breaking.

The B-factories have measured CP asymmetries in the τ → πKS and D → KSπ modes. The KS state is identified by its decay to two pions at a time that is close to the KS lifetime. Within the Standard Model and many of its extensions, the asymmetries in these modes come from CP violation in K0 - K 0 mixing. We emphasize that the interference between the amplitudes of intermediate KS and KL is as important as the pure KS amplitude. Consequently, the measured asymmetries depend on the times over which the relevant decay rates are integrated and on features of the experiment.

### 2011

New physics at a high scale λ can affect top-related observables at O(1/λ2) via the interference of effective four quark operators with the SM amplitude. The (ūγμγ5Tau)(t̄γμγ5Tat) operator modifies the large Mtt̄ forward-backward asymmetry, and can account for the recent CDF measurement. The (ūγμTau)(t̄γμTat) operator modifies the differential cross section, but cannot enhance the cross section of ultra-massive boosted jets by more than 60%. The hint for a larger enhancement from a recent CDF measurement may not persist future experimental improvements, or may be a QCD effect that is not accounted for by leading order and matched Monte Carlo tools or naive factorization. If it comes from new physics, it may stem from new light states or an O(1/λ4) new physics effect.

A large forward-backward asymmetry in tt̄ production, for large invariant mass of the tt̄ system, has been recently observed by the CDF collaboration. Among the scalar mediated mechanisms that can explain such a large asymmetry, all colored representations are inconsistent by more than 2σ with at least one other top-related measurement. In contrast, the t-channel exchange of a color-singlet weak-doublet scalar is consistent with the differential and with the integrated tt̄ cross section measurements. Constraints from flavor changing processes dictate a very specific structure for the Yukawa couplings of such a new scalar. No sizable deviation in the differential or integrated tt̄ production cross section is expected at the LHC.

### 2010

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2158 new measurements from 551 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. Among the 108 reviews are many that are new or heavily revised including those on neutrino mass, mixing, and oscillations, QCD, top quark, CKM quark-mixing matrix, V-ud & V-us, V-cb & V-ub, fragmentation functions, particle detectors for accelerator and non-accelerator physics, magnetic monopoles, cosmological parameters, and big bang cosmology.A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review. All tables, listings, and reviews (and errata) are also available on the Particle Data Group website: http://pdg.1b1.gov.

Models of minimal lepton flavor violation where the seesaw scale is higher than the relevant flavor scale predict that all lepton flavor violation is proportional to the charged lepton Yukawa matrix. If extra vectorlike leptons are within the reach of the LHC, it will be possible to test the resulting predictions in ATLAS/CMS.

Over the past decade, much progress in experimentally measuring and theoretically understanding flavor physics has been achieved. Specifically, the accuracy of the determination of the CKM elements has been greatly improved, and a large number of (a) flavor-changing neutral-current processes involving b -> d, b -> s, and c -> u transitions and (b) CP-violating asymmetries have been measured. No evidence for new physics has been established. Consequently, strong constraints on new physics at a high scale apply. In particular, the flavor structure of new physics at the teraelectron-volt scale is strongly constrained. We review these constraints and discuss future prospects to better understand the flavor structure of physics beyond the Standard Model.

We study electroweak baryogenesis and electric dipole moments in the presence of the two leading-order, non-renormalizable operators in the Higgs sector of the MSSM. Significant qualitative and quantitative differences from MSSM baryogenesis arise due to the presence of new CP-violating phases and to the relaxation of constraints on the supersymmetric spectrum (in particular, both stops can be light). We find: (1) spontaneous baryogenesis, driven by a change in the phase of the Higgs vevs across the bubble wall, becomes possible; (2) the top and stop CP-violating sources can become effective; (3) baryogenesis is viable in larger parts of parameter space, alleviating the well-known finetuning associated with MSSM baryogenesis. Nevertheless, electric dipole moments should be measured if experimental sensitivities are improved by about one order of magnitude.

The D0 collaboration has recently announced evidence for a dimuon CP asymmetry in B_{d,s} decays of order one percent. If confirmed, this asymmetry requires new physics. We argue that for minimally flavor violating (MFV) new physics, and at low tanβ = ν_{u}/ν_{d}, there are only two four-quark operators (Q_{2,3}) that can provide the required CP violating effect. The scale of such new physics must lie below 260 GeV √tanβ. The effect is universal in the B_{s} and B _{d} systems, leading to S_{ψk} ∼ sin 2β-0.15 and S_{ψφ} ∼ 0.25. The effects on ∈K and on electric dipole moments are negligible. The most plausible mechanism is tree-level scalar exchange. MFV supersymmetry with low tanβ will be excluded. Finally, we explain how a pattern of deviations from the Standard Model predictions for S_{ψφ}, S_{ψ}k and ∈K can be used to test MFV and, if MFV holds, to probe its structure in detail.

Flavor physics may help us understand theories beyond the standard model. In the context of supersymmetry, if we can measure the masses and mixings of sleptons and squarks, we may learn something about supersymmetry and supersymmetry breaking. Here we consider a hybrid gauge-gravity supersymmetric model in which the observed masses and mixings of the standard model leptons are explained by a U(1)×U(1) flavor symmetry. In the supersymmetric sector, the charged sleptons have reasonably large flavor mixings, and the lightest is metastable. As a result, supersymmetric events are characterized not by missing energy, but by heavy metastable charged particles. Many supersymmetric events are therefore fully reconstructible, and we can reconstruct most of the charged sleptons by working up the long supersymmetric decay chains. We obtain promising results for both masses and mixings, and conclude that, given a favorable model, precise measurements at the LHC may help shed light not only on new physics, but also on the standard model flavor parameters.

Future high-precision flavor experiments may discover a pattern of deviations from the standard model predictions for flavor-changing neutral current processes. One of the interesting questions that can be answered then will be whether the flavor structure of the new physics is related to that of the standard model or not. We analyze this aspect of flavor physics within a specific framework: supersymmetric models where the soft breaking terms are dominated by gauge-mediation but get non-negligible contributions from gravitymediation. We compare the possible patterns of non-minimally flavor-violating effects that arise if the gravity-mediated contributions are anarchical vs. the case that they are structured by a Froggatt-Nielsen symmetry. We show that combining information on flavor and CP violation from meson mixing and electric dipole moments is indicative for the flavor structure of gravity-mediation.

### 2009

We propose a method for determining the mass difference between two particles, l

An impressive progress in measurements of the D0-D̄0 mixing parameters has been made in recent years. We explore the implications of these measurements to models of new physics, especially in view of recent upper bounds on the amount of CP violation. We update the constraints on nonrenormalizable four-quark operators. We show that the experiments are close to probing minimally flavor violating models with large tan β. The data challenge models with a scale of order TeV where the flavor violation in the down sector is suppressed by alignment and, in particular, certain classes of supersymmetric models and of warped extra dimension models.

If new CP violating physics contributes to neutral meson mixing, but its contribution to CP violation in decay amplitudes is negligible, then there is a model independent relation between four (generally independent) observables related to the mixing: the mass splitting (x), the width splitting (y), the CP violation in mixing (1-|q/p|), and the CP violation in the interference of decays with and without mixing (). For the four neutral meson systems, this relation can be written in a simple approximate form: ytan x(1-|q/p|). In the K system, all four observables have been measured and obey the relation to excellent accuracy. For the Bs and D systems, new predictions are provided. The success or failure of these relations will probe the physics that is responsible for the CP violation.

In recent years, the CKM picture of flavor and CP violation has been confirmed, mainly due to B decay data. Yet, it is likely that there are small corrections to this picture. We expect to find new physics not much above the weak scale. This new physics could modify flavor changing processes compared to their SM expectations. Much larger B decay data sets, which are expected from LHCb and super-B-factories, will be used to search for these deviations with much improved sensitivity. The combination of low and high energy data will be particularly useful to probe the structure of new physics.

New physics at high energy scale often contributes to K0-K̄0 and D0-D̄0 mixings in an approximately SU(2)L invariant way. In such a case, the combination of measurements in these two systems is particularly powerful. The resulting constraints can be expressed in terms of misalignments and flavor splittings.

