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S. T. Petcov

Publications and source records attributed to S. T. Petcov.

At least 19 recordsLinked to original sources
arXiv2026

Dirac-Phase CP-Violation in the Low-Scale Type-I Seesaw with Three Right-Handed Neutrinos

We study the low-scale type-I seesaw with three right-handed neutrinos (i.e. heavy Majorana neutrinos) when the CP-violation arises solely from the low-energy Dirac phase $δ$ of the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) neutrino mixing matrix and the heavy neutrinos have testable mixings. We derive a CP-conserving and non-real structure of the $3\times 3$ orthogonal matrix entering the Casas-Ibarra parametrisation in terms of two real angles and one single imaginary parameter, ensuring that the only CP-violating phases in the neutrino Yukawa couplings are those of the PMNS matrix. We then focus on the case of CP-violation from $δ$ alone and discuss the phenomenological implications of this hypothesis. We concentrate on quasi-degenerate heavy Majorana neutrinos with masses within $\sim (0.1-100)\,\text{GeV}$, as relevant for low-scale leptogenesis. Only certain subregions of the full ternary space defined by the ratios $Θ^2_e:Θ^2_μ:Θ^2_τ$ -- where $Θ^2_α$ denotes the squared coupling of the heavy neutrinos to leptons of flavour $α= e,\,μ,\,τ$ -- are compatible with Dirac-phase CP-violation while being testable at collider experiments. Our assumption also implies specific forms of the effective Majorana mass parameter that can be tested at neutrinoless double-beta decay searches. Finally, low-scale leptogenesis under this restrictive scenario can still reproduce the observed baryon asymmetry of the Universe (BAU) in the entire testable region of the parameter space. The BAU vanishes in the exact limit of CP-conserving values of the Dirac phase $δ= 0,\,π,\,2π$, but the observed BAU can be reproduced within the testable region even if $δ$ deviates from these values by a factor as small as $\mathcal{O}(10^{-5})$, with important implications for ultraviolet completions with approximate CP-symmetry.

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arXiv2026

The meV frontier of neutrinoless double beta decay in the JUNO era

Observing neutrinoless double beta decay would establish lepton number violation and the Majorana nature of neutrinos. Within the standard 3-flavour paradigm, the rate of this process is controlled by the effective Majorana mass $|\langle m \rangle|$, which may be severely suppressed if the neutrino mass spectrum presents normal ordering. Taking into account the first JUNO results, which significantly reduce the uncertainties on solar neutrino oscillation parameters, we provide updated conditions under which $|\langle m \rangle|_\text{NO}$ is guaranteed to exceed the $10^{-3}$ eV ($5\times 10^{-3}$ eV) threshold. We analyse both the generic case, as well as scenarios where the two Majorana phases either take CP conserving values, or at least one of them takes a CP-violating value, that are in line with predictive schemes combining flavour and generalised CP symmetries.

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arXiv2026

Viability of $A_4$, $S_4$ and $A_5$ Flavour Symmetries in Light of the First JUNO Result

We update the analysis of the viability of the lepton mixing patterns originating from $A_4$, $S_4$ and $A_5$ discrete flavour symmetries and leading to predictions for the solar neutrino mixing angle, $θ_{12}$. We perform a statistical analysis using as an input (i) the results of the latest global fit to neutrino oscillation data, and (ii) the first JUNO measurement of $\sin^2θ_{12}$. Out of the five (four) cases compatible with the global data at $3σ$ for normal (inverted) neutrino mass ordering, only three (two) cases remain compatible with the global data at the same confidence level after taking into account the JUNO result.

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arXiv2026

$S^\prime_4$ Quark Flavour Model in the Vicinity of the Fixed Point $τ= i\infty$

We study in the bottom-up framework the possibility to generate the quark mass hierarchies without fine-tuning, the quark mixing and CP-violation (CPV) in a flavour model with $S^\prime_4$ modular symmetry having minimal number of parameters. The model is considered in the vicinity of the fixed point $τ_\text{T}= i\infty$, $τ_\text{vev} \sim τ_\text{T}$, $τ_\text{vev}$ being the vacuum expectation value (VEV) of the modulus $τ$, which allows to explain the hierarchies of the quark masses. The ten quark observables are described by nine real parameters. The CP-symmetry is broken explicitly since, as is well known, reproducing the observed CPV in the quark sector in the case of spontaneous breaking of CP-symmetry by $τ_\text{vev}$ is highly problematic in the class of minimal modular quark flavour models (explaining the quark mass hierarchies without fine-tuning) of the type we consider. We perform a statistical analysis of the model and show that it is phenomenologically viable and consistent, in particular, with the ``inclusive'' decay data on the $|V_{ub}|$ and $|V_{cb}|$ elements of the CKM matrix and, in the case of a very high scale of supersymmetry breaking, with the current ``average'' experimental values of $|V_{ub}|$ and $|V_{cb}|$.

