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This is a review on structure of the fermion mass terms in quantum field theory, under the perspective of its practical applications in the real physics of Nature -- specifically, we discuss fermion mass structure in the Standard Model of high energy physics, which successfully describes fundamental physics up to the TeV scale. The review is meant to be pedagogical, with detailed mathematics presented beyond the level one can find any easily in the textbooks. The discussions, however, bring up important subtleties and ambiguities about the subject that may be less than well appreciated. In fact, the naive perspective of the nature and masses of fermions as one would easily drawn from the presentations of fermion fields and their equations of motion from a typical textbook on quantum field theory leads to some confusing or even wrong statements which we clarify here. In particular, we illustrate clearly that a Dirac fermion mass eigenstate is mathematically equivalent to two degenerated Majorana fermion mass eigenstates at least so long as the mass terms are concerned. There are further ambiguities and subtleties in the exact description of the eigenstate(s). Especially, for the case of neutrinos, the use of the Dirac or Majorana terminology may be mostly a matter of choice. The common usage of such terminology is rather based on the broken $SU(2)$ charges of the related Weyl spinors hence conventional and may not be unambiguously extended to cover more complicate models., Comment: 15 pages. Version published in Annals of Physics

We summarized our report on leptonic flavor violating Higgs decay into mu + tau under the scheme of a generic supersymmetric standard model without R parity. With known experimental constraints imposed, important combinations of R-parity violating parameters which can give notable branching ratios are listed., Comment: Proceeding of SUSY2012 conference. 4 pages

In this paper we examine thoroughly the Higgs boson to mu tau decay via processes involving R parity violating couplings. By means of full one-loop diagrammatic calculations, we found that even if known experimental constraints, particularly including the stringent sub-eV neutrino mass bounds, give strong restrictions on some of the R parity violating parameters, the branching ratio could still achieve notable value in the admissible parameter space. Hence, the flavor violating leptonic decay is of interest to future experiments. We present here key results of our analysis. Based on the analysis, we give some comments on h -> e mu and h -> e tau also., Comment: 35 pages, 3 figures, 8 tables. Version published in Physical Review D

In this letter, we report on lepton flavor violating Higgs decay into mu+tau in the framework of the generic supersymmetric standard model without R parity and list interesting combinations of R-parity violating parameters. We impose other known experimental constraints on the parameters of the model and show our results from the R-parity violating parameters. In our analysis, the branching ratio of Higgs to mu+tau can exceed 10^{-5} within admissible parameter space., Comment: 16 pages, 3 figures, 1 table. Version published in Europhysics Letters

We study the theoretical features in relation to dynamical mass generation and symmetry breaking for the recently proposed holomorphic supersymmetric Nambu--Jona-Lasinio model. The basic model has two different chiral superfields (multiplets) with a strongly coupled dimension five four-superfield interaction. In addition to the possibility of generation of Dirac mass between the pair established earlier, we show here the new option of generation of Majorana masses for each chiral superfield. We also give a first look at what condition may prefer Dirac over Majorana mass, illustrating that a split in the soft supersymmetry breaking masses is crucial. In particular, in the limit where one of the soft masses vanish, we show that generation of the Majorana mass is no longer an option, while the Dirac mass generation survives well. The latter is sensitive mostly to the average of the two soft masses. The result has positive implication on the application of the model framework towards dynamical electroweak symmetry breaking with Higgs superfields as composites., Comment: 15 pages, 1 figure. Revised version matches the accepted one for publication in Phy.Rev.D Journal

With a more relaxed perspective on what constitutes a relativity symmetry mathematically, we revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions. We focus on the contractions of an $SO(m,n)$ symmetry as a relativity symmetry on an $m+n$ dimension geometric arena, which generalizes the notion of spacetime, and discuss systematically contractions that reduce the dimension one at a one, aiming at going one step beyond what has been discussed in the literature. Our key results are five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension $m+n-1$, e.g. a G(m,n-1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for "quantum spacetime". The contractions from G(1,3) may be relevant to real physics., Comment: 23 pages in revtex with 1 figure incorporated

