The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the $Γ_4\cong S_4$ symmetry, which have calculable deviations from the usual Golden Mass Relation.
We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework coupling constants such as Yukawa couplings are also transformed under the flavor symmetry. We show that the low-energy effective theory of magnetized torus models is invariant under a specific subgroup of the modular group. Since Yukawa couplings as well as chiral zero modes transform under the modular group, the above modular subgroup (referred to as modular f…
We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including $Γ_N$ and $Γ'_N$ as the flavor symmetry. The theory of vector-valued modular forms provide a method of differential equation to construct the modular multiplets, and it also reveals the simple structure of the modular invariant mass models. We review the theory of vector-valued modular forms and give general results for the lower dimensional vector-valued mod…
We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in heterotic orbifold models. The $T^2/Z_4$ orbifold model has the same modular symmetry as the magnetized brane model with $M=2$, and its flavor symmetry $D_4$ is a subgroup of the modular symmetry.
We study a scenario to derive four-dimensional modular flavor symmetric models from higher dimensional theory by assuming the compactification consistent with the modular symmetry. In our scenario, wavefunctions in extra dimensional compact space are modular forms. That leads to constraints on combinations between modular weights and $Γ_N$ ($Γ_N')$ representations of matter fields. We also present illustrating examples.
We study the spontaneous $CP$ violation through the stabilization of the modulus $τ$ in modular invariant flavor models. The $CP$-invaraiant potentential has the minimum only at ${\rm Re}[τ] = 0$ or 1/2. From this prediction, we study $CP$ violation in modular invariant flavor models. The physical $CP$ phase is vanishing. The important point for the $CP$ conservation is the $T$ transformation in the modular symmetry. One needs the violation of $T$ symmetry to realize the spontaneous $CP$ violation.
The Standard Model is extended minimally with a new flavor-violating family symmetry ${\rm U(1)}_λ$, which acts only on leptons including the right-handed neutrinos. The model is anomaly free with family-dependent ${\rm U(1)}_λ$ charges, and consistent with the observed neutrino mixing angles. It predicts charged lepton flavor-violating processes mediated by a new gauge boson. Under certain conditions, the smallness of $θ_{13}$ of neutrino mixing can be justified in terms of the muon-to-tau mass ratio, at the same time explaining the electron-to-tau large mass hierarchy.
The framework of compactified heterotic string theory offers consistent ultraviolet (UV) completions of the Standard Model (SM) of particle physics. In this approach, the existence of flavor symmetries beyond the SM is imperative and the flavor symmetries can be derived from the top-down. Such a derivation uncovers a unified origin of traditional discrete flavor symmetries, discrete modular flavor symmetries, discrete R symmetries of supersymmetry, as well as CP symmetry - altogether called the eclectic flavor symmetry. I will show a specific example of such a top-down derived eclectic flavor …
We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion mass hierarchies and sizable CP-breaking effects. We investigate whether one can dynamically fix the moduli values in the vicinity of the fixed points in the context of Type IIB string theory. It is found that the string landscape prefers $|δτ| \simeq 10^{-5}$ for the deviation of the complex structure modulus from all fixed points and the CP-breaking vacuum is…
We study the soft supersymmetry (SUSY) breaking terms due to the modulus F-term in the modular flavor models of leptons. It is found that the soft SUSY breaking terms are constrained by the modular forms, and specific patterns are derived. Those phenomenological implications are discussed in such as the lepton flavor violation, $μ\rightarrow e + γ$ decay. In order to examine numerically, two modular flavor $A_4$ models are taken. The SUSY breaking scale is significantly constrained by inputting the observed upper bound of the $μ\rightarrow e + γ$ decay. The SUSY mass scale is larger than aroun…
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 vector-like leptons are within the reach of the LHC, it will be possible to test the resulting predictions in ATLAS/CMS.
We discuss the impact of fermion mass matrices on some lepton number violating processes, namely baryogenesis via leptogenesis and neutrinoless double beta decay, and on some lepton flavor violating processes, namely radiative lepton decays in supersymmetric seesaw models.
