Charged Lepton Sector Research Articles

Quark and lepton mixing patterns from a common discrete flavor symmetry with a generalized CP symmetry

We have studied two approaches to predict quark and lepton mixing patterns from the same flavor symmetry group in combination with CP symmetry. The first approach is based on the residual symmetry $Z_2$ in the charged lepton sector and $Z_2\times CP$ in the neutrino sector. All lepton mixing angles and CP violation phases depend on three real parameters $\theta_{l}$, $\delta_{l}$ and $\theta_{\nu}$. This approach is extended to the quark sector, the up and down quark mass matrices are assumed to be invariant under a $Z_2$ subgroup and $Z_2\times CP$. The necessary and sufficient conditions for the equivalence of two mixing patterns are derived. The second approach has an abelian subgroup and a single CP transformation as residual symmetries of the charged lepton and neutrino sectors respectively. The lepton mixing would be determined up to a real orthogonal matrix multiplied from the right hand side. Analogously we assume that a single CP transformation is preserved by the down (or up) quark mass matrix, and the residual symmetry of the up (or down) quark sector is be an abelian subgroup. As an example, we analyze the possible mixing patterns which can be obtained from the breaking of $\Delta(6n^2)$ and CP symmetries. We find $\Delta(294)$ combined with CP is the smallest flavor group which can give a good fit to the experimental data of quark and lepton mixing in both approaches.

Assessing the viability of A4 , S4 , and A5 flavor symmetries for description of neutrino mixing

We consider the $A_4$, $S_4$ and $A_5$ discrete lepton flavour symmetries in the case of 3-neutrino mixing, broken down to non-trivial residual symmetries in the charged lepton and neutrino sectors in such a way that at least one of them is a $Z_2$. Such symmetry breaking patterns lead to predictions for some of the three neutrino mixing angles and/or the leptonic Dirac CP violation phase $\delta$ of the neutrino mixing matrix. We assess the viability of these predictions by performing a statistical analysis which uses as an input the latest global data on the neutrino mixing parameters. We find 14 phenomenologically viable cases providing distinct predictions for some of the mixing angles and/or the Dirac phase $\delta$. Employing the current best fit values of the three neutrino mixing angles, we perform a statistical analysis of these cases taking into account the prospective uncertainties in the determination of the mixing angles, planned to be achieved in currently running (Daya Bay) and the next generation (JUNO, T2HK, DUNE) of neutrino oscillation experiments. We find that only six cases would be compatible with these prospective data. We show that this number is likely to be further reduced by a precision measurement of $\delta$.

A light Higgs at the LHC and the B-anomalies

After the Higgs discovery, the LHC has been looking for new resonances, decaying into pairs of Standard Model (SM) particles. Recently, the CMS experimen observed an excess in the di-photon channel, with a di-photon invariant mass of about 96 GeV. This mass range is similar to the one of an excess observed in the search for the associated production of Higgs bosons with the Z neutral gauge boson at LEP, with the Higgs bosons decaying to bottom quark pairs. On the other hand, the LHCb experiment observed a discrepancy with respect to the SM expectations of the ratio of the decay of B-mesons to K-mesons and a pair of leptons, {R}_{K^{left(ast right)}}=BRleft(Bto {K}^{left(ast right)}{mu}^{+}{mu}^{-}right)/BRleft(Bto {K}^{left(ast right)}{e}^{+}{e}^{-}right) . This observation provides a hint of the violation of lepton-flavor universality in the charged lepton sector and may be explained by the existence of a vector boson originating form a U{(1)_{L_{mu}}}_{-{L}_{{}_{tau }}} symmetry and heavy quarks that mix with the left-handed down quarks. Since the coupling to heavy quarks could lead to sizable Higgs di-photon rates in the gluon fusion channel, in this article we propose a common origin of these anomalies identifying a Higgs associated with the breakdown of the U{(1)_{L_{mu}}}_{-{L}_{{}_{tau }}} symmetry and at the same time responsible to the quark mixing, with the one observed at the LHC. We also discuss the constraints on the identification of the same Higgs with the one associated with the bottom quark pair excess observed at LEP.