In this paper we discuss Nambu-Jona-Lasinio model as a classical model for dynamical mass generation and symmetry breaking. In addition we discuss the possible supersymmetric extensions of this model resulting from interaction terms with four chiral superfields that may be regarded as a supersymmetric generalization of the four-fermion interactions of the Nambu-Jona-Lasinio model. A four-superfield interaction terms can be constructed as either dimension 6 or dimension 5 operators. Through analyzing solutions to the gap equations, we discuss the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible., Comment: 7 pages, 2 figures, talk presented in the 2011 International Workshop on Future Linear Colliders (LCWS11), Granada, Spain

We investigate the dynamical mass generation resulted from interaction terms with four chiral superfields. The kind of interactions maybe considered a supersymmetric generalization of the four-fermion interactions of the classic Nambu--Jona-Lasinio model. A four-superfield interaction that contains a four-fermion interaction as one of its component terms has been the standard supersymmetrization of the NJL model for decades. Recently, we introduced a holomorphic variant with a dimension five interaction term instead. The latter is a main target of the present analysis. With the introduction of a new perspective on the superfield gap equation, we derive it for each one of the four-superfield interactions, using the supergraph technique. Through analyzing solutions to the gap equations, we illustrate the dynamical generation of superfield Dirac mass, including a supersymmetry breaking part. A dynamical symmetry breaking generally goes along with the dynamical mass generation, for which a bi-superfield condensate is responsible. The explicit illustration of dynamical symmetry breaking from the holomorphic dimension five interaction is reported for the first time. It has rich and novel features, which would be easily missed without the superfield approach developed here. We also discuss the nature of the bi-superfield condensate and its role of the effective Higgs superfield picture for both cases, illustrating their difference. Note that such a holomorphic quark superfield interaction term can successful account for the electroweak symmetry breaking with Higgs superfields as composites.

The Poincar\'e-Snyder relativity was introduced in an earlier paper of ours as an extended form of Einstein relativity obtained by appropriate limiting setting of the full Quantum Relativity. The latter, with fundamental constants $\hbar$ and $G$ built into the symmetry, is supposed to be the relativity of quantum space-time. Studying the mechanics of Poincar\'e-Snyder relativity is an important means to get to confront the great challenge of constructing the dynamics of Quantum Relativity. The mechanics will also be of interest on its own, plausibly yielding prediction accessible to experiments. We write the straightforward canonical formulation here, and show that it yields sensible physics pictures. Besides the free particle case, we also give an explicit analysis of two particle collision as dictated by the formulation, as well as the case of a particle rebouncing from an insurmountable potential barrier in the time direction. The very interesting solution of particle-antiparticle creation and annihilation as interpreted in a the usual time evolution picture can be obtained, in the simple classical mechanics setting. We consider that a nontrivial success of the theory, giving confidence that the whole background approach is sensible and plausibly on the right track. We also sketch the quantum mechanics formulation, direct from the familiar canoincal quantization, matching to a relativity group geometric quantization formulation in a previous publication., Comment: 27 pages in Revtex; 2 figures in 3 eps files incorporated

Based on a linear realization formulation of a quantum relativity -- the proposed relativity for quantum `space-time', we introduce the Poincar\'e-Snyder relativity and Snyder relativity as relativities in between the latter and the well known Galilean and Einstein cases. We discuss how the Poincar\'e-Snyder relativity may provide a stronger framework for the description of the usual (Einstein) relativistic quantum mechanics and beyond. In particular, we discuss a geometric quantization picture through the U(1) central extension of the relativity group, which had been establish to work well for the Galilean case but not for the Einstein case. We discuss similarities and differences between our Poincar\'e-Snyder picture with a still not fully understood $\sigma$ variable as the `evolution' parameter and some use of an invariant time or the proper time parameter in some earlier formulations with very similar mathematical structure. The study is a first step towards the investigation of physics of the $\sigma$ variable at the Poincar\'e-Snyder setting, plausible leading to experimental signatures to be studied., Comment: 17 pages in revtex, no figure

