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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.
The idea of modular invariance provides a novel explanation of flavour mixing. Within the context of finite modular symmetries $Gamma_N$ and for a given element $gamma in Gamma_N$, we present an algorithm for finding stabilisers (specific values for
We use QCD Laplace sum-rules to predict masses of open-flavour heavy-light hybrids where one of the hybrids constituent quarks is a charm or bottom and the other is an up, down, or strange. We compute leading-order, diagonal correlation functions of
We develop a general formalism for multiple moduli and their associated modular symmetries. We apply this formalism to an example based on three moduli with finite modular symmetries $S_4^A$, $S_4^B$ and $S_4^C$, associated with two right-handed neut
Neutrino mass sum rules have recently gained again more attention as a powerful tool to discriminate and test various flavour models in the near future. A related question which was not yet discussed fully satisfactorily was the origin of these sum r
We investigate a model QCD sum rule for the pion wave function $varphi_{pi}(x)$ based on the non-diagonal correlator whose perturbative spectral density vanishes and $Phi(x,M^2)$, the theoretical side of the sum rule, consists of condensate contribut