Toward a unified interpretation of quark and lepton mixing from flavor and CP symmetries

We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to Z2 × CP in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters θl and θν varying in the range of [0, π). As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group Δ(6n2) and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters θu and θd. A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group Δ(6n2) and CP, and accordingly the smallest value of the group index n is n = 7.

Neutrino mixing and leptonic CP violation from S4 flavour and generalised CP symmetries

We consider a class of models of neutrino mixing with S4 lepton flavour symmetry combined with a generalised CP symmetry, which are broken to residual Z2 and Z2 × HCPν symmetries in the charged lepton and neutrino sectors, respectively, HCPν being a remnant CP symmetry of the neutrino Majorana mass term. In this set-up the neutrino mixing angles and CP violation (CPV) phases of the neutrino mixing matrix depend on three real parameters — two angles and a phase. We classify all phenomenologically viable mixing patterns and derive predictions for the Dirac and Majorana CPV phases. Further, we use the results obtained on the neutrino mixing angles and leptonic CPV phases to derive predictions for the effective Majorana mass in neutrinoless double beta decay.

Neutrino mass matrices with three or four vanishing cofactors and nondiagonal charged lepton sector

We investigate the texture structures of lepton mass matrices with four (five) non-zero elements in the charged lepton mass matrix and three (four) vanishing cofactors in the neutrino mass matrix. Using weak basis transformations, all possible textures for three and four vanishing cofactors in $M_{\nu}$ are grouped into 7 classes and predictions for the unknown parameters such as the Dirac CP violating phase and the effective Majorana mass for the phenomenologically allowed textures have been obtained. We, also, illustrate how such texture structures can be realized using discrete Abelian flavor symmetries.

Implications of residual CP symmetry for leptogenesis in a model with two right-handed neutrinos

We analyze the interplay between leptogenesis and residual symmetry in the framework of two right-handed neutrino model. Working in the flavor basis, we show that all the leptogenesis CP asymmetries are vanishing for the case of two residual CP transformations or a cyclic residual flavor symmetry in the neutrino sector. If a single remnant CP transformation is preserved in the neutrino sector, the lepton mixing matrix is determined up to a real orthogonal matrix multiplied from the right side. The $R$-matrix is found to depend on only one real parameter, it can take three viable forms, and each entry is either real or purely imaginary. The baryon asymmetry is generated entirely by the CP violating phases in the mixing matrix in this scenario. We perform a comprehensive study for the $\Delta(6n^2)$ flavor group and CP symmetry which are broken to a single remnant CP transformation in the neutrino sector and an abelian subgroup in the charged lepton sector. The results for lepton flavor mixing and leptogenesis are presented.

Leptonic flavour mixing influenced by flavon cross couplings

We develop an economical approach to connect flavon cross couplings with flavour mixing. A non-zero reactor mixing angle and almost maximal CP violation arise from cross couplings between flavons in the charged lepton and neutrino sectors. Within this approach, we analyze how cross couplings contribute to charged lepton-flavour-violating decays. We find branching ratio sum rules of these processes and observe that the electroweak-scale flavour symmetry is consistent with current experimental data.

Lepton sector phases and their roles in flavor and generalized CP symmetries

We study the effects of considering nontrivial unphysical lepton sector phases on the group theoretical properties of the flavor and generalized CP symmetry elements in the case where there are three light, distinct Majorana neutrino species. We highlight the similarities and differences between the charged lepton and neutrino sectors and further elucidate the group properties of the flavor and generalized CP symmetry elements. We show how the inclusion of these leptonic phases affects the bottom-up constructions of these symmetry elements and discuss the implications for top-down model building based on discrete symmetry groups.