We discuss a 4D noncommutative space-time as suggested by the version of quantum (deformed) relativity which provides a classical geometry picture as an `AdS_5'. The 4D noncommutative space-time is more like a part of a phase space description, in accordance with the quantum notion -- quantum mechanics talks about only states but not configurations. The `AdS_5' picture also illustrates the classical 4D space-time is to be described as part of a bigger geometry beyond space-time at the quantum level. The radically new picture of quantum 'space-time' is expected to provide the basis for a (still to be formulated) new approach to quantum gravity with fundamental constants (quantum) hbar and Newton's constant G put at a similar level as c, the speed of light., Comment: 8 pages latex, talk given at SMP 40 (2008), Torun, Poland

We study the electric dipole moment (EDM) and the anomalous magnetic dipole moment (MDM) of the muon in the CP-violating Minimal Supersymmetric extension of the Standard Model (MSSM). We take into account the contributions from the chargino- and neutralino-mediated one-loop graphs and the dominant two-loop Higgs-mediated Barr-Zee diagrams. We improve earlier calculations by incorporating CP-violating Higgs-boson mixing effects and the resummed threshold corrections to the Yukawa couplings of the charged leptons as well as that of the bottom quark. The analytic correlation between the muon EDM and MDM is explicitly presented at one- and two-loop levels and, through several numerical examples, we illustrate its dependence on the source of the dominant contributions. We have implemented the analytic expressions for the muon EDM and MDM in an updated version of the public code CPsuperH2.0., Comment: 26 pages, 10 figures, references added, more references added, to appear in JHEP

We present a detailed analysis together with exact numerical calculations on one-loop contributions to the branching ratio of the radiative decay of $\mu$ and $\tau$, namely $\mu \to e \gamma$, $\tau \to e \gamma$, and $\tau \to\mu \gamma$ from supersymmetry without R parity, focusing on contributions involving bilinear couplings. A numerical study is performed to obtain explicit bounds on the parameters under the present experimental limit. We present, and use in the calculation, formulas for exact mass eigenstate effective couplings. In this sense, we present an exact analysis free from approximation for the first time. After comparing our results against the closest early analysis, we discovered a major difference in resulted constraints on some ${\mu_i^*} {B_j}$ combinations. Constraints from neutrino masses on the parameters were considered. Our result indicates that the branching ratio measurement on $\mu \to e \gamma$ down to $10^{-13}-10^{-14}$ and beyond, as targeted by the MEG experiment, has a chance of observing decay from the R-parity violating scenario., Comment: Comments: 24 pages, 12 figures, 3 table, RevTex; Corrected typos, 2 added references for section 1. The proof-read version to be published in Phys. Rev. D

We present a detailed analysis of the neutron, deuteron and mercury electric dipole moment from supersymmetry without R parity, focusing on the quark-scalar loop contributions. Being proportional to top Yukawa and top mass, such contributions are often large. Analytical expressions illustrating the explicit role of the R-parity violating parameters are given following perturbative diagonalization of mass-squared matrices for the scalars. Dominant contributions come from the combinations $B_i \lambda^{\prime}_{ij1}$ for which we obtain robust bounds. It turns out that neutron and deuteron EDMs receive much stronger contributions than mercury EDM and any null result at the future deuteron EDM experiment or Los Alamos neutron EDM experiment can lead to extra-ordinary constraints on RPV parameter space. Even if R-parity violating couplings are real, CKM phase does induce RPV contribution and for some cases such a contribution is as strong as contribution from phases in the R-parity violating couplings.Hence, we have bounds directly on $|B_i \lambda^{\prime}_{ij1}|$ even if the RPV parameters are all real. Interestingly, even if slepton mass and/or $\mu_0$ is as high as 1 TeV, it still leads to neutron EDM that is an order of magnitude larger than the sensitivity at Los Alamos experiment. Since the results are not much sensitive to $\tan \beta$, our constraints will survive even if other observables tighten the constraints on $\tan \beta$., Comment: 16 pages, 10 figures, accepted for publication in Physical Review D

