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 study the space-time geometry generated by coupling a free scalar field with a noncanonical kinetic term to general relativity in (2+1) dimensions. After identifying a family of scalar Lagrangians that yield exact analytical solutions in static and circularly symmetric scenarios, we classify the various types of solutions and focus on a branch that yields asymptotically flat geometries. We show that the solutions within such a branch can be divided in two types, namely naked singularities and nonsingular objects without a center. In the latter, the energy density is localized around a maximum and vanishes only at infinity and at an inner boundary. This boundary has vanishing curvatures and cannot be reached by any time-like or null geodesic in finite affine time. This allows us to consistently interpret such solutions as nonsingular, lump-like, static compact scalar objects whose eventual extension to the (3+1)-dimensional context could provide structures of astrophysical interest.

Abstract: Third -generation dark matter detectors will be fully sensitive to the 8 B solar neutrino flux. Because of this, the characterization of such a background has been the subject of extensive analyses over the last few years. In contrast, little is known about the impact of reactor neutrinos. In this paper, we report on the implications of such a flux for dark matter direct -detection searches. We consider five potential detector deployment sites envisioned by the recently established XLZD Consortium: SURF, SNOLAB, Kamioka, LNGS, and Boulby. By using public reactor data, we construct five reactor clusters -involving about 100 currently operating commercial nuclear reactors each -and determine the net neutrino flux at each detector site. Assuming a xenon -based detector and a 50 ton -year exposure, we show that in all cases the neutrino event rate may be sizable, depending on energy recoil thresholds. Of all possible detector sites, SURF and LNGS are those with the smallest reactor neutrino background. On the contrary, SNOLAB and Boulby are subject to the strongest reactor neutrino fluxes, with Kamioka being subject to a more moderate background. Our findings demonstrate that reactor neutrino fluxes should be taken into account in the next round of dark matter searches. We argue that this background may be particularly relevant for directional detectors, provided they meet the requirements we have employed in this analysis.