Lepton Mass Research Articles

Radiative lepton mass and muon g \u2212 2 with suppressed lepton flavor and CP violations

The recent experimental status, including the confirmation of the muon g − 2 anomaly at Fermilab, indicates a Beyond Standard Model (BSM) satisfying the following properties: 1) it enhances the g − 2 2) suppresses flavor violations, such as μ → eγ, 3) suppresses CP violations, such as the electron electric dipole moment (EDM). In this letter, I show that the eigenbasis of the mass matrix and higher dimensional photon operators can be automatically aligned if the masses of heavy leptons are generated radiatively together with the g − 2. As a result, the muon g − 2 is enhanced but the EDM of the electron and μ → eγ rate are naturally suppressed. Phenomenology and applications of the mechanism to the B-physics anomalies are argued.

Parameter space exploration of the minimal SU(5) unification

We present phenomenological study of the most minimal realistic $SU(5)$ model that owns its predictivity solely to the gauge symmetry and the representational content. The model is built entirely out of the fields residing in the first five lowest dimensional representations that transform non-trivially under the $SU(5)$ gauge group. It has eighteen real parameters and fourteen phases, all in all, to address experimental observables of the Standard Model fermions and accomplishes that via simultaneous use of three different mass generation mechanisms. Furthermore, it inextricably links the origin of the neutrino mass to the experimentally observed difference between the down-type quark and charged lepton masses. The main predictions of the model are that $(i)$ the neutrinos are Majorana particles, $(ii)$ one neutrino is massless, $(iii)$ the neutrinos have normal mass ordering, and $(iv)$ there are four new scalar multiplets at or below a $120$ TeV mass scale. A one-loop analysis demonstrates that an improvement of the current $p \rightarrow \pi^0 e^+$ partial lifetime limit by a factor of $2$, $15$, and $96$ would require these four scalar multiplets to reside at or below the $100$ TeV, $10$ TeV, and $1$ TeV mass scales, respectively.

Explicit perturbations to the stabilizer \u03c4 = i of modular {A}_5^{prime } symmetry and leptonic CP violation

In a class of neutrino mass models with modular flavor symmetries, it has been observed that CP symmetry is preserved at the fixed point (or stabilizer) of the modulus parameter τ = i, whereas significant CP violation emerges within the neighbourhood of this stabilizer. In this paper, we first construct a viable model with the modular {A}_5^{prime } symmetry, and explore the phenomenological implications for lepton masses and flavor mixing. Then, we introduce explicit perturbations to the stabilizer at τ = i, and present both numerical and analytical results to understand why a small deviation from the stabilizer leads to large CP violation. As low-energy observables are very sensitive to the perturbations to model parameters, we further demonstrate that the renormalization-group running effects play an important role in confronting theoretical predictions at the high-energy scale with experimental measurements at the low-energy scale.

Modulus \u03c4 linking leptonic CP violation to baryon asymmetry in A4 modular invariant flavor model

We propose an A4 modular invariant flavor model of leptons, in which both CP and modular symmetries are broken spontaneously by the vacuum expectation value of the modulus τ. The value of the modulus τ is restricted by the observed lepton mixing angles and lepton masses for the normal hierarchy of neutrino masses. The predictive Dirac CP phase δCP is in the ranges [0°, 50°], [170°, 175°] and [280°, 360°] for Re [τ] < 0, and [0°, 80°], [185°, 190°] and [310°, 360°] for Re [τ] > 0. The sum of three neutrino masses is predicted in [60, 84] meV, and the effective mass for the 0νββ decay is in [0.003, 3] meV. The modulus τ links the Dirac CP phase to the cosmological baryon asymmetry (BAU) via the leptogenesis. Due to the strong wash-out effect, the predictive baryon asymmetry YB can be at most the same order of the observed value. Then, the lightest right-handed neutrino mass is restricted in the range of M1 = [1.5, 6.5] × 1013 GeV. We find the correlation between the predictive YB and the Dirac CP phase δCP. Only two predictive δCP ranges, [5°, 40°] (Re [τ] > 0) and [320°, 355°] (Re [τ] < 0) are consistent with the BAU.