Lorentz violation bounds from torsion trace fermion sector and galaxy M 51 data and chiral dynamos

Earlier we have computed a Lorentz violation (LV) bound for torsion terms via galactic dynamos and found bounds similar to the one obtained by Kostelecky et al. (Phys Rev Lett 100:111102, 2008) which is of the order of 10^{-31} GeV. Their result was found making use of the axial torsion vector in terms of Dirac spinors and minimal torsion coupling in flat space-time of fermions. In this paper, a torsion dynamo equation obtained using the variation of the torsion trace and galaxy M51 data of 500 pc are used to place an upper bound of 10^{-26} GeV in LV, which agrees with the one by Kostelecky and his group using an astrophysical framework background. Their lowest bound was obtained in earth laboratory using dual masers. One of the purposes of this paper is to apply the Faraday self-induction magnetic equation, recently extended to torsioned space-time, by the author to show that it lends support to physics in Riemann–Cartan space-time, in several distinct physical backgrounds. Backreaction magnetic effects are used to obtain the LV bounds. Previously Bamba et al. (JCAP 10:058, 2012) have used the torsion trace in their teleparallel investigation of the IGMF, with the argument that the torsion trace leads to less weaker effects than the other irreducible components of the torsion tensor. LV is computed in terms of a chiral-torsion-like current in the new dynamo equation analogous to the Dvornikov and Semikoz dynamo equation with chiral magnetic currents. Making use of the chiral-torsion dynamo equation we estimate the LV bounds in the early universe to be of the order of 10^{-24} GeV, which was the order of the charged-lepton sector. Our main result is that it is possible to obtain more stringent bounds than the ones found in the fermion sector of astrophysics in the new revised 2017 data table for CPT and Lorentz violation by Kostelecky and Mewes. They found in several astrophysical backgrounds, orders of magnitude such as 10^{-24} and 10^{-23} GeV which are not so stringent as the one found here, of 10^{-26} GeV, in the torsion fermionic sector with the help of galaxy M51 data. It is also shown that non-gauge invariance of chiral dynamos and axial anomalies are obtained from the noninvariance of the electric fields under torsion spatial translations.

Fermion masses and mixing in SU(5)×D4 × U(1) model

We propose a supersymmetric SU(5)×Gf GUT model with flavor symmetry Gf=D4×U(1) providing a good description of fermion masses and mixing. The model has twenty eight free parameters, eighteen are fixed to produce approximative experimental values of the physical parameters in the quark and charged lepton sectors. In the neutrino sector, the TBM matrix is generated at leading order through type I seesaw mechanism, and the deviation from TBM studied to reconcile with the phenomenological values of the mixing angles. Other features in the charged sector such as Georgi–Jarlskog relations and CKM mixing matrix are also studied.

Alternative schemes of predicting lepton mixing parameters from discrete flavor and CP symmetry

We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the residual groups of the structure $Z_2\times CP$ in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters $\theta_{\nu}$ and $\theta_{l}$. This type of breaking pattern is extended to the quark sector. In the second scheme, an abelian subgroup contained in the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant $CP$ transformation, all lepton mixing parameter are determined in terms of three free parameters $\theta_{1, 2, 3}$. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters $\theta_{\nu, l}$ and $\theta_{1, 2, 3}$ is taken into account. We have studied the lepton mixing patterns arising from the flavor group $S_4$ and $CP$ symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.

Lepton-flavour violation in a Pati-Salam model with gauged flavour symmetry

Combining Pati-Salam (PS) and flavour symmetries in a renormalisable setup, we devise a scenario which produces realistic masses for the charged leptons. Flavour-symmetry breaking scalar fields in the adjoint representations of the PS gauge group are responsible for generating different flavour structures for up- and down-type quarks as well as for leptons. The model is characterised by new heavy fermions which mix with the Standard Model quarks and leptons. In particular, the partners for the third fermion generation induce sizeable sources of flavour violation. Focusing on the charged-lepton sector, we scrutinise the model with respect to its implications for lepton-flavour violating processes such as $\mu \rightarrow e\gamma$, $\mu\rightarrow 3e$ and muon conversion in nuclei.