We extend the notion of Minimal Flavor Violation to the lepton sector. We introduce a symmetry principle which allows us to express lepton flavor violation in the charged lepton sector in terms of neutrino masses and mixing angles. We explore the dependence of the rates for flavor changing radiative charged lepton decays (ell(i) -> ell(j) + gamma) and mu-to-e conversion in nuclei on the scales for total lepton number violation, lepton flavor violation and the neutrino masses and mixing angles. Measurable rates are obtained when the scale for total lepton number violation is much larger than th…
In this talk, I will present the status of lepton flavor physics in composite Higgs models with partial compositeness in the light of recent data in the lepton sector. I will consider anarchic flavor setups, scenarios with flavor symmetries, and minimal incarnations of the see-saw mechanism that naturally predict non-negligible lepton compositeness. The focus will be on lepton flavor violating processes, dipole moments, and on probes of lepton flavor universality, all providing stringent tests of partial compositeness. The expected size of effects in the different approaches to lepton flavor a…
The observation of charged lepton flavor violation is a clear sign of physics beyond the Standard Model (SM). In this work, we investigate the sensitivity of future lepton colliders to charged lepton flavor violation via on-shell production of bileptons, and compare their sensitivity with current constraints and future sensitivities of low-energy experiments. Bileptons couple to two charged leptons with possibly different flavors and are obtained by expanding the general SM gauge invariant Lagrangians with or without lepton number conservation. We find that future lepton colliders will provide…
We show that in supersymmetric models with explicit flavor lepton number violation due to soft supersymmetry breaking mass terms there could be detectable flavor lepton number violation in slepton decays. We estimate LHC discovery potential of the lepton flavor number violation in slepton decays.
Now the bounds on the lepton-flavor violating (LFV) decay modes of tau lepton are being improved by the Belle experiment in the KEK B factory. In this paper the LFV decay of tau lepton is discussed in the supersymmetric seesaw model, using the current neutrino oscillation data.
I discuss different theories of leptonic flavor and their capability of describing the features of the lepton sector, namely charged lepton masses, neutrino masses, lepton mixing angles and leptonic (low and high energy) CP phases. In particular, I show examples of theories with an abelian flavor symmetry G_f, with a non-abelian G_f as well as theories with non-abelian G_f and CP.
We propose a new mechanism to explain neutrino masses with lepton number conservation, in which the Dirac neutrino masses are generated at the two-loop level involving a dark matter candidate. In this model, branching ratios of lepton flavor violating decays of the Higgs boson can be much larger than those of lepton flavor violating decays of charged leptons. If lepton flavor violating decays of the Higgs boson are observed at future collider experiments without detecting lepton flavor violating decays of charged leptons, most of the models previously proposed for tiny neutrino masses are excl…
We study the supersymmetric model with the A4 lepton flavor symmetry, in particular soft supersymmetry breaking terms, which are predicted from the A4 lepton flavor symmetry. We evaluate soft slepton masses and A-terms within the framework of supergravity theory. Constraints due to experiments of flavor changing neutral current processes are examined.
We study the radiative lepton flavor violating l_i -> l_jγdecays in the two Higgs doublet model, respecting the Randall Sundrum scenario and estimate the contributions of the KK modes of left (right) handed charged lepton doublets (singlets) on the branching ratios. We observe that the branching ratios are sensitive to the contributions of the charged lepton KK modes.
Large mixing parameters of neutrino mass eigenstates in the neutrino flavor eigenstates are determined, and interpreted as closely related to the neutrino and charged lepton mass-ratio patterns. The three known seemingly different charged lepton and quasi-degenerate neutrino deviation-from-extreme hierarchies are shown to be three particular manifestations of one unifying quadratic hierarchy-rule in lepton flavor physics.
We analyze four-lepton contact interactions that lead to lepton flavor violating processes, with violation of individual family lepton number but total lepton number conserved. In an effective Lagrangian framework, the assumption of gauge invariance leads to relations among branching ratios and cross sections of lepton flavor violating processes. In this paper, we work out how to use these relations systematically. We also study the consequences of loop-induced processes.
