arXiv subjects

Anjan S. Joshipura

Publications and source records attributed to Anjan S. Joshipura.

At least 19 recordsLinked to original sources

arXiv2026

Restoring minimal modular neutrino masses via Kähler $R$-parity violation

The possibility of describing neutrino masses through a single multiplet of modular forms in a modular symmetric framework is reanalysed. The minimal model achieving this is Feruglio's model based on modular $A_4$ symmetry, which contains a chiral flavon triplet $ϕ$, with all neutrino masses and mixing determined by a superfield triplet of modular forms $Y(τ)$. We point out that, in local supersymmetry, these superfields by themselves allow an additional $R$-parity-violating contribution to neutrino masses originating from the Kähler potential of the model. The $R$ violation manifests through a bilinear term $ε_i L_i H_u$ in the effective superpotential, with parameters $ε_i$ determined in terms of $Y(τ)$ and its derivatives. The Kähler potential also mixes neutrinos with the fermionic component of $ϕ$, leading to seesaw neutrino masses when these fermions are massive. Two separate cases are analysed, with neutrinos obtaining mass through the Weinberg operator or through the $ϕ$-induced seesaw. Unlike the original model, adding the $R$-violating contribution allows accurate reproduction of neutrino mixing angles and mass ratios for both the normal and inverted orderings in either case, with the Weinberg operator predicting a sum of neutrino masses close to the cosmological limit and the seesaw mechanism predicting ones comfortably below it.

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arXiv2024

Soft supersymmetry breaking as the sole origin of neutrino masses and lepton number violation

We discuss a scenario in which the supergravity induced soft terms, conventionally used for breaking supersymmetry, also lead to non-zero Majorana neutrino masses. The soft terms lead to the spontaneous violation of the lepton number at the gravitino mass scale $m_{3/2}$ which in turn leads to (i) the Majorana masses of ${\cal O} (m_{3/2})$ for the right-handed neutrinos and (ii) the $R$-parity breaking at the same scale. The former contributes to light neutrino masses through the type I seesaw mechanism, while the latter adds to it through neutrino-neutralino mixing. Both contributions can scale inversely with respect to $m_{3/2}$ given that gaugino and Higgsino masses are also of order $m_{3/2}$. Together, these two contributions adequately explain observed neutrino masses and mixing. One realization of the scenario also naturally leads to a $μ$ parameter of ${\cal O} (m_{3/2})$. Despite the lepton number symmetry breaking close to the weak scale, the Majoron in the model exhibits very weak coupling to leptons, satisfying existing constraints on Majoron-lepton interactions. The right-handed neutrinos in the model have a large coupling to Higgsinos. This coupling and the relatively large heavy-light neutrino mixing induced through the seesaw mechanism may lead to the observable signals at colliders in terms of displaced vertices.

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arXiv2021

Weak scale right-handed neutrino as pseudo-Goldstone fermion of spontaneously broken $U(1)_{L_μ-L_τ}$

Possibility of a Right-Handed (RH) neutrino being a Goldstone fermion of a spontaneously broken global $U(1)$ symmetry in a supersymmetric theory is considered. This fermion obtains mass from the supergravity effects leading to a RH neutrino at the electroweak scale with a mass similar to the gravitino mass. A prototype model realizing this scenario contains just three gauge singlet superfields needed for the type I seesaw mechanism. Masses of the other two neutrinos are determined by the $U(1)$ breaking scale which too can be around the electroweak scale. Light neutrinos obtain their masses in this scenario through (a) mixing with the RH neutrinos (type I seesaw), (b) mixing with neutralinos ($R$-parity breaking), (c) indirectly through mixing of the RH neutrinos with neutralinos, and (d) radiative corrections. All these contributions are described by the same set of a small number of underlying parameters and provide a very constrained and predictive framework for the neutrino masses which is investigated in detail for various choices of $U(1)$ symmetries. It is found that flavour independent $U(1)$ symmetries cannot describe neutrino masses if the soft supersymmetry breaking terms are flavour universal and one needs to consider flavour dependent symmetries. Considering a particular example of $L_μ- L_τ$ symmetry, it is shown that viable neutrino masses and mixing can be obtained without introducing any flavour violation in the soft sector. The leptonic couplings of Majoron are worked out in the model and shown to be consistent with various laboratory, astrophysical and cosmological constraints. The neutrino data allows sizeable couplings between the RH neutrinos and Higgsinos which can be used to probe the pseudo-Goldstone fermion at colliders through its displaced decay vertex.

