arXiv subjects

Ketan M. Patel

Publications and source records attributed to Ketan M. Patel.

At least 19 recordsLinked to original sources

arXiv2026

Testing predictions of discrete flavour and modular symmetries at DUNE and Hyper-K with JUNO constraints

We study fixed-column predictions of the lepton mixing matrix that arise from residual symmetries originating in a class of discrete flavour and modular symmetries. While the recent high-precision determination of $\sin^{2}θ_{12}$ by JUNO already constrains part of these predictions, the remaining viable scenarios are primarily characterized by non-trivial correlations between $\sin^{2}θ_{23}$ and the Dirac CP phase $δ_{\rm CP}$, which are currently only weakly constrained. This motivates a detailed investigation of the sensitivities of next-generation long-baseline neutrino experiments to these scenarios. For the phenomenologically viable fixed-column predictions that can constitute a column of the lepton mixing matrix, we derive precise $\sin^{2}θ_{23}$--$δ_{\rm CP}$ correlations and use them to generate test-event samples, marginalising over the remaining oscillation parameters. We perform detailed simulations for DUNE and Hyper-K, presenting the allowed regions in the $\sin^{2}θ_{23}$--$δ_{\rm CP}$ plane. We also evaluate, as a function of experimental exposure (determined by the run time), the fraction of $δ_{\rm CP}$ values for which these theoretical predictions can be ruled out at more than $3σ$ CL. Our results show that the combined sensitivity of DUNE and Hyper-K provides a robust test of fixed-column lepton-mixing predictions.

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arXiv2026

Graph-theoretic determination of massless modes in latticized theory-space models

A graph-theoretic method is introduced for analyzing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as vertices and nonvanishing mass terms as edges. The number of massless modes is shown to be fixed by the cardinality of a maximum matching of the associated graph. Moreover, the wave-function support of these modes is restricted to fields reachable from exposed or unmatched vertices by even-length maximum-matching-alternating paths, as characterized by the Dulmage-Mendelsohn decomposition. These results depend only on the topology of latticized theory space and are independent of model parameters. The method enables a systematic construction of latticized models with prescribed numbers and localization properties of massless modes.

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arXiv2026

Flavour hierarchies from radiative corrections in latticed theory space

It has recently been shown that when $N_f$ generations of chiral fermions are coupled in a specific manner to $N$ (with $N \geq 2N_f-1$) pairs of vectorlike fermions whose mass terms form a one-dimensional lattice-like structure in theory space, locality along the lattice ensures that only a single fermion generation acquires a mass at tree level. Radiative corrections can induce controlled departures from locality in the latticed space, thereby generating suppressed but non-vanishing masses for the remaining $N_f-1$ generations. In this work, we present an explicit implementation of this mechanism to address the flavour hierarchies of the Standard Model. After delineating the minimal extensions of the gauge, scalar, and Yukawa sectors required for feasible implementation of the mechanism, we demonstrate that the framework successfully reproduces the observed charged-fermion mass spectrum and quark mixing pattern. We analyse the new-physics effects arising from the extended sectors and confront them with existing constraints from direct, indirect searches and precision measurements. It is shown that a viable realisation of the mechanism allows the spectrum of vectorlike fermions and additional gauge boson to lie at scales as low as $\mathcal{O}(5)\,\mathrm{TeV}$ with the lightest states typically corresponding to top partners. This stands in sharp contrast to conventional radiative mass-generation scenarios, in which phenomenological constraints typically impose a lower bound on the new-physics scale of order a few hundred to several thousand TeV.

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arXiv2025

Partially flavour non-universal $U(1)$ and radiative fermion masses

We investigate an extension of the Standard Model with a partially flavour non-universal abelian gauge symmetry that enables radiative mass generation for lighter fermions. With flavour-universal charges for the first two generations, gauge-induced loop corrections generate second-generation masses while keeping the first generation massless. Small first-generation masses can arise from subdominant scalar loops within this framework. A single anomaly-free $U(1)$ is sufficient for a realistic model, and the partial universality relaxes the gauge boson mass bound from several thousand TeV to about 200 TeV compared with previous frameworks of this type. We also identify an alignment limit matching the lightest scalar to the observed Higgs and compute its couplings with the fermions, which largely agree with Standard Model values but show testable deviations.