We systematically analyze the correlations between the various leptonic and hadronic flavor violating processes arising in SUSY Grand Unified Theories. Using the GUT-symmetric relations between the soft SUSY breaking parameters, we assess the impact of hadronic and leptonic flavor observables on the SUSY sources of flavor violation.
Due to the smallness of the lepton Yukawa couplings, higher-dimensional operators can give a significant contribution to the lepton masses. In this case, the lepton mass matrix and the matrix of lepton-Higgs couplings are misaligned leading to lepton flavor violation (LFV) mediated by the Standard Model Higgs boson. We derive model-independent bounds on the Higgs flavor violating couplings and quantify LFV in decays of leptons and electric dipole moments for a class of lepton-Higgs operators contributing to lepton masses. We find significant Higgs-mediated LFV effects at both 1-loop and 2-loop…
In a generic supersymmetric extension of the Standard Model, there will be lepton flavor violation at a neutral gaugino vertex due to misalignment between the lepton Yukawa couplings and the slepton soft masses. Sleptons produced at the LHC through the cascade decays of squarks and gluinos can give a sizable number of events with 4 leptons. This channel could give a clean signature of supersymmetric lepton flavor violation under conditions which are identified.
The study for lepton flavor violation combined with the neutrino oscillation may provide more information about the lepton flavor structure of the grand unified theory. In this paper, we study two lepton flavor violation processes, $τ\to μγ$ and $Z\to τμ$, in the context of supersymmetric SO(10) grand unified models. We find the two processes are both of phenomenological interest. In particular the latter may be important in some supersymmetric parameter space where the former is suppressed. Thus, Z-dacay may offer another chance for looking for lepton flavor violation.
The field of lepton flavor violation will live an era of unprecedented developments in the near future, with dedicated experiments in different fronts. The observation of a flavor violating process involving charged leptons would be a clear evidence of physics beyond the Standard Model, thus motivating the great effort in this direction. Furthermore, in case a positive signal is found, a proper theoretical understanding of the lepton flavor anatomy of a given model would become necessary. Here I briefly review the current situation, emphasizing the most relevant theoretical and phenomenologica…
The observation of lepton flavor violation indicates new physics beyond the Standard Model. Lepton colliders are ideal facilities to probe charged lepton flavor violation (CLFV) signals induced by new physics at high energy. In this work we perform a comprehensive study of the sensitivity of future lepton colliders to charged lepton flavor violation. We consider the most general renormalizable Lagrangian coupling two leptons to new bosonic particles, involving both $ΔL=0$ and $ΔL=2$ interactions. The CLFV processes are introduced by the exchange of off-shell new particles at tree-level. We fin…
We discuss charged lepton flavor violation in supersymmetric models with extended leptonic sectors at low energies. Contrary to the usual high-scale realizations of the seesaw mechanism, these non-minimal supersymmetric models have new superfields and/or interactions at the supersymmetric scale. As a consequence of this, the resulting lepton flavor violating phenomenology may be very different from that of minimal models.
Supposing only Lorentz and the gauge invariances of the Lagrangian, we derive energy and angular distributions for $τ^\pm \to μ^\pm μ^\pm μ^\mp$ lepton flavor violating decay process. Using these results, we discuss methods to determine the parameters associated with the lepton flavor violating interactions.
We study the lepton flavor violating $μ^- \to e^{-}2γ$ decay induced by the mediation of heavy leptons such as the excited and fourth generation leptons. We have examined the effects of these leptons in the $μ^- \to e^{-}2γ$ decay. We have found that branching ratio of this decay is very sensitive to excited and fourth generation leptons. Furthermore, we have obtained the bounds on model parameters by using the current experimental limit of this decay.
We predict the branching ratios of the lepton flavor violating Higgs decays H^0->e^{\pm} μ^{\pm}, H^0-> e^{\pm} τ^{\pm} and H^0->μ^{\pm} τ^{\pm} in the case that the lepton flavor violation is carried by the scalar unparticle mediation. We observe that their branching ratios are strongly sensitive to the unparticle scaling dimension and they can reach to the values of the order of $10^{-4}$, for the heavy lepton flavor case and for the small values of the scaling dimension.
