Yukawa Coupling Matrices Research Articles

Non-holomorphic modular S4 lepton flavour models

In the formalism of the non-supersymmetric modular invariance approach to the flavour problem the elements of the Yukawa coupling and fermion mass matrices are expressed in terms of polyharmonic Maaß modular forms of level N in addition to the standard modula forms of the same level and a small number of constant parameters. Non-trivial polyharmonic Maaß forms exist for zero, negative and positive integer modular weights. Employing the finite modula group S4 as a flavour symmetry group and assuming that the three left-handed lepton doublets furnish a triplet irreducible representation of S4, we construct all possible 7- and 8-parameter lepton flavour models in which the neutrino masses are generated either by the Weinberg effective operator or by the type-I seesaw mechanism. We identify the phenomenologically viable models and obtain predictions for each of these models for the neutrino mass ordering, the absolute neutrino mass scale, the Dirac and Majorana CP-violation phases and, correspondingly, for the sum of neutrino masses and the neutrinoless double beta decay effective Majorana mass. We comment on how these models can be tested and conclude that they are all falsifiable. Detailed analyses are presented in the case of three representative benchmark lepton flavour scenarios.

Conditions for suppressing dimension-five proton decay in renormalizable SUSY SO(10) GUT

The SUSY SO(10) GUT is in severe tension with the experimental bounds on proton partial lifetimes because proton decay mediated by colored Higgsinos (dimension-five proton decay) is too rapid. In this paper, we pursue the possibility that a texture of the Yukawa coupling matrices in a renormalizable SUSY SO(10) GUT model suppresses dimension-five proton decay. We focus on a general renormalizable SUSY SO(10) GUT model which contains 10 + 126 + overline{textbf{126}} + 120 representation fields and where the Yukawa coupling matrices of the 16 matter fields with the 10, overline{textbf{126}} , 120 fields, Y10, Y126, Y120, provide the quark and lepton Yukawa couplings and Majorana mass of the singlet neutrinos. We find that if components in certain flavor bases, {left({Y}_{10}right)}_{u_R{d}_R} , {left({Y}_{126}right)}_{u_R{d}_R} , {left({Y}_{10}right)}_{u_R{s}_R} , {left({Y}_{126}right)}_{u_R{s}_R} , {left({Y}_{10}right)}_{u_L{d}_L} , {left({Y}_{126}right)}_{u_L{d}_L} , {left({Y}_{10}right)}_{u_L{s}_L} , {left({Y}_{126}right)}_{u_L{s}_L} , {left({Y}_{10}right)}_{u_L{u}_L} , {left({Y}_{126}right)}_{u_L{u}_L} , are all on the order of the up quark Yukawa coupling, dimension-five proton decay can be suppressed while the Yukawa coupling matrices still reproduce the realistic quark and lepton masses and flavor mixings. We numerically obtain specific Yukawa coupling matrices satisfying the above conditions, calculate proton partial lifetimes from them and evaluate how dimension-five proton decay is suppressed when these conditions are met.

Phenomenology of one zero texture Yukawa matrix in a flavor symmetric scotogenic model

The scotogenic model is well known for accommodating small neutrino mass and dark matter. Here, we have realized the scotogenic model with the help of discrete flavor symmetry [Formula: see text]. We have obtained three one zero textures of Yukawa coupling matrices from the model and have studied its impact on neutrino phenomenology and related aspects of cosmology. On the basis of [Formula: see text] symmetry, we have further discarded two structures of one zero texture Yukawa coupling matrix. We further analyze if the effective mass of active neutrinos obtained by the virtue of the Yukawa coupling matrix is consistent with the KamLAND-Zen limit for [Formula: see text]. Also different lepton flavor violating (LFV) processes such as [Formula: see text] and [Formula: see text] are implemented and their influence on neutrino phenomenology is studied corresponding to the Yukawa coupling matrix. The entire work is carried out considering the dark matter mass [Formula: see text] in the region 450–750 GeV. We have also obtained some significant results for baryon asymmetry of the Universe in agreement with the one zero texture of the coupling matrices. Furthermore, interesting results for relic abundance on the basis of distinct mass splittings are between the inert scalars.

Two-body lepton-flavour-violating decays in a 2HDM with soft family-lepton-number breaking

We evaluate the decays {ell}_1^{pm } → {ell}_2^{pm}gamma , Z → {ell}_1^{+}{ell}_2^{-} , and h → {ell}_1^{+}{ell}_2^{-} , where ℓ1 and ℓ2 are charged leptons with different flavours and h is the scalar particle with mass 125.25 GeV, in a two-Higgs-doublet model where all the Yukawa-coupling matrices conserve the lepton flavours but the Majorana mass terms of the right-handed neutrinos break the flavour lepton numbers. We find that (1) the decays {ell}_1^{pm } → {ell}_2^{pm}gamma require large Yukawa couplings and very light right-handed neutrinos in order to be visible, (2) the decays Z → {ell}_1^{+}{ell}_2^{-} will be invisible in all the planned experiments, except in a very restricted range of circumstances, but (3) the decays h → {ell}_1^{+}{ell}_2^{-} may be detected in future experiments for rather relaxed sets of input parameters.