The addition of non-renormalizable terms involving the Higgs fields to the MSSM (BMSSM) ameliorates the little hierarchy problem of the MSSM. We analyze in detail the two main cosmological issues affected by the BMSSM: dark matter and baryogenesis. The regions for which the relic abundance of the LSP is consistent with WMAP and collider constraints are identified, showing that the bulk region and other previously excluded regions are now permitted. Requiring vacuum stability limits the allowed regions. Based on a two-loop finite temperature effective potential analysis, we show that the electroweak phase transition can be sufficiently first order in regions that for the MSSM are incompatible with the LEP Higgs mass bound, including parameter values of tan β≲5, m _{-t1}1m _{t}, m _{Q}

We consider supersymmetric models where gauge mediation provides the dominant contributions to the soft supersymmetry breaking terms while gravity mediation provides sub-dominant yet non-negligible contributions. We further assume that the gravity-mediated contributions are subject to selection rules that follow from a Froggatt-Nielsen symmetry. This class of models constitutes an example of viable and natural non-minimally flavor violating models. The constraints from K ^{0}- ^{0} mixing imply that the modifications to the Standard Model predictions for B _{d}- _{d} and B _{s}- _{s} mixing are generically at most at the percent level, but can be of order ten percent for large tan β. The modifications for D ^{0}- ^{0} mixing are generically at most of order a few percent, but in a special subclass of models they can be of order one. We point out ΔB = 1 processes relevant for flavor violation in hybrid mediation.

### 2008

This biennial Review summarizes much of particle physics. Using data from previous editions., plus 2778 new measurements from 645 papers, we list, evaluate, and average measured properties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors., probability, and statistics. Among the 108 reviews are many that are new or heavily revised including those on CKM quark-mixing matrix, V-ud & V-us, V-cb & V-ub, top quark, muon anomalous magnetic moment, extra dimensions, particle detectors, cosmic background radiation, dark matter, cosmological parameters, and big bang cosmology.

Leptogenesis is a class of scenarios where the baryon asymmetry of the Universe is produced from a lepton asymmetry generated in the decays of heavy singlet neutrinos. We explain the motivation for leptogenesis. We review the basic mechanism, and describe subclasses of models. We then focus on recent developments in the understanding of leptogenesis: finite temperature effects, spectator processes, and in particular the significance of flavour physics.

Taking the MSSM as an effective low-energy theory, with a cutoff scale of a few TeV can make significant modifications to the predictions concerning the Higgs and stop sectors. We investigate the consequences of such a scenario for electroweak baryogenesis. We find that the window for MSSM baryogenesis is extended and, most important, can be made significantly more natural. Specifically, it is possible to have one stop lighter than the top and the other significantly lighter than TeV simultaneously with the Higgs mass above the LEP bound. In addition, various aspects concerning CP violation are affected. Most notably, it is possible to have dynamical phases in the bubble walls at tree level, providing CP violating sources for standard model fermions.

Can the Large Hadron Collider explain the masses and mixings of the known fermions? A promising possibility is that these masses and mixings are determined by flavor symmetries that also govern new particles that will appear at the LHC. We consider well-motivated examples in supersymmetry with both gravity and gauge mediation. Contrary to spreading belief, new physics need not be minimally flavor violating. We build nonminimally flavor violating models that successfully explain all known lepton masses and mixings, but span a wide range in their predictions for slepton flavor violation. In natural and favorable cases, these models have metastable sleptons and are characterized by fully reconstructible events. We outline many flavor measurements that are then possible and describe their prospects for resolving both the standard model and new physics flavor puzzles at the Large Hadron Collider.

The mixing between third and second (or first) generation squarks is very small in supersymmetric models with minimal flavor violation such as gauge-, anomaly- or gaugino-mediation. An opportunity to measure this mixing will arise if the lightest stop is close enough in mass to the lightest neutralino, so that the decays into third generation quarks are kinematically forbidden. We analyze under which circumstances it might become possible to measure at the Large Hadron Collider (LHC) the rate of the flavor changing stop decays.

In the first fractions of a second after the Big Bang lingers a question at the heart of our very existence: why does the universe contain matter but almost no antimatter? The laws of physics tell us that equal amounts of matter and antimatter were produced in the early universe—but then something odd happened. Matter won out over antimatter; had it not, the universe today would be dark and barren.But how and when did this occur? In The Mystery of the Missing Antimatter, Helen Quinn and Yossi Nir guide readers into the very heart of this mystery—and along the way offer an exhilarating grand tour of cutting-edge physics.

### 2007

If the LHC experiments discover new particles that couple to the standard model fermions, then measurements by ATLAS and CMS can contribute to our understanding of the flavor puzzles. We demonstrate this statement by investigating a scenario where extra SU(2)-singlet down-type quarks are within the LHC reach. By measuring masses, production cross sections, and relative decay rates, minimal flavor violation (MFV) can in principle be excluded. Conversely, these measurements can probe the way in which MFV applies to the new degrees of freedom. Many of our conclusions are valid in a much more general context than this specific extension of the standard model.

We argue that fast interactions of the lightest singlet neutrino N1 would project part of a preexisting lepton asymmetry Lp onto a direction that is protected from N1 washout effects, thus preventing it from being erased. In particular, we consider an asymmetry generated in N2 decays, assuming that N1 interactions are fast enough to bring N1 into full thermal equilibrium. If N1 decays occur at T 109GeV, that is, before the muon Yukawa interactions enter into thermal equilibrium, then generically part of Lp survives. In this case some of the constraints implied by the standard N1 leptogenesis scenario hold only if Lp≈0. For T 109GeV, Lp is generally erased, unless special alignment or orthogonality conditions in flavor space are realized.

We obtain model independent relations among neutrino masses and leptogenesis parameters. We find exact relations that involve the CP asymmetries _{Nα}, the washout parameters _{α} and θ_{αβ}, and the neutrino masses m_{i} and M_{α}, as well as powerful inequalities that involve just _{α} and m_{i}. We prove that the Yukawa interactions of at least two of the heavy singlet neutrinos are in the strong washout region (_{α} 10^{-3}eV).

The BaBar and Belle experiments have recently presented evidence for D-0 - (D-0) over bar mixing. We explain the following points: (i) The measurements imply width difference y similar to 0.01. In the limit of small CP violation, the CP -odd state is longer-lived; (ii) y similar to 0.01 is consistent with the Standard Model. It suggests that SU(3) breaking from phase space effects is likely to play a major role; (iii) There is no evidence for either large mass splitting or CP violation. Consequently, there is no hint for new ohysics; (iv) The stronger bounds on the mass splitting and on CP violation imply that, if squarks are observed at the LHC, it is unlikely that they will be non-degenerate.

We analyze various theoretical aspects of CP violation in singly Cabibbo suppressed (SCS) D meson decays, such as D→KK,ππ. In particular, we explore the possibility that CP asymmetries will be measured close to the present level of experimental sensitivity of O(10-2). Such measurements would signal new physics. We make the following points: (i) The mechanism at work in neutral D decays could be indirect or direct CP violation (or both). (ii) One can experimentally distinguish between these possibilities. (iii) If the dominant CP violation is indirect, then there are clear predictions for other modes. (iv) Tree-level direct CP violation in various known models is constrained to be much smaller than 10-2. (v) SCS decays, unlike Cabibbo favored or doubly Cabibbo suppressed decays, are sensitive to new contributions from QCD penguin operators and especially from chromomagnetic dipole operators. This point is illustrated with supersymmetric gluino-squark loops, which can yield direct CP violating effects of O(10-2).

### 2006

This biennial Review summarizes much of particle physics. Using data from previous editions, plus 2633 new measurements from 689 papers, we list, evaluate, and average measured properties of guage bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. among the 110 reviews are many that are new or heavily revised including those on CKM quark-mixing, V-ud & V-us, V-cb & V-ub, top quark, muon anomalous magnetic moment, extra dimensions, particle detectors, cosmic background radiation, dark matter, cosmological parameters, and big bang cosmology.

New physics contributions to Bs-B̄s mixing can be parametrized by the size (rs2) and the phase (2θs) of the total mixing amplitude relative to the standard model amplitude. The phase has so far been unconstrained. We first use the D0 measurement of the semileptonic CP asymmetry ASL to obtain the first constraint on the semileptonic CP asymmetry in Bs decays, ASLs=-0.008±0. 011. Then we combine recent measurements by the CDF and D0 Collaborations-the mass difference (ΔMs), the width difference (ΔΓs), and ASLs-to constrain 2θs. The errors on ΔΓs and ASLs should still be reduced to have a sensitive probe of the phase, yet the central values are such that the regions around 2θs∼3π/2 and, in particular, 2θs∼π/2, are disfavored.