We study lepton flavor models with the $S_4$ flavor symmetry. We construct simple models with smaller numbers of flavon fields and free parameters, such that we have predictions among lepton masses and mixing angles. The model with a $S_4$ triplet flavon is not realistic, but we can construct realistic models with two triplet flavons, or one triplet and one doublet flavons.
Lepton flavor violation at linear collider experiments is discussed. We show that detectable lepton flavor violation could occur through scalar lepton pair production and decay in the supersymmetric SU(5) grand unified theory in spite of the stringent present experimental constraints by rare process searches. Possible cross sections about 40fb for an e+e- collider and 280fb for an e-e- collider are illustrated.
Lepton flavor violating decays $Z \to μτ$ and $J/Ψ, Υ\to μτ$ are considered. It is shown that these decays can reach sizeable magnitudes if some specific lepton-flavor violating 4-fermion operators are generated by low scale quantum gravity effects, or by some other new physics at a TeV scale.
The impact of possible sources of lepton-flavor mixing on $K \to πν\barν$ decays is analysed. At the one-loop level lepton-flavor mixing originated from non-diagonal lepton mass matrices cannot generate a CP-conserving $K_L \to π^0ν\barν$ amplitude. The rates of these modes are sensitive to leptonic flavor violation when there are at least two different leptonic mixing matrices. New interactions that violate both quark and lepton universalities could enhance the CP-conserving component of $Γ(K_L \to π^0ν\barν)$ and have a substantial impact. Explicit examples of these effects in the context of…
The following proceedings contain a theory perspective on the flavor changing neutral current anomalies reported by LHCb on the ratios $B\to K^{(*)} μμ/B\to K^{(*)} ee$
We investigate the potentials of high energy lepton-proton colliders to detect a flavor changing $l-l^{\prime}-Z$ or $l-l^{\prime}-γ$ couplings from the processes $ep\toμ(τ)X$ and $μp\to τX$. For the $l-l^{\prime}-Z$ coupling we consider string inspired $E_6$ model whereas $l-l^{\prime}-γ$ coupling is analyzed in the framework of anomalous magnetic moment type interaction (AMMI) model.
Flavor symmetric model is one of the attractive Beyond Standard Models (BSMs) to reveal the flavor structure of the Standard Model (SM). A lot of efforts have been put into the model building and we find many kinds of flavor symmetries and setups are able to explain the observed fermion mass matrices. In this paper, we look for common predictions of physical observables among the ones in flavor symmetric models, and try to understand how to test flavor symmetry in experiments. Especially, we focus on the BSMs for leptons with extra Higgs $SU(2)_L$ doublets charged under flavor symmetry. In man…
We present and discuss constraints on supersymmetric type I seesaw models imposed by neutrino data, charged lepton flavor violation and thermal leptogenesis.
In a supersymmetric extension of the standard model with local gauged baryon and lepton numbers (BLMSSM), there are new sources for lepton flavor violation, because the right-handed neutrinos and new gauginos are introduced. In BLMSSM, we study the charged lepton flavor violating processes $l_j\rightarrow l_i+γ$ and $l_j\rightarrow 3l_i$ in detail. The numerical results show that in some parameter space the branching ratios for charged lepton flavor violating processes can be large enough to be detected in the near future.
We predict the contribution of scalar unparticle to the branching ratios of the lepton flavor conserving Z -> l^+ l^- decays and we study the discrepancy between the experimental and the QED corrected standard model branching ratios. We observe that these decays are sensitive to the unparticle scaling dimension d_u for its small values, especially for heavy lepton flavor output.