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.

Radiative neutrino masses, lepton flavor mixing and muon g \u2212 2 in a leptoquark model

We propose a leptoquark model with two scalar leptoquarks {S}_1left(overline{3},1,frac{1}{3}right) and {tilde{R}}_2left(3,2,frac{1}{6}right) to give a combined explanation of neutrino masses, lepton flavor mixing and the anomaly of muon g − 2, satisfying the constraints from the radiative decays of charged leptons. The neutrino masses are generated via one-loop corrections resulting from a mixing between S1 and {tilde{R}}_2 . With a set of specific textures for the leptoquark Yukawa coupling matrices, the neutrino mass matrix possesses an approximate μ-τ reflection symmetry with (Mν)ee = 0 only in favor of the normal neutrino mass ordering. We show that this model can successfully explain the anomaly of muon g − 2 and current experimental neutrino oscillation data under the constraints from the radiative decays of charged leptons.

A bottom-up approach to fermion mass hierarchy: a case with vector-like fermions

Abstract We propose a bottom-up approach in which a structure of high-energy physics is explored by accumulating existence proofs and/or no-go theorems in the standard model or its extension. As an illustration, we study fermion mass hierarchies based on an extension of the standard model with vector-like fermions. It is shown that the magnitude of elements of Yukawa coupling matrices can become $O(1)$ and a Yukawa coupling unification can be realized in a theory beyond the extended model, if vector-like fermions mix with three families. In this case, small Yukawa couplings in the standard model can be highly sensitive to a small variation of matrix elements, and it seems that the mass hierarchy occurs as a result of fine tuning.

Towards a minimal SU(5) GUT

We propose a simple $SU(5)$ model that connects the neutrino mass generation mechanism to the observed disparity between the masses of charged leptons and down-type quarks. The model is built out of $5$-, $10$-, $15$-, $24$-, and $35$-dimensional representations of $SU(5)$ and comprises two (three) $3 \times 3$ ($3 \times 1$) Yukawa coupling matrices to accommodate all experimentally measured fermion masses and mixing parameters. The gauge coupling unification considerations, coupled with phenomenological constraints inferred from experiments that probe neutrino masses and mixing parameters and/or look for proton decay, fix all relevant mass scales of the model. The proposed scenario places several multiplets at the scales potentially accessible at the LHC and future colliders and correlates this feature with the gauge boson mediated proton decay signatures. It also predicts that one neutrino is massless.

Renormalization group evolution of dimension-seven operators in standard model effective field theory and relevant phenomenology

We showed in a previous publication that there are six independent dimension-seven operators violating both lepton and baryon numbers (L = −B = 1) and twelve ones violating lepton but preserving baryon number (L = 2, B = 0) in standard model effective field theory, and we calculated one-loop renormalization for the former six operators. In this work we continue our efforts on renormalization of the operators. It turns out this could become subtle because the operators are connected by nontrivial relations when fermion flavors are counted. This kind of relations does not appear in lower dimensional operators. We show how we can extract anomalous dimension matrix for a flavor-specified basis of operators from counterterms computed for the above flavor-blind operators without introducing singular inverse Yukawa coupling matrices. As a phenomenological application, we investigate renormalization group effects on nuclear neutrinoless double β decay. We also discuss very briefly its analog in the meson sector, K± → π∓μ±μ±, and indicate potential difficulties to compute its decay width.

Combining texture zeros with a remnant CP symmetry in the minimal type-I seesaw

In the framework of the two right-handed neutrino seesaw model, we consider maximally-restrictive texture-zero patterns for the lepton Yukawa coupling and mass matrices, together with the existence of a remnant CP symmetry. Under this premise, we find that several textures are compatible with the most recent data coming from neutrino oscillation and neutrinoless double beta decay experiments. It is shown that, the maximum number of allowed texture zeros in the Dirac Yukawa coupling matrix is two, for an inverted neutrino mass spectrum. In contrast, for Yukawa coupling matrices with just one texture zero, both normal and inverted orderings of neutrino masses are compatible with data. In all cases, the predictions for the low-energy Dirac and Majorana CP-violating phases, and for the effective mass parameter relevant in neutrinoless double-beta decay experiments, are presented and discussed. We also comment on the impact of future experimental improvements in scrutinising texture-zero patterns with a remnant CP symmetry, within the minimal version of the seesaw mechanism considered here.