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arXiv2025

Discrete flavour and CP symmetries in light of JUNO and neutrino global fit

Working within the reference three-neutrino mixing framework, we confront the lepton mixing predictions derived using non-Abelian discrete flavour and CP symmetries with the first JUNO data on the solar neutrino mixing parameters $\sin^2θ_{12}$ and with the results of the latest global neutrino data analysis. We focus on symmetry breaking patterns for which the lepton PMNS mixing matrix depends only on one or two free real parameters. Performing a comprehensive statistical analysis in each of the considered cases, we report the best fit values, the $3σ$ C.L. allowed ranges and the $χ^2$-distributions of the lepton mixing observables - the three mixing angles and the three CP-violation phases. We find that the JUNO measurements can disfavour or rule out a number of the mixing patterns associated with specific types of breaking of the discrete flavour and CP symmetries. The synergy of JUNO, DUNE and T2HK data can provide an exhaustive test of the considered approach to lepton mixing based on non-Abelian discrete lepton flavour symmetries combined with the CP symmetry.

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arXiv2025

Modular-symmetry-protected seesaw

In the presence of a finite modular flavour symmetry, fermion mass hierarchies may be generated by a slight deviation of the modulus from a symmetric point. We point out that this small parameter governing charged-lepton mass hierarchies may also be responsible for the breaking of lepton number in a symmetry-protected low-scale seesaw, sourcing active neutrino masses and the mass splitting of a pseudo-Dirac pair of heavy neutrinos. We discuss the phenomenological implications of this mechanism, including the possibility to test the considered models at future planned and proposed heavy neutral lepton searches.

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arXiv2024

Neutrino Tomography of the Earth: the Earth Total Mass, Moment of Inertia and Hydrostatic Equilibrium Constraints

We investigate the implications of the constraints following from the precise knowledge of the total Earth mass, $M_\oplus$, and moment of inertia, $I_\oplus$, and from the requirement that Earth be in hydrostatic equilibrium (EHE), in the neutrino tomography studies of the Earth density structure. In order to estimate the sensitivity of a given neutrino detector to possible deviations of the inner core (IC), outer core (OC), core (IC + OC) and mantle Earth densities from those obtained using geophysical and seismological data and described by the preliminary reference Earth model (PREM), in the statistical analyses performed within the neutrino tomography studies one typically varies the density of each of these structures. These variations, however, must respect the $M_\oplus$, $I_\oplus$ and EHE constraints. Working with PREM average densities we derive the $M_\oplus$, $I_\oplus$ and EHE constraints on the possible density variations when one approximates the Earth density structure with i) three layers - mantle, outer core and inner core, and ii) four layers - upper mantle, lower mantle, outer core and inner core. We get drastically different results in the two cases.

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arXiv2024

Interplay and Correlations Between Quark and Lepton Observables in Modular Symmetry Models

In a predictive modular invariant theory of flavour there should exist correlations between the quark and lepton observables. So far these observables have been analyzed separately, making it impossible to investigate their interconnections. We perform for the first time a joint analysis of quark and lepton observables (22 altogether) in a modular flavour model. The model is based on $2O$ flavour symmetry and, within its class, it is characterized by the minimal number of free parameters (14 real constants). The joint analysis shows that the model is in good agreement with the experimental data for normal neutrino mass ordering, while predicting the leptonic Dirac CP-violating (CPV) phase ($δ_{CP}$), the two Majorana CPV phases ($η_1$, $η_2$), the lightest neutrino mass ($m_1$) and the effective neutrino masses probed by beta and neutrinoless double beta decay ($m_β$ and $m_{ββ}$). A detailed comparison of the separate (lepton-only and quark-only) and combined (lepton and quark) fit results shows differences in best-fit values and jointly allowed regions, that reflect a nontrivial interplay between quark and lepton observables in the model. Most importantly, our analysis highlights the existence of significant correlations between various pairs of such observables. For instance, the ratio of the strange and bottom quark masses, $r_{sb}$, is strongly negatively correlated with each of the three lepton mixing angles and with $δ_{CP}$, $m_1$, $m_β$ and $m_{ββ}$, while being positively correlated with $η_1$ and $η_2$. These findings, that are missed in separate analyses of quark and lepton flavour sectors, fall within ranges that can be tested by current and future experiments.