We study leptogenesis from the out-of-equilibrium decays of the lightest heavy neutrino N_{1} in the medium (low) temperature regime, T≲10^{12} GeV (10^{9} GeV), where the rates of processes mediated by the τ (and μ) Yukawa coupling are non negligible, implying that the effects of lepton flavors must be taken into account. We find important quantitative and qualitative differences with respect to the case where flavor effects are ignored: (i) The cosmic baryon asymmetry can be enhanced by up to one order of magnitude; (ii) The sign of the asymmetry can be opposite to what one would predict from the sign of the total lepton asymmetry ε_{1}; (iii) Successful leptogenesis is possible even with ε_{1} ≤ 0.

We consider a large class of models where the SU(5) gauge symmetry and a Froggatt-Nielsen (FN) Abelian flavor symmetry arise from a U(5)×U(5) quiver gauge theory. An intriguing feature of these models is a relation between the gauge representation and the horizontal charge, leading to a restricted set of possible FN charges. Requiring that quark masses are hierarchical, the lepton flavor structure is uniquely determined. In particular, neutrino mass anarchy is predicted.

We discuss the effects of various processes that can be active during the leptogenesis era, and present the Boltzmann equations that take them into account appropriately. A non-vanishing Higgs number asymmetry is always present, enhancing the washout of the lepton asymmetry. This is the main new effect when leptogenesis takes place at 10^{12}$">T>10^{12} GeV, reducing the final baryon asymmetry and tightening the leptogenesis bound on the neutrino masses. If leptogenesis occurs at lower temperatures, electroweak sphalerons partially transfer the lepton asymmetry to a baryonic one, while Yukawa interactions and QCD sphalerons partially transfer the asymmetries of the left-handed fields to the right-handed ones, suppressing the washout processes. Depending on the specific temperature range in which leptogenesis occurs, the final baryon asymmetry can be enhanced or suppressed by factors of order 20%-40% with respect to the case when these effects are altogether ignored.

### 2005

The CP asymmetry in the B→KSKSKS decay is being measured by the two B factories. A large deviation of the CP asymmetry SKSKSKS from -SψKS and/or of CKSKSKS from zero would imply new physics in b→s transitions. We try to put upper bounds on the Standard Model size of these deviations, using SU(3) flavor relations and experimental data on the branching ratios of various decay modes that proceed via b→d transitions. We point out several subtleties that distinguish the case of three-body final states from two body ones. We present several simple relations that can become useful once all relevant modes are measured accurately enough.

New CP violating physics in b → s transitions will modify the CP asymmetries in B decays into final CP eigenstates (φK_{S}, η′K_{S}, π^{0}K_{S}, ωK_{S}, ρ^{0}K_{S} and ηK_{S}) from their Standard Model values. In a model independent analysis, the pattern of deviations can be used to probe which Wilson coefficients get a significant contribution from the new physics. We demonstrate this idea using several well-motivated models of new physics, and apply it to current data.

### 2004

We argue that neutrino flavor parameters may exhibit features that are very different from those of quarks and charged leptons. Specifically, within the Froggatt-Nielsen (FN) framework, charged fermion parameters depend on the ratio between two scales, while for neutrinos a third scale - that of lepton number breaking - is involved. Consequently, the selection rules for neutrinos may be different. In particular, if the scale of lepton number breaking is similar to the scale of horizontal symmetry breaking, neutrinos may become flavor-blind even if they carry different horizontal charges. This provides an attractive mechanism for neutrino flavor anarchy.

This is a report of the low energy and flavour physics working group at WHEPP-8, held at the Indian Institute of Technology, Mumbai, India, during 5-16 January 2004.

We argue that neutrino flavor parameters may exhibit features that are very different from those of quarks and charged leptons. Specifically, within the Froggatt-Nielsen (FN) framework, charged fermion parameters depend on the ratio between two scales, while for neutrinos a third scale - that of lepton number breaking - is involved. Consequently, the selection rules for neutrinos may be different. In particular, if the scale of lepton number breaking is similar to the scale of horizontal symmetry breaking, neutrinos may become flavor-blind even if they carry different horizontal charges. This provides an attractive mechanism for neutrino flavor anarchy.

Soft supersymmetry breaking terms involving heavy singlet sneutrinos provide new sources of lepton number violation and of CP violation. In addition to the CP violation in mixing, investigated previously, we find that 'soft leptogenesis' can be generated by CP violation in decay and in the interference of mixing and decay. These additional ways to leptogenesis can be significant for a singlet neutrino Majorana mass that is not much larger than the supersymmetry breaking scale, M ≲ 10^{2}m_{SUSY}- In contrast to CP violation in mixing, for some of these new contributions the sneutrino oscillation rate can be much faster than the decay rate, so that the bilinear scalar term need not be smaller than its natural scale.

The dynamics of baryogenesis or baryon asymmetry, which was produced at the electroweak phase transition (EWPT) by the Kobayashi-Maskawa (KM) phase, was investigated. The standard model (SM), which fulfilled the Sakharov conditions required for baryogenesis, was also discussed. It was found that KM mechanism was unable to account for the baryogenesis as the smallness of the quark flavor parameters suppresed CP violation strongly, while the mass of the Higgs boson is heavy for firstorder EWPT to occur. It was concluded that the baryogenesis is explained by the KM mechanism, provided there were no strong dilution factors coming from the dynamics.

Recent experimental results on B → ρρ decays indicate that the CP asymmetry S_{ρ+ρ-} will give an interesting determination of α=arg[-(V_{td},V*_{tb})/(V_{ud}V* _{ub})]. In the limit when the ρ width is neglected, the B → ππ isospin analysis can also be applied to B → ρρ, once an angular analysis is used to separate transversity modes. The present bound on the shift of S_{ρ+ρ-} from the true sin 2α is already stronger than it is for S_{π+π-}. We point out a subtle violation of the isospin relations when the two ρ mesons are observed with different invariant masses, and how to constrain this effect experimentally.

We study the standard model prediction for the mass difference between the two neutral D meson mass eigenstates, Δm. We derive a dispersion relation based on heavy quark effective theory that relates Am to an integral of the width difference of heavy mesons, ΔΓ, over varying values of the heavy meson mass. Modeling the m_{D} dependence of certain D decay partial widths, we investigate the effects of SU(3) breaking from phase space on the mass difference. We find that Δm may be comparable in magnitude to ΔΓ in the standard model.

### 2003

Measurements of various features of the fluxes of atmospheric and solar neutrinos have provided evidence for neutrino oscillations and therefore for neutrino masses and mixing. The authors review the phenomenology of neutrino oscillations in vacuum and in matter. They present the existing evidence from solar and atmospheric neutrinos as well as the results from laboratory searches, including the final status of the Liquid Scintillator Neutrino Detector (LSND) experiment. The theoretical inputs that are used to interpret the experimental results are described in terms of neutrino oscillations. The allowed ranges for the mass and mixing parameters are derived in two frameworks: First, each set of observations is analyzed separately in a two-neutrino framework; Second, the data from solar and atmospheric neutrinos are analyzed in a three-active-neutrino framework. The theoretical implications of these results are then discussed, including the existence of new physics, the estimate of the scale of this new physics, and the lessons for grand unified theories, for models of extra dimensions and singlet fermions in the bulk, and for flavor models.

Recent measurements of CP violating asymmetries have led to a significant progress in our understanding of CP violation. The implications of the experimental results for the Kobayashi-Maskawa mechanism and for new physics are explained.

We show that soft supersymmetry breaking terms involving the heavy sneutrinos can lead to sneutrino-antisneutrino mixing and to new sources of [Formula presented] violation, which are present even if a single generation is considered. These terms are naturally present in supersymmetric versions of leptogenesis scenarios, and they induce indirect [Formula presented] violation in the decays of the heavy sneutrinos, eventually generating a baryon asymmetry. This new contribution can be comparable to or even dominate over the asymmetry produced in traditional leptogenesis scenarios.