Flavor physics in the multi-Higgs doublet models induced by the left-right symmetry

In this paper, we discuss the multi-Higgs doublet models, that could be effectively induced by the extended Standard Model (SM). In particular, we focus on the phenomenology in the supersymmetric model with left-right (LR) symmetry, where the down-type and the up-type Yukawa couplings are unified and the Yukawa coupling matrices are expected to be hermitian. In this model, several Higgs doublets are introduced to realize the realistic fermion mass matrices, and the heavy Higgs doublets have flavor changing couplings with quarks and leptons. The LR symmetry is assumed to break down at high energy to realize the Type-I seesaw mechanism. The supersymmetry breaking scale is expected to be around 100 TeV to achieve the 125 GeV Higgs. In such a setup, the flavor-dependent interaction of the Higgs fields becomes sizable, so that we especially discuss the flavor physics induced by the heavy Higgs fields in our work. Our prediction depends on the structure of neutrinos, e.g., the neutrino mass ordering. We demonstrate how the flavor structure of the SM affects the flavor violating couplings. In our analysis, we mainly focus on the four-fermi interaction induced by the scalar exchanging, and we propose a simple parameterization for the coefficients. Then, we find the correlations among the flavor observables and, for instance, see that our prediction for the μ → 3e process could be covered by the future experiment, in one case where the neutrino mass hierarchy is normal.

Resurrecting minimal Yukawa sector of SUSY SO(10)

Supersymmetric SO(10) models with Yukawa coupling matrices involving only a 10H and a {overline{126}}_H of Higgs fields can lead to a predictive and consistent scenario for fermion masses and mixings, including the neutrino sector. However, when coupled minimally to a symmetry breaking sector that includes a 210H and a 126H, these models lead either to an unacceptably small neutrino mass scale, or to non-perturbative values of the gauge couplings. Here we show that with the addition of a 54H to the symmetry breaking sector, the successful predictions of these models for fermion masses and mixings can be maintained. The 54H enables a reduction of the B − L symmetry breaking scale to an intermediate value of order 1012 GeV, consistent with the observed neutrino mass spectrum, while preserving perturbative gauge coupling unification. We obtain an excellent fit to all fermion masses and mixings in this framework. We analyze carefully the prediction of the model for CP violation in neutrino oscillations. Consistency with proton lifetime, however, requires a mini-split SUSY spectrum with the squarks and sleptons having masses of order 100 TeV, accompanied by TeV scale gauginos and Higgsinos. Such a spectrum may arise from pure gravity mediation, which would predict the partial lifetime for the decay pto overline{nu}{K}^{+} to be an order of magnitude above the current experimental limit.

Flavor conservation in two-Higgs-doublet models

In extensions of the Standard Model with two Higgs doublets, flavor-changing Yukawa couplings of the neutral scalars may be present at tree level. In this work, we consider the most general scenario in which those flavor-changing couplings are absent. We revise the conditions that the Yukawa coupling matrices must obey for such general flavour conservation (gFC) and study the one-loop renormalization group evolution of such conditions in both the quark and lepton sectors. We show that gFC in the leptonic sector is one-loop stable under the renormalization group evolution, and in the quark sector, we present some new Cabibbo-like solution also one-loop stable under renormalization group evolution. At a phenomenological level, we obtain the regions for the different gFC parameters that are allowed by the existing experimental constraints related to the 125 GeV Higgs.

High scale flavor alignment in two-Higgs doublet models and its phenomenology

The most general two-Higgs doublet model (2HDM) includes potentially large sources of flavor changing neutral currents (FCNCs) that must be suppressed in order to achieve a phenomenologically viable model. The flavor alignment ansatz postulates that all Yukawa coupling matrices are diagonal when expressed in the basis of mass-eigenstate fermion fields, in which case tree-level Higgs-mediated FCNCs are eliminated. In this work, we explore models with the flavor alignment condition imposed at a very high energy scale, which results in the generation of Higgs-mediated FCNCs via renormalization group running from the high energy scale to the electroweak scale. Using the current experimental bounds on flavor changing observables, constraints are derived on the aligned 2HDM parameter space. In the favored parameter region, we analyze the implications for Higgs boson phenomenology.

Top and bottom partners, Higgs boson on the brane, and the tth signal

Current LHC results indicate a possible enhancement in the production of Higgs bosons in association with top quarks (tth) over the Standard Model (SM) expectations, suggesting an increase in the top Yukawa coupling. To explain these results, we study the effect of adding to the SM a small set of vector-like partners of the top and bottom quarks with masses of order ~1 TeV. We consider Yukawa coupling matrices with vanishing determinant and show that then, Higgs production through gluon fusion is not affected by deviations in the top quark Yukawa coupling, and in fact depends only on deviations in the bottom quark Yukawa coupling. We call this scenario the "Brane Higgs Limit", as it can emerge naturally in models of warped extra-dimensions with all matter fields in the bulk, except the Higgs (although it could also occur in 4D scenarios with vector-like quarks and special flavor symmetries forcing the vanishing of the Yukawa determinants). We show that the scenario is highly predictive for all Higgs production/decay modes, making it easily falsifiable, maybe even at the LHC RUN 2 with higher luminosity.