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arXiv2024

Finite modular symmetries and the strong CP problem

Recently, it was shown that modular symmetry may solve the strong CP problem without axions, by producing a vanishing QCD angle while generating a large quark CP violation phase. We extend this framework to finite modular groups, systematically identifying the allowed mass textures. We find quark fields must furnish 1D representations and scan the minimal model landscape.

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arXiv2024

Non-holomorphic Modular $S_4$ 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 $S_4$ as a flavour symmetry group and assuming that the three left-handed lepton doublets furnish a triplet irreducible representation of $S_4$, 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.

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arXiv2024

$A_4$ modular invariance and the strong CP problem

We present simple effective theory of quark masses, mixing and CP violation with level $N=3$ ($A_4$) modular symmetry, which provides solution to the strong CP problem without the need for an axion. The vanishing of the strong CP-violating phase $\bar θ$ is ensured by assuming CP to be a fundamental symmetry of the Lagrangian of the theory. The CP symmetry is broken spontaneously by the vacuum expectation value (VEV) of the modulus $τ$. This provides the requisite large value of the CKM CP-violating phase while the strong CP phase $\bar θ$ remains zero or is tiny. Within the considered framework we discuss phenomenologically viable quark mass matrices with three types of texture zeros, which are realized by assigning both the left-handed and right-handed quark fields to $A_4$ singlets ${\bf 1}$, ${\bf 1'}$ and ${\bf 1''}$ with appropriate weights. The VEV of $τ$ is restricted to reproduce the observed CKM parameters. We discuss cases in which the modulus VEV is close to the fixed points $i$, $ω$ and $i\infty$. In particular, we focus on the VEV of $τ$, which gives the absolute minima of the supergravity-motivated modular- and CP-invariant potentials for the modulus $τ$, so called, modulus stabilisation. We present a successful model, which is consistent with the modulus stabilisation close to $τ=ω$.

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arXiv2024

Fermion Mass Hierarchies, Large Lepton Mixing and Residual Modular Symmetries

In modular-invariant models of flavour, hierarchical fermion mass matrices may arise solely due to the proximity of the modulus $τ$ to a point of residual symmetry. This mechanism does not require flavon fields, and modular weights are not analogous to Froggatt-Nielsen charges. Instead, we show that hierarchies depend on the decomposition of field representations under the residual symmetry group. We systematically go through the possible fermion field representation choices which may yield hierarchical structures in the vicinity of symmetric points, for the four smallest finite modular groups, isomorphic to $S_3$, $A_4$, $S_4$, and $A_5$, as well as for their double covers. We find a restricted set of pairs of representations for which the discussed mechanism may produce viable fermion (charged-lepton and quark) mass hierarchies. We present two lepton flavour models in which the charged-lepton mass hierarchies are naturally obtained, while lepton mixing is somewhat fine-tuned. After formulating the conditions for obtaining a viable lepton mixing matrix in the symmetric limit, we construct a model in which both the charged-lepton and neutrino sectors are free from fine-tuning.

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arXiv2023

Quarks at the modular $S_4$ cusp

We analyse the possibility of describing quark masses, mixing and CP violation in $S'_4$ modular flavour models without flavons. We focus on the case where the closeness of the modulus to the point of residual $\mathbb{Z}^{ST}_3$ symmetry (the cusp) plays a role in generating quark mass hierarchies and discuss the role modular form normalisations play in such constructions. We find that fitting quark data requires explicit CP breaking, unless a second modulus is introduced.

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arXiv2023

$A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $τ= i\infty$

We study the possibility to generate the quark mass hierarchies as well as the CKM quark mixing and CP violation without fine-tuning in a quark flavour model with modular $A_4$ symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point $τ= i\infty$, $τ$ being the vacuum expectation value of the modulus. We consider first a model in which the up-type and down-type quark mass matrices $M_u$ and $M_d$ involve modular forms of level 3 and weights 6, 4 and 2 and each depends on four constant parameters. We also consider the case of $M_u$ and $M_d$ depending on the same $τ$ and involving modular forms of weights 8, 4, 2 and 6, 4, 2, respectively, with $M_u$ receiving a tiny SUSY breaking or higher dimensional operator contribution. Both the mass hierarchies of up-type and down-type quarks as well and the CKM mixing angles and CP violating phase are reproduced successfully with one complex parameter and all parameters being in magnitude of the same order. The relatively large value of ${\rm Im}\,τ$, needed for describing the down-type quark mass hierarchies, is crucial for obtaining the correct up-type quark mass hierarchies.