We study the consequences of time variations in the scale of grand unification, M-U, when the Planck scale and the value of the unified coupling at the Planck scale are held fixed. We show that the relation between the variations of the low energy gauge couplings is highly model dependent. It is even possible, in principle, that the electromagnetic coupling alpha varies, but the strong coupling alpha(3) does not (to leading approximation). We investigate whether the interpretation of recent observations of quasar absorption lines in terms of time variation in alpha can be accounted for by time variation in M-U. Our formalism can be applied to any scenario where a time variation in an intermediate scale induces, through threshold corrections, time variations in the effective low scale couplings.

We consider CP asymmetries in neutral B meson decays to ηK_{S}, ΦK_{S}, and K^{+}K^{-} K_{S}. We use SU(3) relations to estimate or bound the contributions to these amplitudes proportional to V*_{ub}V_{us}. Such contributions induce a deviation of the S_{f} terms measured in these time dependent CP asymmetries from that measured for ψK_{S}. For the K ^{+}K^{-}K_{S} mode, we estimate the deviation to be of order 0.1. For the η′ K_{S} mode, we obtain an upper bound on this deviation of order 0.3. For the ΦK_{S} mode, we have to add a mild dynamical assumption to the SU(3) analysis due to insufficient available data, yielding an upper bound of order 0.25. These bounds may improve significantly with future data. While they are large at present compared to the usually assumed standard model contribution, they are obtained with minimal assumptions and hence provide more rigorous tests for new physics. If measurements yield |S_{f}- S_{ΦK}K| that are much larger than our bounds, it would make a convincing case for new physics.

### 2002

Further experimental and theoretical studies of the physics of flavor and CP violation are well motivated. Within the supersymmetric framework, higher precision measurements will allow to explore classes of models with stronger degree of universality: first, models with no universality, such as alignment or heavy first two squark generations; second, models with approximate universality, such as dilaton dominance or AMSB; and finally models of exact universality, such as GMSB. A broad program, including various rare processes or CP asymmetries in B, D and K decays, will provide detailed information about viable extensions of the Standard Model. Some highlights of future B-physics experiments (the present B-factories with integrated luminosity of 0.5 ab(-1), hadron machines, and future high-luminosity B-factories) are described.

Recent experimental searches for A_{SL}, the CP asymmetry in semileptonic B decay, have reached an accuracy of the order of one percent. Consequently, they give meaningful constraints on new physics. We find that cancellations between the standard model (SM) and new physics contributions to B^{0}-B̄^{0} mixing cannot be as strong as was allowed prior to these measurements. The predictions for this asymmetry within the SM and within models of minimal flavor violation (MFV) are below the reach of present and near future measurements. Including order m_{c}^{2}/m_{b}^{2} and Λ_{QCD}/m_{b} corrections we obtain the SM prediction -1.3x10^{-3}

We reexamine the possibility that the solution to the supersymmetric flavor problem is related to small mixing angles in gaugino couplings induced by approximate horizontal Abelian symmetries. We prove that, for a large class of models, there is a single viable structure for the down quark mass matrix with four holomorphic zeros. Consequently, we are able to obtain both lower and upper bounds on the supersymmetric mixing angles and predict the contributions to various flavor changing neutral current processes. We find that the most likely signals for alignment are Δm_{D} close to the present bound, significant CP violation in D^{0}-D̄^{0} mixing, and shifts of the order of a few percent in various CP asymmetries in B^{0} and B_{s} decays. In contrast, the modifications to radiative B decays, to ε′/ε and to K→πvv̄ decays are small. We further investigate a new class of alignment models, where supersymmetric contributions to flavor changing processes are suppressed by both alignment and RGE-induced degeneracy.

We study grand unified theories (GUT) based on an (Formula presented) gauge group in which the GUT scale, (Formula presented) is the vacuum expectation value of an exact or approximate modulus, and in which fast proton decay is avoided through a combination of a large triplet mass and small triplet couplings. These features are achieved by discrete symmetries. In many of our models, (Formula presented) is generated naturally by the balance of higher dimension terms that lift the GUT modulus potential, and soft supersymmetry breaking masses. The theories often lead to interesting patterns of quark and lepton masses. We also discuss some distinctions between grand unified theories and string unification.

Keywords: ELECTRIC-DIPOLE MOMENT; DYNAMICAL SUPERSYMMETRY BREAKING; KOBAYASHI-MASKAWA MATRIX; U(2) FLAVOR SYMMETRY; B-MESON DECAYS; STANDARD-MODEL; ISOSPIN ANALYSIS; QCD FACTORIZATION; BARYON ASYMMETRY; PHENOMENOLOGICAL IMPLICATIONS

### 2001

Measurements of CP-violating observables in neutrino oscillation experiments have been studied in the literature as a way to determine the CP-violating phase in the mixing matrix for leptons. Here we show that such observables also probe new neutrino interactions in the production or detection processes. Genuine CP violation and fake CP violation due to matter effects are sensitive to the imaginary and real parts of new couplings. The dependence of the CP asymmetry on the source-detector distance is different from the standard one and, in particular, enhanced at short distances. We estimate that future neutrino factories will be able to probe in this way new interactions that are up to four orders of magnitude weaker than the weak interactions. We discuss the possible implications for models of new physics.

The possible existence of maximal or near-maximal lepton mixing constitutes an intriguing challenge for fundamental theories of flavor. We study the phenomenological consequences of maximal and near-maximal mixing of the electron neutrino with other (cursive chi=tau and/or muon) neutrinos. We describe the deviations from maximal mixing in terms of a parameter ∈≡1-2 sin^{2} θ_{ecursive chi} and quantify the present experimental status for |∈|

Supersymmetric models with a high supersymmetry breaking scale give, in general, large contributions to ε_{K} and/or to various electric dipole moments, even when contributions to CP conserving, flavor changing processes are sufficiently suppressed. Some examples are models of dilaton dominance, alignment, nonAbelian flavor symmetries, heavy first two generation sfermions, anomaly mediation and gaugino mediation. There is then strong motivation for "approximate CP," that is, a situation where all CP violating phases are small. In contrast, in Supersymmetric models with a low breaking scale it is quite plausible that the CKM matrix is the only source of flavor and CP violation. Gauge mediation provides a concrete example. Approximate CP is then unacceptable. Upcoming measurements of the CP asymmetry in B→ψK_{s} might exclude or support the idea of approximate CP and consequently probe the scale of supersymmetry breaking.

### 2000

New measurements of the CP asymmetry in B --> psiK(S), a(psi Ks), by the BABAR and BELLE collaborations are consistent with the Standard Model prediction for sin 2 beta. These measurements, however, leave open the possibility that a(psi Ks) is well below the Standard Model prediction. We identify deviations from the "reasonable ranges" of hadronic parameters that can lead to low values of sin 2 beta. New physics, mainly in B-0 - (B-0) over bar mixing and/or K-0 - (K-0) over bar mixing, can explain low values of a(psi Ks) in two ways: either by allowing for values of sin 2 beta below the Standard Model prediction or by modifying the relation between a(psi Ks) and sin 2 beta.

If the true values of the D^{0} - D̄^{0} mixing parameters lie within the one sigma ranges of recent measurements, then there is strong evidence for a large width difference, y ≥ 0.01, and large SU(3) breaking effects in strong phases, δ ≥ π/4. These constraints are model independent, and would become stronger if |M_{12}/Γ_{12}|

Neutrino masses and mixings have important implications for models of fermion masses, and, most directly, for the charged lepton sector. We consider supersymmetric Abelian flavor models, where neutrino mass parameters are related to those of charged leptons and sleptons. We show that processes such as (Formula presented) (Formula presented) and (Formula presented) conversion provide interesting probes. In particular, some existing models are excluded by current bounds, while many others predict rates within reach of proposed near future experiments. We also construct models in which the predicted rates for charged lepton flavor violation are below even the proposed experimental sensitivities, but argue that such models necessarily involve loss of predictive power.

