Abstract: 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 Gamma 4 approximately equal to S4 symmetry, which have calculable deviations from the usual Golden Mass Relation.

Abstract: The exquisite capabilities of liquid Argon Time Projection Chambers make them ideal to search for weakly interacting particles in Beyond the Standard Model scenarios. Given their location at CERN the ProtoDUNE detectors may be exposed to a flux of such particles, produced in the collisions of 400 GeV protons (extracted from the Super Proton Synchrotron accelerator) on a target. Here we point out the interesting possibilities that such a setup offers to search for both long-lived unstable particles (Heavy Neutral Leptons, axion-like particles, etc) and stable particles (e.g. light dark matter, or millicharged particles). Our results show that, under conservative assumptions regarding the expected luminosity, this setup has the potential to improve over present bounds for some of the scenarios considered. This could be done within a short timescale, using facilities that are already in place at CERN, and without interfering with the experimental program in the North Area at CERN.

Abstract: We study the mass spectrum of light pseudoscalar and vector mesons in the presence of an external uniform magnetic field B., considering the effects of the mixing with the axial-vector meson sector. The analysis is performed within a two-flavor NJL-like model which includes isoscalar and isovector couplings together with a flavor mixing 't Hooft-like term. The effect of the magnetic field on charged particles is taken into account by retaining the Schwinger phases carried by quark propagators, and expanding the corresponding meson fields in proper Ritus-like bases. The spin-isospin and spin-flavor decomposition of meson mass states is also analyzed. For neutral pion masses it is shown that the mixing with axial vector mesons improves previous theoretical results, leading to a monotonic decreasing behavior with B that is in good qualitative agreement with lattice QCD (LQCD) calculations, both for the case of constant or B-dependent couplings. Regarding charged pions, it is seen that the mixing softens the enhancement of their mass with B. As a consequence, the energy becomes lower than the one corresponding to a pointlike pion, improving the agreement with LQCD results. The agreement is also improved for the magnetic behavior of the lowest.thorn energy state, which does not vanish for the considered range of values of B-a fact that can be relevant in connection with the occurrence of meson condensation for strong magnetic fields.