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arXiv2021

Inflation and long-range force from clockwork $D$-term

Cosmic inflation driven by the vacuum energy associated with the $D$-term of a supersymmetric abelian gauge group and a possible existence of long-range force mediated by an ultra-light gauge boson $Z^\prime$ are two extreme examples of models based on extra $U(1)$ symmetries. Large vacuum energy sets the scale of inflation while the scales of long-range forces induced by anomaly free extra gauged $U(1)$ symmetries are constrained by neutrino oscillations, binary pulsar timings and invisible neutrino decay. There exists a difference of about 40 orders of magnitude between the scales of these two. Also, gauge couplings associated with the long-range forces are very small compared to the standard model couplings and the one required for inflation. We propose a framework based on clockwork mechanism in which these vastly different scales and associated new physics can coexist without invoking any arbitrarily small or large parameter in the fundamental theory. A chain of $U(1)$ is introduced with characteristic nearest-neighbour interactions. A large $D$-term introduced at one end governs the dynamics of inflation. $Z^\prime$ is localized on the other end of the chain, and it can be massless or can get naturally suppressed mass. The standard model fields can be charged under one of the intermediate $U(1)$ in the chain to give rise to their small effective coupling $g^\prime$ with $Z^\prime$. Constraints on $g^\prime$ and $M_{Z^\prime}$ are discussed in the context of the long-range forces of type $L_μ- L_τ$, $L_e - L_μ$ and $B-L$. These, along with the inflation observables, are used to constraint the parameters of the underlying clockwork model.

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arXiv2020

Generalised $μ$-$τ$ symmetries and calculable gauge kinetic and mass mixing in $U(1)_{L_μ-L_τ}$ models

Extensions of the standard model with a $U(1)$ gauge symmetry contain gauge invariant kinetic mixing, $\sinχ$, and gauge non-invariant mass mixing, $δM^2$, between the hypercharge and the new gauge boson $Z'$. These represent a priori incalculable but phenomenologically important parameters of the theory. They become calculable if there exist spontaneously or softly broken symmetries which forbid them at tree level but allow their generation at the loop level. We discuss various symmetries falling in this category in the context of the gauged $L_μ-L_τ$ models and their interplay with lepton mixing. It is shown that one gets phenomenologically inconsistent lepton mixing parameters if these symmetries are exact. Spontaneous breaking of these symmetries can lead to consistent lepton mixing and also generates finite and calculable values of these parameters at one or two loop order depending on the underlying symmetry. We calculate these parameters in two specific cases: (i) the standard seesaw model with $μ$-$τ$ symmetry broken by the masses of the right-handed neutrinos and (ii) in a model containing a pair of vectorlike charged leptons which break $μ$-$τ$ symmetry. In case (i), the right-handed neutrinos are the only source of gauge mixing. The kinetic mixing parameters are suppressed and vanish if the right-handed neutrinos decouple from the theory. In contrast, there exists a finite gauge mixing in case (ii) which survives even when the masses of vectorlike leptons are taken to infinity, exhibiting non-decoupling behaviour. The seesaw model discussed here represents a complete framework with practically no kinetic mixing and hence can survive a large number of experimental probes used to rule out specific ranges in the coupling $g^\prime$ and mass $M_{Z^\prime}$. The model can generate non-universality in tau decays, which can be tested in future experiments.