Charged-lepton decays from soft flavour violation

We consider a two-Higgs-doublet extension of the Standard Model, with three right-handed neutrino singlets and the seesaw mechanism, wherein all the Yukawa-coupling matrices are lepton flavour-diagonal and lepton flavour violation is soft, originating solely in the non-flavour-diagonal Majorana mass matrix of the right-handed neutrinos. We consider the limit mR→∞ of this model, where mR is the seesaw scale. We demonstrate that there is a region in parameter space where the branching ratios of all five charged-lepton decays ℓ1−→ℓ2−ℓ3+ℓ3− are close to their experimental upper bounds, while the radiative decays ℓ1−→ℓ2−γ are invisible because their branching ratios are suppressed by mR−4. We also consider the anomalous magnetic moment of the muon and show that in our model the contributions from the extra scalars, both charged and neutral, can remove the discrepancy between its experimental and theoretical values.

Testing neutrino mass generation mechanisms from the lepton flavor violating decay of the Higgs boson

We investigate how observations of the lepton flavor violating decay of the Higgs boson ($h \to \ell\ell^\prime$) can narrow down models of neutrino mass generation mechanisms, which were systematically studied in Refs. [1,2] by focusing on the combination of new Yukawa coupling matrices with leptons. We find that a wide class of models for neutrino masses can be excluded if evidence for $h \to \ell\ell^\prime$ is really obtained in the current or future collider experiments. In particular, simple models of Majorana neutrino masses cannot be compatible with the observation of $h \to \ell\ell^\prime$. It is also found that some of the simple models to generate masses of Dirac neutrinos radiatively can be compatible with a significant rate of the $h \to \ell\ell^\prime$ process.

SO(10) models with flavour symmetries: classification and examples

Renormalizable SO(10) grand unified theory (GUT) models equipped with flavour symmetries are a popular framework for addressing the flavour puzzle. Usually, the flavour symmetry group has been an ad hoc choice, and no general arguments limiting this choice were known. In this paper, we establish the full list of flavour symmetry groups which may be enforced, without producing any further accidental symmetry, on the Yukawa-coupling matrices of an SO(10) GUT with arbitrary numbers of scalar multiplets in the , , and representations of SO(10). For each of the possible discrete non-Abelian symmetry groups, we present examples of minimal models which do not run into obvious contradiction with the phenomenological fermion masses and mixings.

Predicting the sparticle spectrum from GUTs via SUSY threshold corrections with SusyTC

Grand Unified Theories (GUTs) can feature predictions for the ratios of quark and lepton Yukawa couplings at high energy, which can be tested with the increasingly precise results for the fermion masses, given at low energies. To perform such tests, the renormalization group (RG) running has to be performed with sufficient accuracy. In supersymmetric (SUSY) theories, the one-loop threshold corrections (TC) are of particular importance and, since they affect the quark-lepton mass relations, link a given GUT flavour model to the sparticle spectrum. To accurately study such predictions, we extend and generalize various formulas in the literature which are needed for a precision analysis of SUSY flavour GUT models. We introduce the new software tool SusyTC, a major extension to the Mathematica package REAP, where these formulas are implemented. SusyTC extends the functionality of REAP by a full inclusion of the (complex) MSSM SUSY sector and a careful calculation of the one-loop SUSY threshold corrections for the full down-type quark, up-type quark and charged lepton Yukawa coupling matrices in the electroweak-unbroken phase. Among other useful features, SusyTC calculates the one-loop corrected pole mass of the charged (or the CP-odd) Higgs boson as well as provides output in SLHA conventions, i.e. the necessary input for external software, e.g. for performing a two-loop Higgs mass calculation. We apply SusyTC to study the predictions for the parameters of the CMSSM (mSUGRA) SUSY scenario from the set of GUT scale Yukawa relations $y_e / y_d = - 1/2$, $y_\mu / y_s = 6$, and $y_\tau / y_b = - 3/2$, which has been proposed recently in the context of SUSY GUT flavour models.

Flavour symmetries in a renormalizable SO(10) model

In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a 10⊕120⊕126‾ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by Zn symmetries, with suitable n, and one case is generated by a Z2×Z2 symmetry. A numerical analysis of the 14 cases reveals that only two of them—dubbed A and B in the present paper—allow good fits to the experimentally known fermion masses and mixings.