Flavon-induced connections between lepton flavour mixing and charged lepton flavour violation processes

In leptonic flavour models with discrete flavour symmetries, couplings between flavons and leptons can result in special flavour structures after they gain vacuum expectation values. At the same time, they can also contribute to the other lepton-flavour-violating processes. We study the flavon-induced LFV 3-body charged lepton decays and radiative decays and we take as example the $A_4$ discrete symmetry. In $A_4$ models, a $Z_3$ residual symmetry roughly holds in the charged lepton sector for the realisation of tri-bimaximal mixing at leading order. The only processes allowed by this symmetry are $\tau^-\to \mu^+ e^- e^-, e^+ \mu^- \mu^-$, and the other 3-body and all radiative decays are suppressed by small $Z_3$-breaking effects. These processes also depend on the representation the flavon is in, whether pseudo-real (case i) or complex (case ii). We calculate the decay rates for all processes for each case and derive their strong connection with lepton flavour mixing. In case i, sum rules for the branching ratios of these processes are obtained, with typical examples $\text{Br}(\tau^-\to \mu^+ e^- e^-) \approx \text{Br}(\tau^-\to e^+ \mu^- \mu^-)$ and $\text{Br}(\tau^-\to e^- \gamma) \approx \text{Br}(\tau^-\to \mu^- \gamma)$. In case ii, we observe that the mixing between two $Z_3$-covariant flavons plays an important role. All processes are suppressed by charged lepton masses and current experimental constraints allow the electroweak scale and the flavon masses to be around hundreds of GeV. Our discussion can be generalised in other flavour models with different flavour symmetries.

A4 and CP symmetry and a model with maximal CP violation

We study a second CP symmetry compatible with the A4 flavor group, which interchanges the representations 1′ and 1″. We analyze the lepton mixing patterns arising from the A4 and CP symmetry broken to residual subgroups Z3 and Z2×CP in the charged lepton and neutrino sectors respectively. One phenomenologically viable mixing pattern is found, and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP phase, trivial Majorana phases and the correlation sin2⁡θ12cos2⁡θ13=1/3. We construct a concrete model based on the A4 and CP symmetry, the above interesting mixing pattern is achieved, the observed charged lepton mass hierarchy is reproduced, and the reactor mixing angle θ13 is of the correct order.

Probing maximal zero textures with broken cyclic symmetry in inverse seesaw

Within the framework of inverse seesaw mechanism we investigate neutrino mass matrices invariant under cyclic symmetry (Z3) with maximal zero texture (6 zero textures). We explore two different approaches to obtain the cyclic symmetry invariant form of the constituent matrices. In the first one we consider explicit cyclic symmetry in the neutrino sector of the Lagrangian which dictates the emerged effective neutrino mass matrix (mν) to be symmetry invariant and hence leads to a degeneracy in masses. We then consider explicit breaking of the symmetry through a dimensionless parameter ϵ′ to remove the degeneracy. It is seen that the method doesn't support the current neutrino oscillation global fit data even after considering the correction from cyclic symmetry invariant charged lepton mass matrix (ml) unless the breaking parameter is too large. In the second method, we assume the same forms of the neutrino mass matrices, however, symmetry is broken in the charged lepton sector. All the structures of the mass matrices are now dictated by an effective residual symmetry of some larger symmetry group in the Lagrangian. For illustration, we exemplify a toy model based on softly broken A4 symmetry group which leads to one of the combinations of ml, mD, MRS and μ to generate effective mν. All the emerged mass matrices predict a constraint range of the CP violating phases and atmospheric mixing angle along with an inverted hierarchical structure of the neutrino masses. Further, significant predictions on ββ0ν decay parameter |m11| and the sum of the three light neutrino masses (Σimi) are also obtained.

Littlest Seesaw model from S 4 × U(1)

We show how a minimal (littlest) seesaw model involving two right-handed neutrinos and a very constrained Dirac mass matrix, with one texture zero and two independent Dirac masses, may arise from $S_4\times U(1)$ symmetry in a semi-direct supersymmetric model. The resulting CSD3 form of neutrino mass matrix only depends on two real mass parameters plus one undetermined phase. We show how the phase may be fixed to be one of the cube roots of unity by extending the $S_4\times U(1)$ symmetry to include a product of $Z_3$ factors together with a CP symmetry, which is spontaneously broken leaving a single residual $Z_3$ in the charged lepton sector and a residual $Z_2$ in the neutrino sector, with suppressed higher order corrections. With the phase chosen from the cube roots of unity to be $-2\pi/3$, the model predicts a normal neutrino mass hierarchy with $m_1=0$, reactor angle $\theta_{13}=8.7^\circ$, solar angle $\theta_{12}=34^\circ$, atmospheric angle $\theta_{23}=44^\circ$, and CP violating oscillation phase $\delta_{\rm CP}=-93^\circ$, depending on the fit of the model to the neutrino masses.