Three of the viable solutions of the solar neutrino problem are consistent with close to maximal leptonic mixing: sin^{2}θ_{12} = 1/2(1 - ε_{12}) with |ε_{12}| ≪ 1. Flavor models can naturally explain close to maximal mixing if approximate horizontal symmetries force a pseudo-Dirac structure on the neutrino mass matrix. An experimental determination of |ε_{12}| and sign(ε_{12}) can constrain the structure of the lepton mass matrices and consequently provide stringent tests of such flavor model. If both |ε_{12}| and Δm_{21}^{2} are known, it may be possible to estimate the mass scale of the pseudo-Dirac neutrinos. Radiative corrections to close to maximal mixing are negligible. Subtleties related to the kinetic terms in Froggatt-Nielsen models are clarified.

### 1999

We argue that there could be significant SU(3) violating resonance contributions to D --> K pi decays which would affect the extraction of the D-0 - (D) over bar(0) mixing parameters from experiment. Such contributions can induce a strong phase in the interference between the doubly Cabibbo suppressed and the mixing induced Cabibbo favored contributions to the D-0 --> K(+)pi(-) and (D) over bar(0) --> K(-)pi(+) decays. Consequently, the interpretation of a large, CP conserving interference term can involve a large mass difference Delta M rather than a large width difference Delta Gamma.

We discuss the supersymmetric contribution to epsilon'/epsilon in various supersymmetric flavor models. We find that in alignment models the supersymmetric contribution could be significant while in heavy squark models it is expected to be small. The situation is particularly interesting in models that solve the flavor problems by either of the above mechanisms and the remaining CP problems by means of approximate CP, that is, all CP violating phases are small. In such models, the standard model contributions cannot account for epsilon'/epsilon and a failure of the supersymmetric contributions to do so would exclude the model. In models of alignment and approximate CP, the supersymmetric contributions can account for epsilon'/epsilon only if both the supersymmetric model parameters and the hadronic parameters assume rather extreme values. Such models are then strongly disfavored by the epsilon'/epsilon measurements. Models of heavy squarks and approximate CP are excluded.

Models with extended quark sector affect the CP asymmetry in the B --> psi K-S decay, a psi K-s, in two ways: First, the top-mediated box diagram is not necessarily the only important contribution to B - (B) over bar mixing. Second, the 3 x 3 CKM matrix is no longer unitary. We analyze the constraints that follow from the CDF measurement, a psi K-S = 0.79(-0.44)(+0.41), on the mixing parameters of extended quark sectors. Most noticeably, we find significant constraints on the phase of the relevant flavor changing Z coupling in models with extra down quarks in vector-like representations. Further implications for the CP asymmetry in semileptonic B decays are discussed.

We investigate supersymmetric models where neither R parity nor lepton number nor baryon number is imposed. The full high energy theory has an exact horizontal U(1) symmetry that is spontaneously broken. Quarks and Higgs fields carry integer horizontal charges but leptons carry half integer charges. Consequently, the effective low energy theory has two special features: a U(1) symmetry that is explicitly broken by a small parameter, leading to selection rules, and an exact residual Z_{2} symmetry, that is lepton parity. As concerns neutrino parameters, the Z_{2} symmetry forbids contributions from R_{p}-violating couplings and the U(1) symmetry induces the required hierarchy. As concerns baryon number violation, the Z_{2} symmetry forbids proton decay and the U(1) symmetry provides sufficient suppression of double nucleon decay and of neutron -antineutron oscillations.

Recently, the CDF collaboration has reported a measurement of the CP asymmetry in the B→ψK_{S} decay: a_{ψ}K_{S}=0.79^{+0.41}_{-0.44.} We analyze the constraints that follow from this measurement on the size and the phase of contributions from new physics to $B-\barB$ mixing. Defining the relative phase between the full M_{12} amplitude and the Standard Model contribution to be 2θ_{d}, we find a new bound: $\sin2\theta_d\gsim-0.6 (-0.87)$ at one sigma (95% CL). Further implications for the CP asymmetry in semileptonic B decays are discussed.

The most sensitive experimental searches for D^{0}-D̄^{0} mixing use D^{0} → K^{+}π^{-} decays. It is often assumed that effects of New Physics and, in particular, CP violation, can appear through the mixing, while the c → dus̄ decay amplitude cannot have significant contributions from New Physics and is, therefore, CP conserving to a good approximation. We examine this assumption in two ways. First, we calculate the contributions to the decay in various relevant models of New Physics: Supersymmetry without R-parity, multi-scalar models, left-right symmetric models, and models with extra quarks. We find that phenomenological constraints imply that the New Physics contributions are indeed small compared to the standard model doubly Cabibbo suppressed amplitude. Second, we show that many of our constraints hold model-independently. We find, however, one case where the model-independent bound is rather weak and a CP violating contribution of order 30% is not excluded.

The experimental data on atmospheric and solar neutrinos are used to test the framework of non-anomalous Abelian horizontal gauge symmetries with only three light active neutrinos. We assume that the hierarchy in mass-squared splittings is not accidental and that the small breaking parameters are not considerably larger than 0.2. We find that the small angle MSW solution of the solar neutrino problem can only be accommodated if the v_{μ} - v_{τ} mass hierarchy depends on the charges of at least three sterile neutrinos. The large angle MSW solution can be accommodated in simpler models if v_{e} and v_{μ} form a pseudo-Dirac neutrino, but it is difficult to induce large enough deviation from maximal mixing. The vacuum oscillation solution can be accommodated rather simply. We conclude that it is possible to accommodate the neutrino parameters in the framework of Abelian horizontal symmetries, but it seems that these parameters by themselves will not provide convincing evidence for this framework.

This is a written version of a series of three lectures aimed at graduate students in the field of experimental high energy physics. The emphasis is on physics that is relevant to B-factories. The main topics covered are: (i) The flavor sector of the Standard Model; (ii) Determination of the mixing parameters; (iii) CP violation in meson decays (a model independent description); (iv) CP violation in the Standard Model; (v) CP violation as a probe of new physics.

### 1998

The ground state of string theory may lie at a point of "maximally enhanced symmetry", at which all of the moduli transform under continuous or discrete symmetries. This hypothesis, along with the hypotheses that the theory at high energies has N = 1 supersymmetry and that the gauge couplings are weak and unified, has definite consequences for low energy physics. We describe these, and offer some suggestions as to how these assumptions might be compatible.

We construct phenomenologically viable supersymmetric models where CP is an approximate symmetry. The full high energy theory has exact CP and horizontal symmetries that are spontaneously broken with a naturally induced hierarchy of scales, Λ_{CP} ≪ Λ_{H}. Consequently, the effective low energy theory, i.e. the supersymmetric Standard Model, has CP broken explicitly but by a small parameter. The ε_{K} parameter is accounted for by supersymmetric contributions. The predictions for other CP-violating observables are very different from the Standard Model. In particular, CP-violating effects in neutral B decays into final CP eigenstates such as B → ψK_{s} and in K → πvv̄ decays are very small.

We study the implications of various supersymmetric models on the rare K^{+} → π^{+} vv̄ and K_{L} → π^{0}vv̄ decays. Although large effects are possible in generic supersymmetric models, most of the known supersymmetric flavor models lead to negligible effects. Thus, it is likely that one can get information about CKM matrix elements from these decays even in the presence of supersymmetry. Moreover, the possibility of large contributions to K → πvv̄ in generic supersymmetry models can be constrained by improved bounds on D - D̄ mixing. We show that it may be possible to distinguish between different supersymmetric flavor models by combining the information from the K →πvv̄ decays with that from B - B̄ and D - D̄ mixing.

Fleischer and Mannel (FM) have shown that it may become possible to constrain the angle γ of the unitarity triangle from measurements of various B → πK decays. This constraint is independent of hadronic uncertainties to the few percent level. We show that, within the Standard Model, the FM bound can give strong constraints on the CKM parameters. In particular, it could predict a well-defined sign for sin2γ and sin2α. In a class of extensions of the Standard Model, where New Physics affects only ΔB = 2 (and, in particular, not ΔB = 1 ) processes, the FM bound can lead to constraints on CP asymmetries in B decays into final CP eigenstates even if B - B mixing is dominated by unknown New Physics. In our analysis, we use a new method to combine in a statistically meaningful way the various measurements that involve CKM parameters.