Neutrino mass observables and non-Hermitian version of Type-I seesaw model

We study the non-Hermitian extension of the Lagrangian of the Standard Model extended by singlet right-handed heavy neutrinos. The Yukawa coupling matrices comprise of Hermitian and non-Hermitian components and the neutrino mass eigenvalues are calculated for three generation case. The increased number of unknown parameters in the theory due to non-Hermitian nature of coupling matrices impose problem for its productiveness. Hence we apply four zero texture for the Yukawa matrices. We consider the normal hierarchy of neutrino mass ordering and find the mixing angles and Dirac CP violating phase by diagonalizing the lepton mass matrices. The parameters of the mixing matrix are obtained in terms of the parameters of the non-Hermitian Yukawa coupling matrix. The values of the angles and phase are compatible with experimental data available for neutrino mass observables and using this the non-Hermitian parameters are constrained.

Analysis of particle masses, nuclear data and parameters of constituent quarks

A combined analysis of the recent empirical particle mass data from the PDG-2020 file, nuclear data and NRCQM constituent quark model parameters allows the development of the Standard Model mentioned by Y. Nambu: force unification and particle mass spectrum estimation. The performed analysis confirmed the role of lepton masses (me, mμ, mτ) and the symmetry motivated relation (1/3:1:16) between the electron mass and NRCQM parameters.

Quark and lepton mass matrices from localization in M-theory on G2 orbifold

M-theory compactified on a ${G}_{2}$ manifold with resolved ${E}_{8}$ singularities realizes four-dimensional $\mathcal{N}=1$ supersymmetric gauge theories coupled to gravity with three families of Standard Model fermions. Beginning with one ${E}_{8}$ singularity, three fermion families emerge when ${E}_{8}$ is broken by geometric engineering deformations to a smaller subgroup with equal rank. In this paper, we use the local geometry of the theory to explain the origin of the three families and their mass hierarchy. We linearize the blowing up of two-cycles associated with resolving ${E}_{8}$ singularities. After imposing explicit constraints on the effectively stabilized moduli, we arrive at Yukawa couplings for the quarks and leptons. We fit the high scale Yukawa couplings approximately which results in the quark masses agreeing reasonably well with the observations, implying that the experimental hierarchy of the masses is achievable within this framework. The hierarchy separation of the top quark from the charm and up is a stringy effect, while the spitting of the charm and up also depends on the Higgs sector. The Higgs sector cannot be reduced to having a single vacuum expectation value (VEV); all three VEVs must be nonzero. Three extra $U(1)\text{ }\text{ }\mathrm{s}$ survive to the low scale but are not massless, so $Z$ states are motivated to occur in the spectrum, but may be massive.

Radiative seesaw mechanism for charged leptons

We discuss a mechanism where charged lepton masses are derived from one-loop diagrams mediated by particles in a dark sector including a dark matter candidate. We focus on a scenario where the muon and electron masses are generated at one loop with new $\mathcal{O}(1)$ Yukawa couplings. The measured muon anomalous magnetic dipole moment, $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$, can be explained in this framework. As an important prediction, the muon and electron Yukawa couplings can deviate significantly from their standard model predictions, and such deviations can be tested at High-Luminosity LHC and future ${e}^{+}{e}^{\ensuremath{-}}$ colliders.

CP symmetry and symplectic modular invariance

We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus g\ge 3g≥3 the definition of CP is unique, while two independent possibilities are allowed when g\le 2g≤2. We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.

The common origin of the family mass hierarchy and CP violation from flavor-dependent vacuum for quarks and leptons

We rewrite the Yukawa interactions of the Standard Model in terms of flavor-dependent vacuum structure to address the family mass hierarchy and CP violation in both the quark sector and lepton sector. It is realized that Yukawa terms only include the same number of degrees of freedom as phenomenological observables with no requirement of extra particle or any new symmetry. The quark and lepton mass hierarchy arises as a natural result of the close-to-flat vacuum in flavor space. The CP violations in CKM mixing and PMNS mixing are explained as general quantum phases between weak gauge eigenstates and Yukawa interaction states. The mechanism is proven by reproduction of all current quark/lepton mass data and the CKM/PMNS mixing parameters.