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arXiv2023

Feebly Interacting Particles: FIPs 2022 workshop report

Particle physics today faces the challenge of explaining the mystery of dark matter, the origin of matter over anti-matter in the Universe, the origin of the neutrino masses, the apparent fine-tuning of the electro-weak scale, and many other aspects of fundamental physics. Perhaps the most striking frontier to emerge in the search for answers involves new physics at mass scales comparable to familiar matter, below the GeV-scale, or even radically below, down to sub-eV scales, and with very feeble interaction strength. New theoretical ideas to address dark matter and other fundamental questions predict such feebly interacting particles (FIPs) at these scales, and indeed, existing data provide numerous hints for such possibility. A vibrant experimental program to discover such physics is under way, guided by a systematic theoretical approach firmly grounded on the underlying principles of the Standard Model. This document represents the report of the FIPs 2022 workshop, held at CERN between the 17 and 21 October 2022 and aims to give an overview of these efforts, their motivations, and the decadal goals that animate the community involved in the search for FIPs.

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arXiv2023

Neutrinoless double beta decay in Left-Right symmetric model with double seesaw mechanism

We discuss a left-right (L-R) symmetric model with the double seesaw mechanism at the TeV scale generating Majorana masses for the active left-handed (LH) flavour neutrinos $ν_{αL}$ and the heavy right-handed (RH) neutrinos $N_{βR}$, $α,β= e,μ,τ$, which in turn mediate lepton number violating processes, including neutrinoless double beta decay. The Higgs sector is composed of two Higgs doublets $H_L$, $H_R$, and a bi-doublet $Φ$. The fermion sector has the usual for the L-R symmetric models quarks and leptons, along with three $SU(2)$ singlet fermion $S_{γL}$. The choice of bare Majorana mass term for these sterile fermions induces large Majorana masses for the heavy RH neutrinos leading to two sets of heavy Majorana particles $N_j$ and $S_k$, $j,k=1,2,3$, with masses $m_{N_j} \ll m_{S_k}$. Working with a specific version of the model in which the $ν_{αL} - N_{βR}$ and the $N_{βR} - S_{γL}$ Dirac mass terms are diagonal, and assuming that $m_{N_j} \sim (1 - 1000)$ GeV and ${\rm max}(m_{S_k}) \sim (1 - 10)$ TeV, $m_{N_j} \ll m_{S_k}$, we study in detail the new ``non-standard'' contributions to the $0νββ$ decay amplitude and half-life arising due to the exchange of virtual $N_j$ and $S_k$. We find that in both cases of NO and IO light neutrino mass spectra, these contributions are strongly enhanced and are dominant at relatively small values of the lightest neutrino mass $m_{1(3)} \sim (10^{-4} - 10^{-2})$ eV over the light Majorana neutrino exchange contribution. In large part of the parameter space, the predictions of the model for the $0νββ$ decay generalised effective Majorana mass and half-life are within the sensitivity range of the planned next generation of neutrinoless double beta decay experiments LEGEND-200 (LEGEND-1000), nEXO, KamlAND-Zen-II, CUPID, NEXT-HD.

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arXiv2023

$A_4$ Modular Flavour Model of Quark Mass Hierarchies close to the Fixed Point $τ= ω$

We investigate the possibility to describe the quark mass hierarchies as well as the CKM quark mixing matrix without fine-tuning in a quark flavour model with modular $A_4$ symmetry. The quark mass hierarchies are considered in the vicinity of the fixed point $τ= ω\equiv \exp({i\,2π/3})$ (the left cusp of the fundamental domain of the modular group), $τ$ being the VEV of the modulus. The model involves modular forms of level 3 and weights 6, 4 and 2, and contains eight constants, only two of which, $g_u$ and $g_d$, can be a source of CP violation in addition to the VEV of the modulus, $τ= ω+ ε$, $(ε)^* \neq ε$, $|ε|\ll 1$. We find that in the case of real (CP-conserving) $g_u$ and $g_d$ and common $τ$ ($ε$) in the down-quark and up-quark sectors, the down-type quark mass hierarchies can be reproduced without fine tuning with $|ε| \cong 0.03$, all other constants being of ${\cal O}(1)$, and correspond approximately to $1 : |ε| : |ε|^2$. The up-type quark mass hierarchies can be achieved with the same $|ε| \cong 0.03$ but allowing $g_u\sim {\cal O}(10)$ and correspond to $1 : |ε|/|g_u| : |ε|^2/|g_u|^2$. In this setting, we discuss the CKM quark mixing and CP violation.

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