Scale-Independent Relations Between Neutrino Mass Parameters

Universe · 2026-02-11

Theories of flavor operate at various scales. Recently it has been pointed out that in the context of modular flavor symmetries, certain combinations of observables are highly constrained, or even uniquely fixed, by modular invariance and holomorphicity. We find that even in the absence of supersymmetry, these combinations are surprisingly immune against quantum corrections.

Modular Flavor Symmetries and Fermion Mass Hierarchies

ArXiv.org · 2025-06-29

We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus $τ$ to be located near one of the critical points, $i$, $i\infty$, or $ω$. We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points $i$ and $ω$. We compare the traditional Froggatt--Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.

Multiple realizations of modular flavor symmetries and their phenomenology

Journal of High Energy Physics · 2025-06-11 · 2 citations

A bstract We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group T ′. Otherwise equivalent models based on different T ′ lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the T ′ is implemented.

Multiple realizations of modular flavor symmetries and their phenomenology

ArXiv.org · 2025-02-17

We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group $T'$. Otherwise equivalent models based on different $T'$ lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the $T'$ is implemented.

Scale-independent relations between neutrino mass parameters

ArXiv.org · 2025-11-06

Theories of flavor operate at various scales. Recently it has been pointed out that in the context of modular flavor symmetries certain combinations of observables are highly constrained, or even uniquely fixed, by modular invariance and holomorphicity. We find that even in the absence of supersymmetry these combinations are surprisingly immune against quantum corrections. This applies, in particular, to the standard model (SM) and certain 2-Higgs doublet models (2HDMs).

Modular flavor symmetries and fermion mass hierarchies

Journal of High Energy Physics · 2025-10-03

A bstract We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus τ to be located near one of the critical points, i, i ∞, or ω . We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points i and ω . We compare the traditional Froggatt–Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.

Modular flavored dark matter

Journal of High Energy Physics · 2024-12-11 · 1 citations

A bstract Discrete flavor symmetries have been an appealing approach for explaining the observed flavor structure, which is not justified in the Standard Model (SM). Typically, these models require a so-called flavon field in order to give rise to the flavor structure upon the breaking of the flavor symmetry by the vacuum expectation value (VEV) of the flavon. Generally, in order to obtain the desired vacuum alignment, a flavon potential that includes additional so-called driving fields is required. On the other hand, allowing the flavor symmetry to be modular leads to a structure where the couplings are all holomorphic functions that depend only on a complex modulus, thus greatly reducing the number of parameters in the model. We show that these elements can be combined to simultaneously explain the flavor structure and dark matter (DM) relic abundance. We present a modular model with flavon vacuum alignment that allows for realistic flavor predictions while providing a successful fermionic DM candidate.

Probing Massive Fields with Multi-Band Gravitational-Wave Observations

arXiv (Cornell University) · 2024-05-19

We investigate the prospect of probing massive fields and testing gravitational theories with multiband observations of gravitational waves emitted from coalescing compact binaries. Focusing on the dipole radiation induced by a massive field, we show that multiband observations can probe the field with mass ranging from $10^{-16} $ to $10^{-15} {\rm eV}$, a parameter space that cannot be probed by the millihertz band observations alone. Multiband observations can also improve the constraints obtained with the LIGO-Virgo-KAGRA binaries by at most 3 orders of magnitude in the mass range. Moreover, we show that multiband observations can discriminate the spin of the field, which cannot be identified with single-band observations.

Modular invariant holomorphic observables

arXiv (Cornell University) · 2024-01-09

In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $τ$ and its conjugate, $\barτ$. We point out that certain combinations of observables depend only on $τ$, i.e. are meromorphic, and in some cases even holomorphic functions of $τ$. These functions, which we dub ``invariants'' in this Letter, are highly constrained, renormalization group invariant, and allow us to derive many of the models' features without the need for extensive parameter scans. We illustrate the robustness of these invariants in two existing models in the literature based on modular symmetries, $Γ_{3}$ and $Γ_{5}$. We find that, in some cases, the invariants give rise to robust relations among physical observables that are independent of $τ$. Furthermore, there are instances where additional symmetries exist among the invariants. These symmetries are relevant phenomenologically and may provide a dynamical way to realize symmetries of mass matrices.

Quark-lepton mass relations from modular flavor symmetry

Journal of High Energy Physics · 2024-02-22 · 2 citations

A bstract The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Γ 4 ≅ S 4 symmetry, which have calculable deviations from the usual Golden Mass Relation.