Fermion masses and mixing from the double cover and metaplectic cover of the A5 modular group

We perform a comprehensive study of the homogeneous finite modular group $A'_5$ which is the double covering of $A_5$. The integral weight and level 5 modular forms have been constructed up to weight 6 and they are decomposed into the irreducible representations of $A'_5$. Then we perform a systematical analysis of the $A'_5$ modular models for lepton masses and mixing. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find out 15 models with 9 real free parameters which can accommodate the experimental data of lepton sector. After including generalized CP symmetry, 9 viable models with 7 free parameters are found out. We apply $A'_5$ modular symmetry to the quark sector, and a quark-lepton unification model is given. The framework of modular invariance is extended to include the rational weight modular forms of level 5. The ring of modular forms at level 5 can be generated by two algebraically independent weight $1/5$ modular forms denoted by $F_1(\tau)$ and $F_2(\tau)$. We give the expressions of the rational weight modular forms of level 5 up to weight $3$ and arrange them into the irreducible multiplets of finite metaplectic group $\widetilde{\Gamma}_5\cong A'_5\times Z_5$. A neutrino mass model with $\widetilde{\Gamma}_5$ modular symmetry is presented, and the phenomenological predictions of the model are analyzed numerically.

Highly Enhanced Contributions of Heavy Higgs Bosons and New Leptons to Muon g-2 and Prospects at Future Colliders.

We show that, in a two Higgs doublet model type II extended by vectorlike leptons, the contributions from heavy neutral and charged Higgs bosons to the anomalous magnetic moment of the muon simultaneously feature chiral enhancement from masses of new leptons and tan^{2}β enhancement from couplings of Higgs bosons. Assuming moderate values of new Yukawa couplings, not exceeding one, that can remain perturbative to very high energy scales, the measured value of muon g-2 can be explained within one standard deviation even with 6.5TeV leptons or 20TeV Higgs bosons. Allowing new couplings near the perturbativity limit, these mass ranges extend to 45TeV for leptons and 185TeV for Higgs bosons. In spite of the high scale of new physics, this scenario can be completely probed at planned future colliders.

Mixed EW-QCD two-loop amplitudes for qoverline{q}to {mathrm{ell}}^{+}{mathrm{ell}}^{-} and \u03b35 scheme independence of multi-loop corrections

We perform a dedicated study of the qoverline{q} -initiated two-loop electroweak-QCD Drell-Yan scattering amplitude in dimensional regularization schemes for vanishing light quark and lepton masses. For the relative order α and αs one-loop Standard Model corrections, details of our comparison to the original literature are given. The infrared pole terms of the mixed two-loop amplitude are governed by a known generalization of the dipole formula and we show explicitly that exactly the same two-loop polarized hard scattering functions are obtained in both the standard ’t Hooft-Veltman-Breitenlohner-Maison γ5 scheme and Kreimer’s anticommuting γ5 scheme.

Model of boson and fermion particle masses

The boson and fermion particle masses are calculated in a finite quantum field theory. The field theory satisfies Poincare invariance, unitarity and microscopic causality, and all loop graphs are finite to all orders of perturbation theory. The infinite derivative nonlocal field interactions are regularized with a mass (length) scale parameter $$\Lambda _i$$ . The W, Z and Higgs boson masses are calculated from finite one-loop self-energy graphs. The $$W^{\pm }$$ mass is predicted to be $$M_W=80.05$$ GeV, and the higher order radiative corrections to the Higgs boson mass $$m_\mathrm{H}=125$$ GeV are damped out above the regulating mass scale parameter $$\Lambda _H=1.57$$ TeV. The three generations of quark and lepton masses are calculated from finite one-loop self-interactions, and there is an exponential spacing in mass between the quarks and leptons.