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arXiv2025

Electroweak Triplet Scalar Contribution to $SO(10)$ Leptogenesis

We show that electroweak triplet scalar can significantly impact baryogenesis via leptogenesis in concrete and predictive $SO(10)$ GUTs, even when light neutrino masses arise predominantly from the type-I seesaw mechanism. This is illustrated within a minimal renormalisable $SO(10)$ model with $\mathbf{10}$ and $\overline{\mathbf{126}}$ scalars in the Yukawa sector and a global Peccei-Quinn-like symmetry. The quark-lepton unification and the flavour structure of the fundamental Yukawa couplings enforce type-I dominance in the light neutrino masses, also suppressing the triplet-induced CP asymmetries in the right-handed neutrino decays. However, the triplet's own decays introduce a new CP-violating source, which can enhance or suppress the total baryon asymmetry. For triplet mass near the right-handed neutrino mass scale, this contribution can dominate, making it essential in assessing the viability of $SO(10)$ leptogenesis scenarios.

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arXiv2025

Hierarchies from deterministic non-locality in theory space Anderson localisation

The nearest-neighbour or local mass terms in theory space among quantum fields, with their generic disordered values, are known to lead to the localisation of mass eigenstates, analogous to Anderson localisation in a one-dimensional lattice. This mechanism can be used to create an exponential hierarchy in the coupling between two fields by placing them at opposite ends of the lattice chain. Extending this mechanism, we show that when copies of such fields are appropriately attached to the lattice chain, it leads to the emergence of multiple massless modes. These vanishing masses are a direct consequence of the locality of interactions in theory space. The latter may break down in an ordered and deterministic manner through quantum effects if additional interactions exist among the chain fields. Such non-locality can induce small masses for the otherwise massless modes without necessarily delocalising the mass eigenstates. We provide examples of interactions that preserve or even enhance localisation. Applications to flavour hierarchies, neutrino mass, and the $μ$-problem in supersymmetric theories are discussed.

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arXiv2025

Loop-induced masses for the first two generations with optimum flavour violation

A mechanism for the masses of third, second, and first generation charged fermions at the tree, 1-loop, and 2-loop levels, respectively, is proposed. The fermionic self-energy corrections that lead to this arrangement are induced through heavy vector bosons of a new gauged flavour symmetry group $G_F$. It is shown that a single Abelian group suffices as $G_F$. Moreover, the gauge charges are optimized to result in relatively smaller flavour violations in processes involving the first and second generation fermions. The scheme is explicitly implemented on the Standard Model fermions in an anomaly-free manner and is shown to be viable with observed charged fermion masses and quark mixings. Constraints from flavour violations dictate the lower limit on the new physics scale in these types of frameworks. Through optimal flavour violation, it is shown that nearly two orders of magnitude improvement can be achieved on the lower limit, leading to the new physics scale $\ge 10^3$ TeV in this case. Further improvements are possible at the cost of the down quark mass deviating more than $3 σ$ from its value extracted from lattice calculations. Options for inducing tiny masses for light neutrinos are also discussed.

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arXiv2024

Residual flavour (anti)symmetries at the modular self-dual point and constraints on neutrino masses and mixing

We explore the implications of symmetries that remain unbroken at the self-dual point $τ=i$ in modular invariant theories. Assuming that (a) the three generations of lepton doublets transform as an irreducible representation of a finite modular group $Γ_N$, and (b) the light neutrino masses arise from the Weinberg operator and are in modular form, we demonstrate that this setup yields a unique residual flavor symmetry or antisymmetry for the neutrinos, depending on the modular weight. In the antisymmetric case, one neutrino is always massless, and the other two can be degenerate if the mass matrix is real. These findings are independent of the level $N$. If the charged leptons are arranged to exhibit an appropriate residual symmetry from the same $Γ_N$, they determine a column of the leptonic mixing matrix, leading to specific correlations between the mixing angles and the Dirac CP phase. The presence of residual (anti)symmetries enables the application of standard flavor symmetry techniques to derive these predictions, and we scan all possible $Γ_N$ satisfying condition (a). Most solutions yield ${\cal O}(1)$ entries in the fixed column, favouring relatively large lepton mixing.

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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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arXiv2024

Quantum corrections and the minimal Yukawa sector of $SU(5)$

It is well-known that the $SU(5)$ grand unified theory, with the standard model quarks and leptons unified in $\overline{5}$ and $10$ and the electroweak Higgs doublet residing in $5$ dimensional representations, leads to relation, $Y_d=Y_e^T$, between the Yukawa couplings of the down-type quarks and the charged leptons. We show that this degeneracy can be lifted in a phenomenologically viable way when quantum corrections to the tree-level matching conditions are taken into account in the presence of one or more copies of gauge singlet fermions. The 1-loop threshold corrections arising from heavy leptoquark scalar and vector bosons, already present in the minimal model, and heavy singlet fermions can lead to realistic Yukawa couplings provided their masses differ by at least two orders of magnitude. The latter can also lead to a realistic light neutrino mass spectrum through the type I seesaw mechanism if the colour partner of the Higgs stays close to the Planck scale. Most importantly, our findings demonstrate the viability of the simplest Yukawa sector when quantum corrections are considered and sizeable threshold effects are present.