Quantum relativity as a generalized, or rather deformed, version of Einstein relativity with a linear realization on a classical six-geometry beyond the familiar setting of space-time offer a new framework to think about the quantum space-time structure. The formulation requires two deformations to be implemented through imposing two fundamental invariants. We take them to be the independent Planck mass and Planck length. Together, they gives the quantum $\hbar$. The scheme leads to {\small \boldmath\protect SO(2,4)} as the relativity symmetry. The quantum world has an AdS$_5$ `classical' geometry, which is parallel to the "conformal universe", but not scale invariant., Comment: 10 pages of revtex, no figure;a largely rewritten presentation of the same results

We study the flavor changing neutral current decays of the MSSM Higgs bosons into strange and bottom quarks. We focus on a scenario of minimum flavor violation here, namely only that induced by the CKM matrix. Taking into account constraint from $b\to s \gamma$, $\delta\rho$ as well as experimental constraints on the MSSM spectrum, we show that the branching ratio of $(\Phi\to b\bar{s})$ and $(\Phi \to \bar{b}s)$ combined, for $\Phi$ being either one of the CP even Higgs states, can reach the order $10^{-4}$-$10^{-3}$ for large $\tan\beta$, large $\mu$, and large $A_t$. The result illustrates the significance of minimal flavor violation scenario which can induce competitive branching fraction for flavor changing Higgs decays. This can be compared with the previous studies where similar branching fraction has been reported, but with additional sources of flavor violations in squark mass matrices. We also discuss some basic features of the flavor violating decays in the generic case., Comment: 16 pages on Revtex, with 5 figures from 10 eps files incorporated; discussion on issues related more precise calculations elaborated; proof-edited version to appear in Phys. Lett. B

The idea of quantum relativity as a generalized, or rather deformed, version of Einstein (special) relativity has been taking shape in recent years. Following the perspective of deformations, while staying within the framework of Lie algebra, we implement explicitly a simple linear realization of the relativity symmetry, and explore systematically the resulting physical interpretations. Some suggestions we make may sound radical, but are arguably natural within the context of our formulation. Our work may provide a new perspective on the subject matter, complementary to the previous approach(es), and may lead to a better understanding of the physics., Comment: 27 pages in Revtex, no figure; proof-edited version to appear in Phys.Rev.D

We present a detailed analysis together with numerical calculations on one-loop contributions to the neutron electric dipole moment from supersymmetry without R parity, focusing on the quark-scalar loop contributions. Complete formulas are given for the various contributions through the quark dipole operators. Analytical expressions illustrating the explicit role of the R-parity violating parameters are given following perturbative diagonalization of mass-squared matrices for the scalars. Dominant contributions come from the combinations $B_i^{\ast} \lambda^{\prime}_{ij1}$ for which we obtain robust bounds. Even if the R-parity violating couplings are real, CKM phase does induce RPV contribution and for some cases such a contribution is as strong as contribution from phases in the R-parity violating couplings. Hence, we have bounds directly on $|B_i^{\ast} \l^{\prime}_{ij1}|$ even if the parameters are all real., Comment: 16 pages, 5 figures

We present a systematic analysis of the decay B--> X_s + gamma at the leading log within the framework of Supersymmetry without R-parity. We point out some new contributions in the form of bilinear-trilinear combination of R-parity violating (RPV) couplings that are enhanced by large tanbeta. We also improve by a few orders of magnitude, bounds on several combinations of R-parity violating parameters., Comment: 5 pages latex. Based on talk given by R. Vaidya at the Pran Nath Fest and PASCOS'04 North-Eastern University, Boston. Necessary style files included