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arXiv2019

Exploring Partial $μ$-$τ$ Reflection Symmetry at DUNE and Hyper-Kamiokande

We study origin, consequences and testability of a hypothesis of `partial $μ$-$τ$' reflection symmetry. This symmetry predicts $ |U_{μi}|=|U_{τi}|~(i=1,2,3) $ for a single column of the leptonic mixing matrix $U$. Depending on whether this symmetry holds for the first or second column of $U$ different correlations between $θ_{23}$ and $ δ_{CP} $ can be obtained. This symmetry can be obtained using discrete flavour symmetries. In particular, all the subgroups of SU(3) with 3-dimensional irreducible representation which are classified as class C or D can lead to partial $μ$-$τ$ reflection symmetry. We show how the predictions of this symmetry compare with the allowed area in the $\sin^2θ_{23} - δ_{CP}$ plane as obtained from the global analysis of neutrino oscillation data. Furthermore, we study the possibility of testing these symmetries at the proposed DUNE and Hyper-Kamiokande (HK) experiments (T2HK, T2HKK), by incorporating the correlations between $θ_{23}$ and $ δ_{CP}$ predicted by the symmetries. We find that when simulated data of DUNE and HK is fitted with the symmetry predictions, the $θ_{23}-δ_{CP}$ parameter space gets largely restricted near the CP conserving values of $ δ_{CP} $. Finally, we illustrate the capability of these experiments to distinguish between the two cases leading to partial $μ-τ$ symmetry namely $|U_{\mu1}| = |U_{τ1}|$ and $|U_{μ2}| = |U_{τ2}|$.

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arXiv2018

Pseudo-Dirac neutrinos from flavour dependent CP symmetry

Discrete residual symmetries and flavour dependent CP symmetries consistent with them have been used to constrain neutrino mixing angles and CP violating phases. We discuss here role of such CP symmetries in obtaining a pseudo-Dirac neutrino which can provide a pair of neutrinos responsible for the solar splitting. It is shown that if (a) $3\times 3$ Majorana neutrino matrix $M_ν$ is invariant under a discrete $Z_2\times Z_2$ symmetry generated by $S_{1,2}$, (b) CP symmetry $X$ transform $M_ν$ as $X^T M_νX=M_ν^*$, and (c) $X$ and $S_{1,2}$ obey consistency conditions $X S_{1,2}^* X^\dagger=S_{2,1}$, then two of the neutrino masses are degenerate independent of specific forms of $X$, $S_1$ and $S_2$. Explicit examples of this result are discussed in the context of $Δ(6 n^2)$ groups which can also be used to constrain neutrino mixing matrix $U$. Degeneracy in two of the masses does not allow complete determination of $U$ but it can also be fixed once the perturbations are introduced. We consider explicit perturbations which break $Z_2\times Z_2$ symmetries but respect CP. These are shown to remove the degeneracy and provide a predictive description of neutrino spectrum. In particular, a correlation $\sin 2θ_{23}\sinδ_{CP}=\pm {\rm Im}[p]$ is obtained between the atmospheric mixing angle $θ_{23}$ and the CP violating phase $δ_{CP}$ in terms of a group theoretically determined phase factor $p$. Experimentally interesting case $θ_{23}=\fracπ{4}$, $δ_{CP}=\pm \fracπ{2}$ emerges for groups which predict purely imaginary $p$. We present detailed predictions of the allowed ranges of neutrino mixing angles, phases and the lightest neutrino mass for three of the lowest $Δ(6 n^2)$ groups with $n=2,4,6$.

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arXiv2018

Perturbed flavour symmetries and predictions of CP violating phase $δ$

It is known that the imposition of a class of residual $Z_2\times Z_2$ symmetries on the neutrino mass matrix $M_ν$ and a residual symmetry $Z_n$ ($n\geq 3$) on the Hermitian combination $M_lM_l^\dagger$ of the charged lepton mass matrix leads to a universal prediction of vanishing Dirac CP phase $δ$ if these symmetries are embedded in $Δ(6 n^2)$ groups and if the leptonic doublets transform as a 3 dimensional irreducible representation of the group. The Majorana phases remain arbitrary but they can also be determined in $Δ(6 n^2)$ by imposing generalized CP symmetry (GenCP) consistent with the $Δ(6 n^2)$ group. We investigate the effects of adding general perturbations on these predictions assuming that perturbations break the $Z_2\times Z_2$ symmetry completely but preserve GenCP. It is found that if the residual symmetries predict the tri-bimaximal mixing (TBM) among leptons and specific CP conserving values for the Majorana phases then addition of the above perturbations always lead to a neutrino mass matrix invariant under the $μ$-$τ$ reflection symmetry in the flavour basis with the result that perturbations turn the vanishing $δ$ into maximal value $\pm \fracπ{2}.$ One gets non-vanishing but generally large $δ$ if the predicted zeroeth order mixing deviates from TBM and/or the predicted Majorana phases are non-trivial. We systematically investigate effects of perturbations in such situations and work out the predicted $δ$ for four of the lowest $Δ(6 n^2)$ groups with $n=2,4,6,8.$