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arXiv2023

Gauged $SU(3)_F$ and loop induced quark and lepton masses

We investigate a local $SU(3)_F$ flavour symmetry for its viability in generating the masses for the quarks and charged leptons of the first two families through radiative corrections. Only the third-generation fermions get tree-level masses due to specific choice of the field content and their gauge charges. Unprotected by symmetry, the remaining fermions acquire non-vanishing masses through the quantum corrections induced by the gauge bosons of broken $SU(3)_F$. We show that inter-generational hierarchy between the masses of the first two families arises if the flavour symmetry is broken with an intermediate $SU(2)$ leading to a specific ordering in the masses of the gauge bosons. Based on this scheme, we construct an explicit and predictive model and show its viability in reproducing the realistic charged fermion masses and quark mixing parameters in terms of not-so-hierarchical fundamental couplings. The model leads to the strange quark mass, $m_s \approx 16$ MeV at $M_Z$, which is $\sim 2.4 σ$ away from its current central value. Large flavour violations are a generic prediction of the scheme which pushes the masses of the new gauge bosons to $10^3$ TeV or higher.

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arXiv2023

Minimal spontaneous CP-violating GUT and predictions for leptonic CP phases

A non-supersymmetric renormalizable $SO(10)$ model, with CP invariant Yukawa sector consisting of Lorentz scalars in $10$ and $\overline{126}$ dimensional representations, is proposed. The elemental Yukawa couplings are real due to CP symmetry. The latter is broken in the low energy effective theory through the standard model Higgs which is a complex linear combination of electroweak doublets residing in $10$ and $\overline{126}$ scalars. As a result, the mass matrices in the quark and lepton sectors, including those of heavy and light neutrinos, depend only on three phases which in turn determine CP violation in both sectors. The model is comprehensively analysed for its viability and predictions including the possibility to generate baryon asymmetry through thermal leptogenesis. It predicts relatively small values for CP phases in the lepton sector. Successful leptogenesis further restricts the ranges to $-0.4 \le \sinδ\le 0.4$ for the Dirac phase and $-0.3 \le \sin η_1 \le 0.2$, $-0.5 \le \sin η_2 \le 0.5$ for the Majorana phases.

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arXiv2023

Spectrum of colour sextet scalars in realistic SO(10) GUT

Incorporation of the standard model Yukawa interactions in a grand unified theory (GUT) often predicts varieties of new scalars that couple to the fermions and lead to some novel observational effects. We assess such a possibility for the colour sextet diquark scalars within the realistic renormalizable models based on $SO(10)$ GUT. The spectrum consists of five sextets: $Σ\sim (6,1,-\frac{2}{3})$, $S \sim (6,1,\frac{1}{3})$, $\overline{S}\sim(\overline{6},1,-\frac{1}{3})$, ${\cal S}\sim(6,1,\frac{4}{3})$ and $\mathbb{S}\sim(\overline{6},3,-\frac{1}{3})$. Computing explicitly their couplings with the quarks, we evaluate their contributions to the neutral meson-antimeson mixing and baryon number-violating processes like neutron-antineutron oscillation. The latter arises because of a $B-L$ violating trilinear coupling between the sextets which also contributes to some of the quartic couplings and perturbativity of the same leads to strong limits on the sextet masses. Using the values of the $B-L$ breaking scale and Yukawa couplings permitted in the realistic models, we derive constraints on the masses of these scalars. It is found that $Σ$ along with any of the remaining sextets cannot be lighter than the $B-L$ breaking scale, simultaneously. In the realm of realistic models, this implies no observable $n$-$\bar{n}$ oscillation in near future experiments. We also point out a possibility in which sub-GUT scale $Σ$ and a pair of $S$, allowed by the other constraints, can viably produce the observed baryon asymmetry of the universe.

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arXiv2022

Radiatively generated fermion mass hierarchy from flavour non-universal gauge symmetries

A framework based on a class of abelian gauge symmetries is proposed in which the masses of only the third generation quarks and leptons arise at the tree level. The fermions of the first and second families receive their masses through radiative corrections induced by the new gauge bosons in the loops. It is shown that the class of abelian symmetries which can viably implement this mechanism are flavour non-universal in nature. Taking the all-fermion generalization of the well-known leptonic $L_μ-L_τ$ and $L_e - L_μ$ symmetries, we construct an explicit renormalizable model based on two $U(1)$ which is shown to reproduce the observed fermion mass spectrum of the Standard Model. The first and second generation fermion masses are loop suppressed while the hierarchy between these two generations results from a gap between the masses of two vector bosons of the extended gauge symmetries. Several phenomenological aspects of the flavourful new physics are discussed and lower limits on the masses of the vector bosons are derived.

