Abstract
Sum rules in the lepton sector provide an extremely valuable tool to classify flavour models in terms of relations between neutrino masses and mixing parameters testable in a plethora of experiments. In this manuscript we identify new leptonic sum rules arising in models with modular symmetries with residual symmetries. These models simultaneously present neutrino mass sum rules, involving masses and Majorana phases, and mixing sum rules, connecting the mixing angles and the Dirac CP-violating phase. The simultaneous appearance of both types of sum rules leads to some non-trivial interplay, for instance, the allowed absolute neutrino mass scale exhibits a dependence on the Dirac CP-violating phase. We derive analytical expressions for these novel sum rules and present their allowed parameter ranges as well as their predictions at upcoming neutrino experiments.
Highlights
This reduction of the parameters in models with modular symmetry leads to a new appealing feature, namely, the existence of new sum rules since the neutrino masses, neutrino mixing and the CPV phases are simultaneously determined by the modular symmetry typically in terms of a limited number of constant parameters
Our results can provide a link between model building, phenomenology, and experiments as they allow to study which models could be distinguished by the experiment and, in the case of an observation, the measurement can be directly linked to certain flavour models
In this manuscript we have studied a new class of leptonic sum rules derived from flavour models based on modular symmetries
Summary
Before we look into actual models we want to discuss in some detail mass sum rules and how we can derive certain phenomenological predictions from them. Mass sum rules relate the three light neutrino masses and two Majorana phases to each other. Using the complex mass eigenvalues mi exp(− i φi) neutrino mass sum rules can be generally parametrised as s(m1, m2, m3, φ1, φ2, θ12, θ13, θ23, δ, d) ≡ f1(θ12, θ13, θ23, δ)(m1 e− i φ1 )d + f2(θ12, θ13, θ23, δ)(m2 e− i φ2 )d + md3 =! The coefficients are functions of the mixing parameters leading to a strikingly different phenomenology of mass sum rules in models with and without modular symmetries. Starting from the parametrisation in eq (2.1) we will discuss in the following how one can derive expressions for observables which are affected by the existence of a mass sum rule
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