The impact of different parameterizations on the interpretation of CP violation in neutrino oscillations

CP violation in the lepton mass matrix will be probed with good precision in upcoming experiments. The amount of CP violation present in oscillations can be quantified in numerous ways and is typically parameterized by the complex phase δPDG in the standard PDG definition of the lepton mixing matrix. There are additional parameterizations of the lepton mixing matrix as well. Through various examples, we explore how, given the current data, different parameterizations can lead to different conclusions when working with parameterization dependent variables, such as δ. We demonstrate how the smallness of |Ue3| governs the scale of these results. We then demonstrate how δ can be misleading and argue that the Jarlskog is the cleanest means of presenting the amount of CP violation in the lepton sector. We also confirm that, among the different parameterizations considered, the standard PDG parameterization has a number of convenient features.

Modular invariant A4 models for quarks and leptons with generalized CP symmetry

We perform a systematical analysis of the A4 modular models with generalized CP for the masses and flavor mixing of quarks and leptons, and the most general form of the quark and lepton mass matrices is given. The CP invariance requires all couplings real in the chosen basis and thus the vacuum expectation value of the modulus τ uniquely breaks both the modular symmetry and CP symmetry. The phenomenologically viable models with minimal number of free parameters and the results of fit are presented. We find 20 models with 7 real free parameters that can accommodate the experimental data of lepton sector. We then apply A4 modular symmetry to the quark sector to explain quark masses and CKM mixing matrix, the minimal viable quark model is found to contain 10 free real parameters. Finally, we give two predictive quark-lepton unification models which use only 16 real free parameters to explain the flavor patterns of both quarks and leptons.

Determination of collinear and TMD photon densities using the Parton Branching method

We present the first determination of transverse momentum dependent (TMD) photon densities with the Parton Branching method. The photon distribution is generated perturbatively without intrinsic photon component. The input parameters for quarks and gluons are determined from fits to precision measurements of deep inelastic scattering cross sections at HERA. The TMD densities are used to predict the mass and transverse momentum spectra of very high mass lepton pairs from both Drell-Yan production and Photon-Initiated lepton processes at the LHC.

Double covering of the modular A5 group and lepton flavor mixing in the minimal seesaw model

In this paper, we investigate the double covering of modular $\Gamma^{}_5 \simeq A^{}_5$ group and derive all the modular forms of weight one for the first time. The modular forms of higher weights are also explicitly given by decomposing the direct products of weight-one forms. For the double covering group $\Gamma^\prime_5 \simeq A^\prime_5$, there exist two inequivalent two-dimensional irreducible representations, into which we can assign two right-handed neutrino singlets in the minimal seesaw model. Two concrete models with such a salient feature have been constructed to successfully explain lepton mass spectra and flavor mixing pattern. The allowed parameter space for these two minimal scenarios has been numerically explored, and analytically studied with some reasonable assumptions.

Twin modular S4 with SU(5) GUT

We discuss the SU(5) grand unified extension of flavour models with multiple modular symmetries. The proposed model involves two modular S4 groups, one acting in the charged fermion sector, associated with a modulus field value τT with residual {Z}_3^T symmetry, and one acting in the right-handed neutrino sector, associated with another modulus field value τSU with residual {Z}_2^{SU} symmetry. Quark and lepton mass hierarchies are naturally generated with the help of weightons, which are SM singlet fields, where their non-zero modular weights play the role of Froggatt-Nielsen charges. The model predicts TM1 lepton mixing, and neutrinoless double beta decay at rates close to the sensitivity of current and future experiments, for both normal and inverted orderings, with suppressed corrections from charged lepton mixing due to the triangular form of its Yukawa matrix.

SU(5) GUTs with A4 modular symmetry

We combine SU(5) Grand Unified Theories (GUTs) with A4 modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. Classifying the models according to the representation assignments of the matter fields under A4, we find that there are seven types of SU(5) models with A4 modular symmetry. We present 53 benchmark models with the fewest free parameters. The parameter space of each model is scanned to optimize the agreement between predictions and experimental data, and predictions for the masses and mixing parameters of quarks and leptons are given at the best fitting points. The best fit predictions for the leptonic CP violating Dirac phase, the lightest neutrino mass and the neutrinoless double beta decay parameter when displayed graphically are observed to cover a wide range of possible values, but are clustered around particular regions, allowing future neutrino experiments to discriminate between the different types of models.