Moduli are generic in string (M) theory. In a large class of gauge-mediated Supersymmetry breaking models, the fermionic components of such fields have very light masses, around the eV scale, and non-negligible mixing with active neutrinos, of order 10^{-4}. Consequently, these fermions could play the role of sterile neutrinos to which active neutrinos oscillate, thus affecting measurements of solar neutrinos or of atmospheric neutrinos. They could also provide warm dark matter, thus affecting structure formation.

Four topics in theory of CP violation are reviewed. (a) CP violation in B decays: We describe a new clean way of constraining the angle gamma of the unitarity triangle and how new CP violation in decay amplitudes can signal new physics. (b) CP violation in K decays: We explain the special features of the decay K-L --> pi(0)nu both as a measurement of Standard Model CP violating parameters and as a probe of new physics. (c) CP violation in D decays: We describe the consequences of CP violation from new physics in D - (D) over bar mixing. (d) CP violation in Supersymmetry: We explain how a combination of measurements of CP violating processes will give insight into the flavor and CP structure of supersymmetry.

The experimental data on atmospheric and solar neutrinos suggest that there is near-maximal mixing between v_{μ} and V_{T} but that their masses are hierarchically separated. In models of Abelian horizontal symmetries, mixing of 0(1) generically implies that the corresponding masses are of the same order of magnitude. We describe two new mechanisms by which a large hierarchy between strongly mixed neutrinos can be achieved in this framework. First, a discrete Abelian symmetry can give the desired result in three ways: mass enhancement, mixing enhancement and mass suppression. Second, holomorphic zeros can give mass suppression.

Within the standard model, and if one assumes that soft rescattering effects are negligible, the (Formula presented) asymmetry (Formula presented) is predicted to be very small and the ratio (Formula presented) provides a bound on the angle (Formula presented) of the unitarity triangle, (Formula presented) We estimate the corrections from soft rescattering effects using an approach based on Regge phenomenology, and find effects of order (Formula presented) with large uncertainties. In particular, we conclude that (Formula presented) and (Formula presented) could not be taken unambiguously to signal new physics. Using SU(3) relations, we suggest experimental tests that could constrain the size of the soft rescattering effects thus reducing the related uncertainty. Finally, we study the effect of various models of new physics on (Formula presented) and on (Formula presented).

### 1997

CP asymmetries in B decays into final CP eigenstates are in many cases theoretically clean. In particular, they do not depend on the values of hadronic parameters. The sign of the asymmetries, however, does depend on the sign of the B_{B} parameter. Furthermore, the information from ε_{K} that all angles of the unitarity triangles lie in the range {0, π} depends on the sign of the B_{K} parameter. Consequently, in the (unlikely) case that the vacuum insertion approximation is such a poor approximation that either B_{B} or B_{K} is negative, the sign of CP asymmetries in neutral B decays will be opposite to the standard predictions. Various subtleties concerning the role of K - K̄ mixing in the case of final states with a single K_{S} or K_{L}, such as the B → ψK_{S} decay, are clarified.

In a large class of models, the only significant new physics effect on the CP asymmetries in B → ψK_{s} and B → ππ decays is a new contribution to the B - B̄ mixing amplitude. This allows a model independent construction of the CKM Unitarity Triangle (up to hadronic uncertainties). Furthermore, the contributions to the mixing from the Standard Model and from the new physics can be disentangled. A serious obstacle to this analysis is an eightfold discrete ambiguity in solving for the angles of the triangle. Several ways to reduce the ambiguity either by making further measurements, or by making further assumptions about the nature of the new physics are described.

We analyze the decay K_{L} → π^{0}νν̄ in a model independent way. If lepton flavor is conserved the final state is (to a good approximation) purely CP even. In that case this decay mode goes mainly through CP violating interference between mixing and decay. Consequently, a theoretically clean relation between the measured rate and electroweak parameters holds in any given model. Specifically, Γ (K_{L} → π^{0}νν̄)/Γ (K^{+} → π^{+}νν̄) = sin^{2} θ (up to known isospin corrections), where θ is the relative CP violating phase between the K - K̄ mixing amplitude and the s → dνν̄ dececay amplitude. The experimental bound on BR(K^{+} → π^{+}νν̄) provides a model independent upper bound: BR(K_{L} → π^{0}νν̄) -8. In models with lepton flavor violation, the final state is not necessarily a CP eigenstate. Then CP conserving contributions can dominate the decay rate.

We study various modifications to the minimal models of gauge-mediated supersymmetry breaking. We argue that, under reasonable assumptions, the structure of the messenger sector is rather restricted. We investigate the effects of possible mixing between messenger and ordinary squark and slepton fields and, in particular, violation of universality. We show that acceptable values for the μ and B parameters can naturally arise from discrete, possibly horizontal, symmetries. We claim that in models where the supersymmetry-breaking parameters A and B vanish at the tree level, tanβ could be large without fine-tuning. We explain how the supersymmetric CP problem is solved in such models.

### 1996

We study neutrino masses and mixing in supersymmetric models without R parity and with generic soft Supersymmetry breaking terms. Neutrinos acquire mass from various sources: tree level neutrino-neutralino mixing, loop effects and non-renormalizable operators. Abelian horizontal symmetries (invoked to explain the smallness and hierarchy in quark parameters) replace R parity in suppressing neutrino masses. We find lower bounds on the mixing angles: sin θ_{ij} ≳ m(l_{i}^{-})/m(l_{j}^{-}) (i e)/m(ν_{μ}) ∼ sin^{2} θ_{12}; m(ν_{i})/m(ν_{τ}) ∼ 10^{-7} sin^{2} θ_{i3} (i = 1, 2). Bounds from laboratory experiments exclude m_{ντ} ≳ 3 MeV and cosmological constraints exclude m_{ντ} ≳ 100 eV. Neither the solar nor the atmospheric neutrino problems are likely to be solved by ν_{μ} - ν_{e} oscillations. These conclusions can be evaded if holomorphy plays an important role in the lepton Yukawa couplings.

Models that combine Abelian horizontal symmetries and spontaneous CP violation can (i) explain the smallness and hierarchy in quark parameters; (ii) satisfactorily suppress supersymmetric contributions to flavor changing neutral current processes; (iii) solve the μ-problem; and (iv) suppress supersymmetric contributions to CP violating observables to an acceptable level. The CKM phase is script O sign(1) and responsible, through Standard Model box diagrams, to ε_{K}. The supersymmetric CP violating phases are suppressed, φ_{A} ∼ λ^{6} and φ_{B} ∼ λ^{8} (λ ∼ 0.2), leading to an electric dipole moment of the neutron that is about 2-3 orders of magnitude below the experimental bound.

If New Physics contributes significantly to neutral-meson mixing, then it is quite likely that it does sc in a CP-violating manner. In D^{0}-D̄^{0} mixing measured through D^{0} → K^{+} π^{-}, CP violation induces a term ∝ t exp[-Γt] with important implications for experiments. For B_{s}-B̄_{s} mixing, a non-vanishing CP asymmetry (above a few percent) α_{CP}(B_{s} → D_{s}^{+} D_{s}^{-}) is a clear signal of New Physics. Interestingly, this would test precisely the same Standard Model ingredients as the question of whether α + β + γ = π.

We report the construction of large new classes of models which break supersymmetry dynamically. We then turn to model building. Two of the principal obstacles to constructing simple models of dynamical supersymmetry breaking are the appearance of Fayet-Iliopoulos D terms and difficulties in generating a µ term for the Higgs fields. Among the new models are examples in which symmetries prevent the appearance of Fayet-Iliopoulos terms. A gauge singlet field, which may play a role in explaining the hierarchy in quark and lepton parameters, can generate a suitable µ term. The result is a comparatively simple model, with a low energy structure similar to that of the MSSM, but with far fewer arbitrary parameters. We begin the study of the phenomenology of these models.

### 1995

We calculate the O(α_{s}) corrections to the charged Higgs mediated inclusive semi-tauonic B decay. By working in the Landau gauge, we demonstrate how to obtain the charged Higgs contributions (both direct and interference terms) from the known QCD corrections to t → bH^{+}. Combining our results with O( 1 m_{b}^{2}) corrections to the spectator model and comparing the theoretical prediction with the recent experimental measurements, we find a model-independent 2σ upper bound on the ratio of Higgs vacuum expectation values, tan β H 1 GeV).