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arXiv2017

Residual $Z_2$ symmetries and leptonic mixing patterns from finite discrete subgroups of $U(3)$

We study embedding of non-commuting $Z_2$ and $Z_m$, $m\geq 3$ symmetries in discrete subgroups (DSG) of $U(3)$ and analytically work out the mixing patterns implied by the assumption that $Z_2$ and $Z_m$ describe the residual symmetries of the neutrino and the charged lepton mass matrices respectively. Both $Z_2$ and $Z_m$ are assumed to be subgroups of a larger discrete symmetry group $G_f$ possessing three dimensional faithful irreducible representation. The residual symmetries predict the magnitude of a column of the leptonic mixing matrix $U_{\rm PMNS}$ which are studied here assuming $G_f$ as the DSG of $SU(3)$ designated as type C and D and large number of DSG of $U(3)$ which are not in $SU(3)$. These include the known group series $Σ(3n^3)$, $T_n(m)$, $Δ(3n^2,m)$, $Δ(6n^2,m)$ and $Δ'(6n^2,j,k)$. It is shown that the predictions for a column of $|U_{\rm PMNS}|$ in these group series and the C and D types of groups are all contained in the predictions of the $Δ(6N^2)$ groups for some integer $N$. The $Δ(6N^2)$ groups therefore represent a sufficient set of $G_f$ to obtain predictions of the residual symmetries $Z_2$ and $Z_m$.

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arXiv2015

Generalized $μ$-$τ$ symmetry and discrete subgroups of O(3)

The generalized $μ$-$τ$ interchange symmetry in the leptonic mixing matrix $U$ corresponds to the relations: $|U_{μi}|=|U_{τi}|$ with $i=1,2,3$. It predicts maximal atmospheric mixing and maximal Dirac CP violation given $θ_{13} \neq 0$. We show that the generalized $μ$-$τ$ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of $O(3)$. The groups $A_4$, $S_4$ and $A_5$ are the only such groups which can entirely fix $U$ at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large $θ_{13}$ in case of (a) while only $A_5$ can provide $θ_{13}$ close to its experimental value in the case (b). We provide an explicit model based on $A_5$ and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized $μ$-$τ$ symmetry in $U$. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, $θ_{23}=π/4$ and $δ_{\rm CP} = \pm π/2$.

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arXiv2015

Neutrino masses and mixing from flavour antisymmetry

We discuss consequences of assuming ($i$) that the (Majorana) neutrino mass matrix $M_ν$ displays flavour antisymmetry, $S_ν^T M_νS_ν=-M_ν$ with respect to some discrete symmetry $S_ν$ contained in $SU(3)$ and ($ii$) $S_ν$ together with a symmetry $T_l$ of the Hermitian combination $M_lM_l^\dagger$ of the charged lepton mass matrix forms a finite discrete subgroup $G_f$ of $SU(3)$ whose breaking generates these symmetries. Assumption ($i$) leads to at least one massless neutrino and allows only four textures for the neutrino mass matrix in a basis with a diagonal $S_ν$ if it is assumed that the other two neutrinos are massive. Two of these textures contain a degenerate pair of neutrinos.Assumption ($ii$) can be used to determine the neutrino mixing patterns. We work out these patterns for two major group series $Δ(3 N^2)$ and $Δ(6 N^2)$ as $G_f$. It is found that all $Δ(6 N^2)$ and $Δ(3 N^2)$ groups with even $N$ contain some elements which can provide appropriate $S_ν$. Mixing patterns can be determined analytically for these groups and it is found that only one of the four allowed neutrino mass textures is consistent with the observed values of the mixing angles $θ_{13}$ and $θ_{23}$. This texture corresponds to one massless and a degenerate pair of neutrinos which can provide the solar pair in the presence of some perturbations. The well-known groups $A_4$ and $S_4$ provide examples of the groups in respective series allowing correct $θ_{13}$ and $θ_{23}$. An explicit example based on $A_4$ and displaying a massless and two quasi degenerate neutrinos is discussed.