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arXiv2022

Anatomy of scalar mediated proton decays in $SO(10)$ models

Realistic models based on the renormalizable grand unified theories have varieties of scalars, many of which are capable of mediating baryon ($B$) and lepton ($L$) number non-conserving processes. We identify all such scalar fields residing in ${\bf 10}$, $\overline{\bf 126}$ and ${\bf 120}$ dimensional irreps of $SO(10)$ which can induce baryon and lepton number violating interactions through the leading order $d=6$ and $d=7$ operators. Explicitly computing their couplings with the standard model fermions, we derive the effective operators including the possibility of mixing between the scalars stemming from a given representation. We find that such interactions at $d=6$ are mediated by only three sets of scalars: $T(3,1,-1/3)$, ${\cal T} (3,1,-4/3)$ and $\mathbb{T}(3,3,-1/3)$ and their conjugates. In the models with ${\bf 10}$ and $\overline{\bf 126}$, only the first has appropriate couplings to mediate the proton decay. While ${\cal T}$ and $\mathbb{T}$ can induce baryon number violating interactions when ${\bf 120}$ is present, ${\cal T}$ does not contribute to the proton decay at tree level because of its flavour antisymmetric coupling. Three additional colour triplets and their conjugates can mediate nucleon decay via $d=7$ operators which violate also the $B-L$. We give general expressions for partial widths of proton in terms of the fundamental Yukawa couplings and use these results to explicitly compute the proton lifetime and branching ratios for the minimal non-supersymmetric $SO(10)$ model based on ${\bf 10}$ and $\overline{\bf 126}$ Higgs. We find that the proton preferably decays into $\overlineν\, K^+$ or $μ^+\, K^0$ and list several distinct features of scalar mediated proton decay. If the latter dominates over the gauge mediated contributions, the proton decay spectrum provides a direct probe to the flavour structure of the underlying grand unified theory.

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arXiv2021

Leptogenesis and fermion mass fit in a renormalizable $SO(10)$ model

A non-supersymmetric renormalizable $SO(10)$ model is investigated for its viability in explaining the observed fermion masses and mixing parameters along with the baryon asymmetry produced via thermal leptogenesis. The Yukawa sector of the model consists of complex $10_H$ and $\overline{126}_H$ scalars with a Peccei-Quinn like symmetry and it leads to strong correlations among the Yukawa couplings of all the standard model fermions including the couplings and masses of the right-handed (RH) neutrinos. The latter implies the necessity to include the second lightest RH neutrino and flavor effects for the precision computation of leptogenesis. We use the most general density matrix equations to calculate the temperature evolution of flavoured leptonic asymmetry. A simplified analytical solution of these equations, applicable to the RH neutrino spectrum predicted in the model, is also obtained which allows one to fit the observed baryon to photon ratio along with the other fermion mass observables in a numerically efficient way. The analytical and numerical solutions are found to be in agreement within a factor of ${\cal O}(1)$. We find that the successful leptogenesis in this model does not prefer any particular value for leptonic Dirac and Majorana CP phases and the entire range of values of these observables is found to be consistent. The model specifically predicts (a) the lightest neutrino mass $m_{ν_1}$ between 2-8 meV, (b) the effective mass of neutrinoless double beta decay $m_{ββ}$ between 4-10 meV, and (c) a particular correlation between the Dirac and one of the Majorana CP phases.

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arXiv2021

Aspects of gravitational decoherence in neutrino lensing

We study decoherence effects in neutrino flavour oscillations in curved spacetime with particular emphasis on the lensing in a Schwarzschild geometry. Assuming Gaussian wave packets for neutrinos, we argue that the decoherence length derived from the exponential suppression of the flavour transition amplitude depends on the proper time of the geodesic connecting the events of the production and detection in general gravitational setting. In the weak gravity limit, the proper time between two events of given proper distance is smaller than that in the flat spacetime. Therefore, in presence of a Schwarzschild object, the neutrino wave packets have to travel relatively more physical distance in space to lapse the same amount of proper time before they decoher. For non-radial propagation applicable to the lensing phenomena, we show that the decoherence, in general, is sensitive to the absolute values of neutrino masses as well as the classical trajectories taken by neutrinos between the source and detector along with the spatial widths of neutrino wave packets. At distances beyond the decoherence length, the probability of neutrino flavour transition due to lensing attains a value which depends only on the leptonic mixing parameters. Hence, the observability of neutrino lensing significantly depends on these parameters and in-turn the lensing can provide useful information about them.

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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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