The smallness and hierarchy in fermion parameters could be the result of selection rules due to an Abelian horizontal symmetry broken by a small parameter. When applied to the lepton sector, then for a large class of models, a number of interesting order of magnitude relations arise: with ii)/m(ν_{jj}) ∼ sin^{2} θ _{ij}; m(ℓ^{-}_{i})/m(ℓ^{-}_{j})≲sinθ_{ij};m(ν_{i})/m(ν_{j}) ≳m^{2}(ℓ^{-}_{i}/m^{2}(ℓ^{-}_{j}; m(ν_{e} ≲ m(ν_{μ}) ≲(ν_{τ}). The relations between neutrino masses and mixings may become exact if the horizontal symmetry together with holomorphy induce certain zero entries in the lepton mass matrices. A full high energy theory is likely to include scalars with flavor changing couplings and heavy leptons in vector representations; however, the masses of these particles are too heavy to be directly observed in experiment. Indirect evidence for the horizontal symmetry may arise from other sectors of the theory: non-degenerate sleptons are allowed as the symmetry aligns lepton and slepton mass matrices; light leptoquarks are allowed as the symmetry can make their couplings diagonal and chiral.

In current searches for D^{0}D^{0} mixing, the time evolution of "wrong-sign" decays is used to distinguish between a potential mixing signal and the dominant background from doubly-Cabibbo-suppressed decays. A term proportional to d M t in the expression for the time evolution is often neglected in theoretical discussions and experimental analyses of these processes. We emphasize that, in general, this term does not vanish even in the case of CP invariance. Furthermore, CP invariance is likely to be violated if the rate of D^{0}D^{0} mixing is close to the experimental bound. The consequence of either of these two facts is that the strongest existing measured bound is not applicable for constraining New Physics.

We investigate low energy implications of string loop corrections to supergravity couplings which break a possible flavor universality of the tree level. If supersymmetry is broken by the dilaton F-term, universal soft scalar masses arise at the leading order but string loop corrections generically induce flavor-non-diagonal soft terms. Constraints from flavor changing neutral currents (FCNC) and CP violation then require a large supersymmetry breading scale and thus heavy gluinos and squarks. If supersymmetry is broken by moduli F-terms, universality at the string tree level can only be guaranteed by extra conditions on the Kahler potential. A large hierarchy between the gluino and squark masses ensures that FCNC and CP-violation constraints are satisfied. If the soft scalar masses vanish at the string tree level, the cosmological problems related to light moduli can be evaded. However, generic string loop corrections violate FCNC bounds and require very heavy squark masses (∼ 100 TeV).

The hierarchy in the Yukawa couplings may be the result of a gauged horizontal U(1) _{h} symmetry. If the mixed anomalies of the Standard Model gauge group with U(1) _{h} are cancelled by a Green-Schwarz mechanism, a relation between the gauge couplings, the Yukawa couplings and the μ-term arises. Assuming that at a high energy scale g_{3}^{2} = g_{2}^{2} = 5 3g_{1}^{2} and (m_{e}m_{μ}m_{τ}) (m_{d}m_{s}m_{b}) ∼ λ (where λ is of the order of the cabibbo angle), the U(1) _{h} symmetry solves the μ-problem with μ ∼ λm_{ 3 2}.

We investigate supersymmetric models where neither R parity nor lepton number is imposed. Neutrino masses can be kept highly suppressed compared to the electroweak scale if the μ terms in the superpotential are aligned with the SUSY-breaking bilinear B terms. This situation arises naturally in the framework of horizontal symmetries. The same symmetries suppress the trilinear R-parity-violating terms in the superpotential to an acceptable level.

### 1994

The smallness of the quark and lepton parameters and the hierarchy between them could be the result of selection rules due to a horizontal symmetry broken by a small parameter. The same selection rules apply to baryon number violating terms. Consequently, the problem of baryon number violation in Supersymmetry may be solved naturally, without invoking any especially-designed extra symmetry. This mechanism is efficient enough even for low-scale flavour physics. Proton decay is likely to be dominated by the modes K^{+}ν_{i} or K^{0}μ^{+}(e^{+}), and may proceed at observable rates.

The smallness of the quark sector parameters and the hierarchy between them could be the result of a horizontal symmetry broken by a small parameter. Such an explicitly broken symmetry can arise from an exact symmetry which is spontaneously broken. Constraints on the scales of new physics arise from new flavor-changing interactions and from Landau poles, but do not exclude the possibility of observable signatures at the TeV scale. Such a horizontal symmetry could also lead to many interesting results: (i) quark-squark alignment that would suppress, without squark degeneracy, flavor-changing neutral currents induced by supersymmetric particles, (ii) exact relations between mass ratios and mixing angles, (iii) a solution of the μ-problem and (iv) a natural mechanism for obtaining hierarchy among various symmetry-breaking scales.

Combining the experimental data on the inclusive decays D --> X enu, B --> X enu, and B --> X --> tau nu, we find severe constraints on the LAMBDABAR and lambda1 parameters of the heavy quark effective theory. In particular, we get LAMBDABAR

Within the Standard Model, x_{s} (the mixing parameter in the B_{s}-B_{s} system) is constrained to the range 7 ≤ x_{s} ≤ 40. We point out that if New Physics contributes significantly to x_{d} (the mixing parameter in the B_{d}-B_{d} system), then 2 ≤ x_{s} ≤ 7 is possible without any fine-tuned cancellations between the Standard Model and the New Physics contributions.

We calculate the diffenretial decay rate for inclusive B→τνX transitions to order 1 m^{2}_{b} in the heavy quark expansion, for both polarized and unpolarized tau leptons. We show that using a systematic 1 m_{b} expansion significantly reduces the theoretical uncertainties in the calculation. We obtain for the total branching ration BR(B→τνX = 2.30 ± 0.25%, and for the tau polarization A_{pol}=-0.706±0.006. From the experimental measurement of the branching ratio at LEP, we derive the upper bound λ_{1}≤0.8 GeV^{2} for one of the parameters of the heavy quark effective theory.

We present a systematic analysis of the B(*) --> pilnu weak decay form factors to order 1/M(b) in the heavy quark effective theory, including a discussion of renormalization-group effects. These processes are described by a set of ten universal functions (two at leading order, and eight at order 1/M(b)), which are defined in terms of matrix elements of operators in the effective theory. In the soft pion limit, the effective theory yields normalization conditions for these functions, which generalize the well-known current algebra relations derived from the combination of heavy quark and chiral symmetries to next-to-leading order in 1/m(b). In particular, the effects of the nearby B* pole are correctly contained in the form factors of the effective theory. We discuss the prospects for a model-independent determination of \V(ub)\ and the BB*pi coupling constant from these processes.

We calculate, in the framework of QCD sum rules and to next-to-leading order in perturbation theory, the universal function ξ3(v•v′;) which appears at order 1mQ in the heavy quark expansion of meson weak decay form factors. We find that radiative corrections of order αs are very important. Over the kinematic range accessible in semileptonic decays, ξ3(v•v′;) is proportional to the leading-order Isgur-Wise function ξ(v•v′;) to very good accuracy. Taking into account all sources of uncertainty we estimate ξ3ξ=(0.6±0.2). This reduces the theoretical uncertainty in the extraction of |Vcb| from B̄→Dν̄ transitions. A measurement of the form factor ratio A2A1 in B̄→D*ν̄ decays can be used to test our prediction.

### 1993

A recent study by Randall and Sundrum shows that models of extended technicolor (ETC) have interesting implications on rare B decays. We extend their study to the decay B --> mu+mu-X. The decay rate is found to be above the standard model prediction roughly by a factor of 4 in the case of ''traditional'' ETC models, and by a factor of order 30 for ETC models with a GIM mechanism. The current experimental bound is a factor of 5-15 above the standard model prediction, depending on the top-quark mass.

In models of three or more scalar doublets, new CP violating phases appear in charged scalar exchange. These phases affect CP asymmetries in neutral B decays, even if Natural Flavor Conservation holds. The recent upper bound on the decay b → sγ constrains the effect to be at most on the order of a few percent. Modification of constraints on the CKM parameters open an interesting new region in the sin 2α-sin2β plane even in the absence of new phases.