We study modular symmetric quark flavor models without fine-tuning. Mass matrices are written in terms of modular forms, and modular forms in the vicinity of the modular fixed points become hierarchical depending on their residual charges. Thus modular symmetric flavor models in the vicinity of the modular fixed points have a possibility to describe mass hierarchies without fine-tuning. Since describing quark hierarchies without fine-tuning requires $Z_n$ residual symmetry with $n\geq 6$, we focus on $Γ_6$ modular symmetry in the vicinity of the cusp $τ=i\infty$ where $Z_6$ residual symmetry r…
The $μν$SSM, one of supersymmetric extensions of the Standard Model, introduces three right-handed neutrino superfields to solve the $μ$ problem and violates lepton number. Within framwork of the $μν$SSM, we investigate the lepton flavor violating (LFV) processes $Z\rightarrow l_i^\pm l_j^\mp$ with slepton flavor mixing. Simultaneously, we consider the LFV processes $l_j^-\rightarrow l_i^-γ$, $l_j^- \rightarrow l_i^- l_i^- l_i^+$ and muon conversion to electron in nuclei.
We derive the upper bounds on certain products of R-parity- and lepton-flavor-violating couplings from the decays of the neutral $B$ meson into two charged leptons. These modes of $B^0$ decays can constrain the product combinations of the couplings with one or more heavy generation indices. We find that most of these bounds are stronger than the previous ones.
We study the renormalization group equations (RGEs) of the neutrino parameters in models of Minimal Lepton Flavor Violation. In such models, the RGEs can be described in terms of flavor spurions, such that only the coefficients depend on the specific model. We explicitly demonstrate this method for the SM and MSSM for both Type-I and Type-III seesaw models. For that purpose, the RGEs of neutrino parameters in the MSSM Type-III seesaw have been computed. We have extended this method to get the evolution equations at second order. The implications for leptogenesis are also discussed.
High precision electroweak tests, such as deviations from the Standard Model expectations of the Lepton Flavor Universality breaking in K->lnu (with l= e or mu), represent a powerful tool to test the Standard Model and, hence, to constrain or obtain indirect hints of New Physics beyond it. We explore such a possibility within Supersymmetric theories. Interestingly enough, a process that in itself does not need lepton flavor violation to occur, i.e. the violation of mu-e non-universality in K_l2, proves to be quite effective in constraining not only relevant regions of SUSY models where lepton …
The article reviews the conditions for lepton-flavor conservation in leptonic interactions. The conditions are similar to those developed in the quark sector. For neutrinos the mass eigenstates are unitary superpositions of flavor states which together with small mass differences produce neutrino oscillations. A new property for neutrinos is the fact that their masses are very small suppressing their couplings to neutral scalar fields. The results are demonstrated in several models.
Exotic Higgs decays are promising channels to discover new physics in the near future. We present a simple model with a new light scalar that couples to the Standard Model through a charged lepton-flavor violating interaction. This can yield exciting new signatures, such as $h \to e^+ e^+ μ^-μ^-$, that currently have no dedicated searches at the Large Hadron Collider. We discuss this model in detail, assess sensitivity from flavor constraints, explore current constraints from existing multi-lepton searches, and construct a new search strategy to optimally target these exotic, lepton-flavor vio…
We predict the branching ratios of the lepton flavor violating Z boson decays Z\to e^{\pm} μ^{\pm}, Z\to e^{\pm} τ^{\pm} and Z\to μ^{\pm} τ^{\pm} in the case that the lepton flavor violation is carried by the scalar unparticle mediation. We observe that their BRs are strongly sensitive to the unparticle scaling dimension and the branching ratios can reach to the values of the order of 10^{-8}, for the heavy lepton flavor case, for the small values of the scaling dimension.
A flavor structure with minimal parameters is proposed to address the fermion mass hierarchy and flavor mixing for quarks and leptons. Yukawa interaction is reconstructed in a new basis to show a homological flat structure for up-type quarks, down-type quarks, charged leptons and Dirac neutrinos. A $SO(2)_{LR}^f$ flavor symmetry is found from the hierarchy masses of quarks and leptons, which dominated CKM mixing for quarks and PMNS for leptons. Since the minimal flavor structure successfully addresses CKM and PMNS even in the mass hierarchy limit, mass hierarchy and flavor mixing are two indep…