We present a systematic analysis of the decay b --> s gamma at the leading log within the framework of Supersymmetry without R-parity. We point out some new contributions in the form of bilinear-trilinear combination of R-parity violating (RPV) couplings that are enhanced by large tanbeta. We also improve by a few orders of magnitude, bounds on several combinations of RPV parameters., Comment: 4 pages. Talk given by R. Vaidya at the SUSY-2004 conference, Tsukuba, Japan, June 17-23, 2004. Title slightly changed from the conference talk. Style file pdproc.sty included

The implementation of the little Higgs mechanism to solve the hierarchy problem provides an interesting guiding principle to build particle physics models beyond the electroweak scale. Most model building works, however, pay not much attention to the fermionic sector. Through a case example, we illustrate how a complete and consistent fermionic sector of the TeV effective field theory may actually be largely dictated by the gauge structure of the model. The completed fermionic sector has specific flavor physics structure, and many phenomenological constraints on the model can thus be obtained beyond gauge, Higgs, and top physics. We take a first look on some of the quark sector constraints., Comment: 14 revtex pages with no figure, largely a re-written version of hep-ph/0307250 with elaboration on flavor sector FCNC constraints; accepted for publication in Phys.Rev.D

The little Higgs mechanism provides an alternative solution to the hierarchy problem, arguably fitting better into the phenomenological hint of the "little hierarchy" which may cause some fine-tuning for the case of supersymmetry. We discuss an aspect of little Higgs physics lacking proper attention -- the construction of an interesting and consistent chiral fermionic sector and its phenomenological implications. At least for the kind of example models to be discussed, the gauge and top sector structure of a model largely dictates, through gauge anomaly cancellation conditions, a specific chiral fermion spectrum. The spectrum has interesting, family non-universal, flavor structure. The implications for flavor physics are specially interesting. We also add a brief comment of little Higgs versus supersymmetry., Comment: $+1 latex pages with pdproc.sty (attached); talk given at SUSY '04

We present a systematic analysis at the leading log order of the influence of combination of bilinear and trilinear R-parity violating couplings on the decay b-->s gamma. Such contributions have never been explored in the context of this decay. We show that influence of charged-slepton-Higgs mixing mediated loops can dominate the SM and MSSM contributions and hence can provide strong bounds on the combination of bilinear-trilinear R-parity violating couplings. Such contributions are also enhanced by large tan beta. With substantially extended basis of operators (28 operators), we provide illustrative analytical formulae of the major contributions to complement our complete numerical results which demonstrate the importance of QCD running effects., Comment: 4 pages, 2 figures

We discuss extensions of the Standard Model through extending the electroweak gauge symmetry. An extended electroweak symmetry requires a list of extra fermionic and scalar states. The former is necessary to maintain cancellation of gauge anomalies, and largely fixed by the symmetry embedding itself. The latter is usually considered quite arbitrary, so long as a vacuum structure admitting the symmetry breaking is allowed. Anomaly cancellation may be used to link the three families of quarks and leptons together, given a perspective on flavor physics. It is illustrated lately that the kind of models may also have the so-called little Higgs mechanism incorporated. This more or less fixes the scalar sector and take care of the hierarchy problem, making such models of extended electroweak symmetries quite appealing candidates as TeV scale effective field theories., Comment: 1+8 pages of latex with ws-procs9x6.cls; talk presented at Coral Gables Conference 2003

We present a systematic analysis of all the contributions at the leading log order to the branching ratio of the inclusive radiative B decay, B --> X_s + gamma in the framework of supersymmetry without R-parity. The relevant set of four-quark operators involved in QCD running are extended from 6 (within SM and MSSM) to 24, with also many new contributions to the Wilson coefficients of (chromo)magnetic penguins for either chiral structure. We present complete analytical results here without any a priori assumptions on the form of R-parity violation. Mass eigenstate expressions are given, hence the results are free from the commonly adopted mass-insertion approximation. In the numerical analysis, we focus here only on the influence of the trilinear lambda-prime couplings and report on the possibility of a few orders of magnitude improvement for the bounds on a few combinations of the lambda-prime couplings. Our study shows that the Wilson coefficients of the current-current operators due to R-parity violation dominate over the direct contributions to the penguins. However, the inter-play of various contributions is complicated due to the QCD corrections which we elaborate here., Comment: 26 pages, 13 figures. A few typos corrected and a few references added. Contents and results unchanged