For generic squark masses, box diagrams with squarks and gluinos give unacceptably large contributions to neutral meson (K, B and D) mixing. The standard solution to this problem is to assume that squarks are degenerate to a very good approximation. We suggest an alternative mechanism to suppress squark contributions to flavor changing neutral currents: the alignment of quark with squark mass matrices. This mechanism arises naturally in the framework of abelian horizontal symmetries.

In LEP searches for the neutral CP-odd scalar A^{0} of a multi-Higgs double model, experiments have searched for Z→h^{0}A^{0} (where h^{0} is the lightest CP-even scalar). No model-independent limit on the A^{0} mass can be deduced from present data if m_{h0}>m_{Z}.In this paper, we compute the rates for Z→A^{0}A^{0}vv and (e^{+}e^{-}→A^{0}A^{0}Z. Assuming that no light CP-even neutral scalars exist, the branching ratio for Z→A^{0}A^{0}vv is found to be less than 1.4×10^{-8} At higher e^{+}e^{-} center-of-mass energies, σ(e^{+}e^{-}→A^{0}A^{0}Z) peaks at 0.5 fb. A comparison with other direct searches for the A^{0} is briefly considered.

It is possible that the hierarchy in the masses and mixing of quarks is a result of a horizontal symmetry. The smallness of various parameters is related to their suppression by high powers of a scale of new physics. We analyze in detail the structure of such symmetries in view of new experimental data and present explicit models consistent with all phenomenological constraints. We show that it is possible that the flavor dynamics can be at accessible energies - as low as a TeV.

We present a QCD sum rule calculation of the spin-symmetry violating universal function χ_{2}(ν·ν′), which appears at order 1 1 m_{Q} in the heavy quark expansion of meson form factors. This function vanishes in the standard approximation, where radiative effects are neglected. For the first time, the complete set of diagrams arising at order α_{s} is evaluated. In particular, we find χ_{2}(1) = -(3.8 ± 1.1)% at zero recoil, indicating that 1/m_{Q} corrections induced by the chromo-magnetic moment operator are small.

The values of sin2 and sin2, where and are angles of the unitarity triangle, will be readily measured in a B factory (and maybe also in hadron colliders). We study the standard model constraints in the sin2-sin2 plane. We use the results from recent analyses of fB and b|Vcb|2 which take into account heavy-quark symmetry considerations. We find sin20.15 and most likely sin20.6, and emphasize the strong correlations between sin2 and sin2. Various schemes for quark mass matrices allow much smaller areas in the sin2-sin2 plane. We study the schemes of Fritzsch, of Dimopoulos, Hall, and Raby, and of Giudice, as well as the "symmetric Cabibbo-Kobayashi-Maskawa" idea, and show how CP asymmetries in B decays will crucially test each of these schemes.

We calculate the contributions arising at order αs in the QCD sum rule for the spin-symmetry-violating universal function χ3(v•v′), which appears at order 1mQ in the heavy quark expansion of meson form factors. In particular, we derive the two-loop perturbative contribution to the sum rule. Over the kinematic range accessible in B→D(*)ν decays, we find that χ3(v•v′) does not exceed the level of ∼ 1%, indicating that power corrections induced by the chromomagnetic operator in the heavy quark expansion are small.

### 1992

The decay h0→A0A0 (where h0 and A0 are the lightest CP-even and CP-odd Higgs bosons of a two-Higgs-doublet model) is kinematically forbidden at the tree level in the minimal supersymmetric model. However, if radiative corrections are included, the mass of h0 can be larger than twice the mass of A0 over part of the supersymmetric parameter space. Moreover, in this parameter regime, h0 must be lighter than the Z. We compute the radiatively corrected width for h0→A0A0 to leading-logarithmic accuracy, and verify that this decay can be the dominant h0 decay mode. Thus, in searches for e+e-→h0A0 at the CERN e+e- colliders LEP and LEP II, one must search for events with A0A0A0 final states in order to set unambiguous limits for the A0 mass.

### 1991

Isospin relations are used to eliminate hadronic uncertainties in various CP asymmetries in B0 decays. In addition to the simple triangle relations for the pi-pi-mode, we study quadrilateral relations for K-pi and pentagon relations for rho-pi. A combined angular and isospin analysis is required for rho-rho. These methods are useful also for three-body decays such as K-pi-pi. The magnitude of the penguin amplitude can be extracted in various modes. The theoretical principles behind this analysis can be experimentally tested through sum rules for decay rates prior to the measurement of CP asymmetries.

Recent experiments suggest that v_{τ} may be a pseudo-Dirac neutrino with m_{vτ}≈ 17 keV. If such a neutrino is to be consistent with constraints from nucleosynthesis, then the mass difference between its two Majorana components should be extremely small. If it is small enough because of see-saw suppression then, in the absence of fine-tuning or additional symmetries, one needs to give up the MSW solution for the solar neutrino problem and the singlet majoron solution for the energy density problem. Thus, additional symmetries that can make v_{τ} an almost exact Dirac neutrino should be sought. Also, the distance required for v_{τ} to oscillate into its sterile Dirac partner becomes unobservably large.

Isospin relations are used to eliminate hadronic uncertainties in various CP asymmetries in B0 decays via buus, e.g., B00KS. A clean measurement of the angle of the unitarity triangle is thus made possible. The magnitudes of the tree and the penguin amplitudes can be measured.

### 1988

We study the implications of the recent B_{d}-B_{d} mixing data on the quark sector parameters - m_{t}, s_{13} and δ - within the three-generation standard model. We derive limits on several experimental quantities: r_{s}, ε\u2032/ε, branching ratios of rare K and B decays. The Fritzsch scheme for quark mass matrices is consistent with the experimental data only if several experimental and theoretical quantities assume values at the limit of their allowed ranges. This allows a unique solution: m_{t} ∼ 85 GeV, s_{13} ∼ 0.0035, δ ∼ 100°, with many definite predictions. The Stech scheme and its extension by Gronau, Johnson and Schechter are inconsistent with the experimental constraints. We study how a direct measurement of m_{t} or s_{13} will improve our constraints and predictions.

We study the possibility that vector-boson self-couplings may differ from their standard model values. We find that known constraints from loop effects and from unitary already imply that such deviations are of order 10^{-2} or less. Consequently, even if the correct model differs from the standard model and even if the energy scale of new physics is as low as 1 TeV, a direct observation of anomalous couplings is very imporabable in the LEP-200 and Tevatron experiments.

### 1987

Using a recent experimental bound on τ decay into three charged leptons and a weak assumption concerning a general "see-saw" mechanism for neutrino masses, we show that both v_{μ} and v_{τ} must be lighter than 65 eV. If the "see-saw" is driven by a right-handed W boson or by a "horizontal" gauge boson, they must be heavier than 50 PeV.

We study the constraints imposed on the masses of ν_{e}, ν_{μ} and ν_{T} on the basis of direct experimental bounds, cosmological bounds, theoretical calculations of neutrino decay rates, experimental bounds on related decay charged leptons and the structure of neutrino mass matrices in the "see-saw" mechanism. We consider standard model amplitudes as well as contributions from all "beyonds standard" models. Assuming a simple "reasonable" form of the see-saw mechanism, we derive the bounds: m(ν_{T}) ≤ 65 eV, m(ν_{ggm}) ≤ 4 eV, m(ν_{e}) ≤ 0.02eV, M(W_{R}) ≥ 50 PeV. Possible ways of evading these boundsare discussed.

### 1986

The mixings of quarks and of squarks, due to W-boson and gluino couplings, are defined by three independent unitary matrices. We discuss the number of physical phase parameters in these matrices. We find the contributions of these phases to ε, ε′ ε and the electric dipole moment of the neutron.

Ward identities leading to higher-order anomalies are discussed from an infrared point of view. As a result a new proof of the relations between various couplings of photons, pions, and axial-vector currents is obtained.

### 1985

If "colored neutrinos" exist, their mass can be much lighter than the scale of compositeness. If they are sufficiently light, the could be produced at the CERN and Fermilab pp colliders. We calculate total cross sections and expected number of events for the relevant energies. The decay of the singly produced colored neutrino should leave an experimental signature of a monojet. We find the angular distribution of these monojets. If "colored electrons" exist, then their mass should be of the order of compositeness scale, and they should be produced in future multi-TeV hadron colliders. We find their total production cross sections and the angular distribution of the gluon-monojet arising from the colored electron decay.