Abstract: In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{U}}{\left(1\right)}_{Y}<^>{3}$$\end{document} based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e+pi 0 channel.

Abstract: We discuss the effective field theory (EFT) for nuclear beta decay. The general quark-level EFT describing charged-current interactions between quarks and leptons is matched to the nucleon-level non-relativistic EFT at the OMeV momentum scale characteristic for beta transitions. The matching takes into account, for the first time, the effect of all possible beyond-the-Standard-Model interactions at the subleading order in the recoil momentum. We calculate the impact of all the Wilson coefficients of the leading and subleading EFT Lagrangian on the differential decay width in allowed beta transitions. As an example application, we show how the existing experimental data constrain the subleading Wilson coefficients corresponding to pseudoscalar, weak magnetism, and induced tensor interactions. The data display a 3.5 sigma evidence for nucleon weak magnetism, in agreement with the theory prediction based on isospin symmetry.

Abstract: We investigate the sensitivity of the FASER nu detector, a novel experimental setup at the LHC, to probe and constrain generalized neutrino interactions (GNI). Employing a comprehensive theoretical framework, we model the effects of generalized neutrino interactions on neutrino-nucleon deep inelastic scattering processes within the FASER nu detector. By considering all the neutrino channels produced at the LHC, we perform a statistical analysis to determine the sensitivity of FASER nu to constrain these interactions. Our results demonstrate that FASER nu can place stringent constraints on the GNI effective couplings. Additionally, we study the relation between GNI and a minimal Leptoquark model where the SM is augmented by a singlet Leptoquark with hypercharge 1/3. We have found that the sensitivities for various combinations of the Leptoquark Yukawa couplings are approximately O(1), particularly when considering a Leptoquark mass in the TeV range.