Double Froggatt–Nielsen mechanism

We present a doubly parametric extension of the standard Froggatt--Nielsen (FN) mechanism. As is well known, mass matrices of the up- and down-type quark sectors and the charged lepton sector in the standard model can be parametrized well by a parameter $\lambda$ which is usually taken to be the sine of the Cabibbo angle ($\lambda = \sin\theta_\text{C} \simeq 0.225$). However, in the neutrino sector, there is still room to realize the two neutrino mass squared differences $\Delta m_\text{sol}^2$ and $\Delta m_\text{atm}^2$, two large mixing angles $\theta _{12}$ and $\theta _{23}$, and non-zero $\theta _{13}$. Then we consider an extension with an additional parameter $\rho$ in addition to $\lambda$. Taking the relevant FN charges for a power of $\lambda~(=0.225)$ and additional FN charges for a power of $\rho$, which we assume to be less than one, we can reproduce the ratio of the two neutrino mass squared differences and three mixing angles. In the normal neutrino mass hierarchy, we show several patterns for taking relevant FN charges and the magnitude of $\rho$. We find that if $\sin \theta_{23}$ is measured more precisely, we can distinguish each pattern. This is testable in the near future, for example in neutrino oscillation experiments. In addition, we predict the Dirac CP-violating phase for each pattern.

Type II seesaw supersymmetric neutrino model forθ13≠0

Using the type II seesaw approach and properties of discrete flavor symmetry group representations, we build a supersymmetric $A_{4}\times A_{3}$\ neutrino model with $\theta_{13}\neq0$. After describing the basis of this model--which is beyond the minimal supersymmetric Standard Model--with a superfield spectrum containing flavons in $A_{4}\times A_{3}$\ representations, we first generate the tribimaximal neutrino mixing which is known to be in agreement with the mixing angles $\theta_{12}$ and $\theta_{23}$. Then, we give the scalar potential of the theory where the $A_{3}$ discrete subsymmetry is used to avoid the so-called sequestering problem. We \textrm{next} study the deviation from the tribimaximal mixing matrix which is produced by perturbing the neutrino mass matrix with a nontrivial $A_{4}$ singlet. Normal and inverted mass hierarchies are discussed numerically. We also study the breaking of $A_{4}$\ down to $Z_{3}$\ in the charged lepton sector, and use the branching ratio of the decay $\tau \rightarrow \mu \mu e$--which is allowed by the residual symmetry $Z_{3}$--to get estimations on the mass of one of the flavons and the cutoff scale $\Lambda$ of the model.

The role of flavon cross couplings in leptonic flavour mixing

In models with discrete flavour symmetries, flavons are critical to realise specific flavour structures. Leptonic flavour mixing originates from the misalignment of flavon vacuum expectation values which respect different residual symmetries in the charged lepton and neutrino sectors. Flavon cross couplings are usually forbidden, in order to protect these symmetries. Contrary to this approach, we show that cross couplings can play a key role and give raise to necessary corrections to flavour-mixing patterns, including a non-zero value for the reactor angle and CP violation. For definiteness, we present two models based on $A_4$. In the first model, all flavons are assumed to be real or pseudo-real, with 7 real degrees of freedom in the flavon sector in total. A sizable reactor angle associated with nearly maximal CP violation is achieved, and, as both originate from the same cross coupling, a sum rule results with a precise prediction for the value of the Dirac CP-violating phase. In the second model, the flavons are taken to be complex scalars, which can be connected with supersymmetric models and multi-Higgs models. The complexity properties of flavons provide new sources for generating the reactor angle. Models in this new approach introduce very few degrees of freedom beyond the Standard Model and can be more economical than those in the framework of extra dimension or supersymmetry.