Interesting contributions to $\Delta a_\mu$ from a two-Higgs-doublet-model is coming from a two-loop Barr-Zee diagram for most part of the parameter space -- a fact that has been overlooked by some Higgs/SUSY experts. A definite positive contribution has requirements that go against precision EW data and other known constraints. For the case without SUSY, in particular, this is almost enough to kill the two-Higgs-doublet-model (II). We will discuss the interplay of all the constraints and their implications., Comment: 1+4 pages of latex with ws-procs9x6.cls,5 figure postscripts included; talk at SUSY03

We discuss the proper starting point to look into flavor physics under the perspective of solving the hierarchy problem with the little Higgs mechanism -- the construction of anomaly free fermionic spectra of the effective theory of extended electroweak gauge symmetry around the TeV scale. Anomaly cancellations among the three SM families, plus extra fermions, are typically needed, giving family non-universal flavor structures. Such a completed and consistent fermionic spectrum supplements a scalar sector little Higgs model, turning the latter into a realistic model the phenomenological viability of which can then be investigated. The implications for flavor physics are specially interesting. We give more elaborated discussion here on our basic perspective, trying to clarify on issues that are in our opinion under-appreciated. We also add a brief comment of little Higgs versus supersymmetry., Comment: 6 pages in revtex; Invited Talk at the 2nd International Conference on Flavor Physics (Oct 2003)

We present an analysis showing how anomaly free fermionic spectra with consistent embeddings of the Standard Model spectrum under $SU(3)_C\times SU(2)_L\times U(1)_Y \subset SU(3)_C\times SU(N)_L\times U(1)_X$ for any $N>2$ can be obtained, with special focus on the $N=3 {and} 4$ cases. The construction is motivated by the little Higgs mechanism. We discuss the relevancy of the fermionic spectra to the latter, concentrating on two N=4 models, without fermions of exotic charges. Such models hold the promise to address and solve all the major theoretical as well as phenomenological problems of the Standard Model at the TeV scale., Comment: 12 pages revtex with 3 tables, no figure

A generic form of the supersymmetric SM naturally gives rise to the lepton number violating neutrino masses and mixings, without the need for extra superfields beyond the minimal spectrum. Hence, SUSY can be consider the origin of beyond SM properties of neutrinos. We have developed a formulation under which one can efficiently analyze the model. Various sources of neutrino masses are discussed in details. Such mass contributions come from lepton number and flavor violating couplings that also give rise to a rich phenomenology of the neutrinos and other leptons, to be discussed., Comment: +8 latex pages with ws-procs9x6.cls (included); talk at NOON 2003

Requiring the two-Higgs-doublet model II to accommodate the 3$\sigma$ deviation in the muon anomalous magnetic moment imposes specific constraints on the Higgs spectrum. We analyze the combination of all the relevant, available, constraints on the model parameter space. The use of constraints from $b\to s \gamma$, the precision electroweak measurements of $R_b$, and the $\rho$ parameter, together with exclusions from direct searches at LEP, give extremely severe restrictions on the model parameters. That is "almost enough" to kill the model altogether. The exclusion would be even stronger if the direct searches can be optimized to complement the other constraints, as will be discussed in details in this work., Comment: 24 pages, 8 figures, RevTeX4, minor changes and new references

We have developed an efficient formulation for the study of the generic supersymmetric standard model, which admits all kind of R-parity violating terms. Using the formulation, we discuss all sources of fermion dipole moment contributions from R-parity violating, or rather lepton number violating, parametersand the constraints obtained. Stringent constraints comparable to those from neutrino masses are resulted in some cases., Comment: 1+6 pages latex with 2 figures incorporated; talk at SUSY'02