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arXiv2014

Discrete flavour symmetries for degenerate solar neutrino pair and their predictions

Flavour symmetries appropriate for describing a neutrino spectrum with degenerate solar pair and a third massive or massless neutrino are discussed. We demand that the required residual symmetries of the leptonic mass matrices be subgroups of some discrete symmetry group $G_f$. $G_f$ can be a subgroup of SU(3) if the third neutrino is massive and we derive general results on the mixing angle predictions for various discrete subgroups of SU(3). The main results are: (a) All the SU(3) subgroups of type C fail in simultaneously giving correct $θ_{13}$ and $θ_{23}$. (b) All the groups of type D can predict a relation $\cos^2θ_{13} \sin^2θ_{23}=\frac{1}{3}$ among the mixing angles which appears to be a good zeroth order approximation. Among these, various $Δ(6n^2)$ groups with $n\geq 8$ can simultaneously lead also to $\sin^2 θ_{13}$ in agreement with global fit at 3$σ$. (c) The group $Σ(168)\cong PSL(2,7)$ predicts near to the best fit value for $θ_{13}$ and $θ_{23}$ within the 1$σ$ range. All discrete subgroups of U(3) with order $<512$ and having three dimensional irreducible representation are considered as possible $G_f$ when the third neutrino is massless. Only seven of them are shown to be viable and three of these can correctly predict $θ_{13}$ and/or $θ_{23}$. The solar angle remains undetermined at the leading order in all the cases due to degeneracy in the masses. A class of general perturbations which can correctly reproduce all the observables are discussed in the context of several groups which offer good leading order predictions.

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arXiv2014

A massless neutrino and lepton mixing patterns from finite discrete subgroups of U(3)

Finite discrete subgroups of $U(3)$ as possible flavour symmetries $G_f$ for a massless neutrinos with predictive mixing angles are studied. This is done by assuming that a residual symmetry $S_ν$ appropriate for describing a massless neutrino is contained in $G_f$. It is shown that all the groups $G_f$ admitting three dimensional faithful irreducible representation and generated from a specific set of $3\times 3$ matrices imply only one of the three flavour compositions for the massless state namely, unmixed, maximally mixed with equal probabilities and bimaximally mixed with probabilities (0,1/2,1/2) and their permutations. This result holds irrespective of the order of $G_f$ and the choice of $S_ν$ within it. All of these lead to unfavourable leading order prediction for the solar mixing angle. Neutrino mixing pattern is then numerically investigated in case of subgroups of $U(3)$ with order less than 512 and it is found that only one of these can lead to a massless neutrino and leading order predictions for all the mixing angles close to their experimental values. Ways to correct for the solar angle prediction are proposed and two concrete examples giving the observed mixing pattern are discussed.

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arXiv2013

Horizontal symmetries of leptons with a massless neutrino

Residual symmetry $G_ν$ of neutrino mass matrix with a massless neutrino and embedding of $G_ν$ and the residual symmetry $G_l$ of the charged lepton mass matrix into finite discrete groups $G$ is discussed. Massless neutrino results if $G_ν$ and hence $G$ are subgroups of $U(3)$ rather than of $SU(3)$. Structure of the resulting leptonic mixing matrix $U_{PMNS}$ is discussed in three specific examples based on groups (a) $Σ(3N^3)$, (b) $Σ(2N^2)$ and (c) $S_4(2) \equiv A_4\rtimes Z_4$. $Σ(3N^3)$ groups are able to reproduce either the second or the third column of $U_{PMNS}$ correctly. $Σ(2N^2)$ groups lead to prediction $θ_{13}=0$, $θ_{23}=\fracπ{4}$ for the reactor and atmospheric mixing angles respectively if neutrino mass hierarchy is inverted. Solar angle remains undetermined in this case. This also gets determined when $G=S_4(2)$ which can give bi-maximal mixing for inverted hierarchy. Examples (b) and (c) provide a good zeroth order approximation to realistic leptonic mixing with a massless neutrino. We also present an example of the specific model based on $S_4(2)$ symmetry in which a massless neutrino and viable leptonic mixing angles are obtained.

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arXiv2013

How good is μ-τsymmetry after results on non-zero θ_{13}?

Viability of the μ-τinterchange symmetry imposed as an approximate symmetry (1) on the neutrino mass matrix {\cal M}_{νf} in the flavour basis (2) simultaneously on the charged lepton mass matrix M_l and the neutrino mass matrix M_νand (3) on the underlying Lagrangian is discussed in the light of recent observation of a non-zero reactor mixing angle θ_{13}. In case (1), μ-τsymmetry breaking may be regarded as small (less than 20-30%) only for the inverted or quasidegenerate neutrino mass spectrum and the normal hierarchy would violate it by a large amount. The case (2) is more restrictive and the requirement of relatively small breaking allows only the quasidegenerate spectrum. If neutrinos obtain their masses from the type-I seesaw mechanism then small breaking of the μ-τsymmetry in the underlying Lagrangian may result in a large breaking in {\cal M}_{νf} and even the hierarchical neutrino spectrum may also be consistent with mildly broken μ-τsymmetry of the Lagrangian. Neutrinoless double beta decay provides a good means of distinguishing above scenarios. In particular, non-observation of signal in future experiments such as GERDA would rule out scenarios (1) and (2).

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arXiv2013

Pseudo-Dirac neutrinos via mirror-world and depletion of UHE neutrinos

We propose a possible particle physics explanation of the non-observation of muon neutrino events at IceCube coincident with GRB gamma ray at the rates predicted by the standard Bahcall-Waxman model, in terms of neutrino oscillations. Our model is based on assuming that (a) all neutrinos are pseudo-Dirac particles and (b) there exists a mirror world interacting gravitationally with the observed world. This scenario has three sterile neutrinos associated with each flavour of ordinary neutrinos. Very tiny mass splitting between these neutrinos is assumed to arise from lepton number violating dimension five operators suppressed by the Planck scale. We show that if a mass splitting of 10^(-15) eV^2 is induced between the four mass eigenstates of a given species, then its flux will be suppressed at IceCube energies by a factor of 4 which could be the explanation of the IceCube observation that the muon neutrino flux is lower than expected. Hierarchies in mass splitting among different flavours may result in different amount of suppression of each flavour and based on this, we predict a difference in the flavour ratios of the observed neutrinos which is significantly different compared to the standard prediction of nu_e:nu_mu:nu_tau=1:1:1 which could serve as a test for this model.

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arXiv2012

Yukawa coupling unification in SO(10) with positive μ and a heavier gluino

The t-b-tau unification with positive Higgs mass parameter μ in the minimal supersymmetric standard model prefers "just so" Higgs splitting and a light gluino < 500 GeV which appears to be ruled out by the recent LHC searches. We reanalyze constraints on soft supersymmetry breaking parameters in this scenario allowing independent splittings among squarks and Higgs doublets at the grand unification scale and show that it is possible to obtain t-b-tau unification and satisfy experimental constraints on gluino mass without raising supersymmetry breaking scale to very high value ~ 20 TeV. We discuss the origin of independent squark and Higgs splittings in realistic SO(10) models. Just so Higgs splitting can be induced without significantly affecting the t-b-tau unification in SO(10) models containing Higgs fields transforming as 10+\bar{126}+126+210. This splitting arises in the presence of non-universal boundary conditions from mixing between 10 and other Higgs fields. Similarly, if additional matter fields are introduced then their mixing with the matter multiplet 16 is shown to generate the squark splitting required to raise the gluino mass within the t-b-tau unified models with positive μ.

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arXiv2012

Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries

We discuss consequences of combining the effective $Z_2\times Z_2$ symmetry of the tri-bimaximal neutrino mass matrix with the CP symmetry. Imposition of such generalized $Z_2\times Z_2$ symmetries leads to predictive neutrino mass matrices determined in terms of only four parameters and leads to non-zero $θ_{13}$ and maximal atmospheric mixing angle and CP violating phase. It is shown that an effective generalized $Z_2\times Z_2$ symmetry of the mass matrix can arise from the $A_4$ symmetry with specific vacuum alignment. The neutrino mass matrix in the considered model has only three real parameters and leads to determination of the absolute neutrino mass scale as a function of the reactor angle $θ_{13}$.

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