Abstract: We revisit the gauge symmetry related to integrable projective transformations in metric-affine formalism, identifying the gauge field of the Weyl (conformal) symmetry as a dynamical component of the affine connection. In particular, we show how to include the local scaling symmetry as a gauge symmetry of a large class of geometric gravity theories, introducing a compensator dilaton field that naturally gives rise to a Stuckelberg sector where a spontaneous breaking mechanism of the conformal symmetry is at work to generate a mass scale for the gauge field. For Ricci-based gravities that include, among others, General Relativity, f(R) and f(R, R μnu R μnu) theories and the EiBI model, we prove that the on-shell gauge vector associated to the scaling symmetry can be identified with the torsion vector, thus recovering and generalizing conformal invariant theories in the Riemann-Cartan formalism, already present in the literature.

Abstract: We explore possible signatures for charged lepton flavour violation (LFV), sparticle discovery at the LHC and dark matter (DM) searches in grand unified theories (GUTs) based on SU(5), flipped SU(5) (FSU(5)) and SU(4)(c) x SU(2)(L) x SU(2)(R) (4-2-2). We assume that soft supersymmetry-breaking terms preserve the group symmetry at some high input scale, and focus on the non-universal effects on different matter representations generated by gauge interactions at lower scales, as well as the charged LFV induced in Type-1 see-saw models of neutrino masses. We identify the different mechanisms that control the relic DM density in the various GUT models, and contrast their LFV and LHC signatures. The SU(5) and 4-2-2 models offer good detection prospects both at the LHC and in LFV searches, though with different LSP compositions, and the SU(5) and FSU(5) models offer LFV within the current reach. The 4-2-2 model allows chargino and gluino coannihilations with neutralinos, and the former offer good detection prospects for both the LHC and LFV, while gluino coannihilations lead to lower LFV rates. Our results indicate that LFV is a powerful tool that complements LHC and DM searches, providing significant insights into the sparticle spectra and neutrino mass parameters in different models.

Abstract: The Dresden-II reactor experiment has recently reported a suggestive evidence for the observation of coherent elastic neutrino-nucleus scattering, using a germanium detector. Given the low recoil energy threshold, these data are particularly interesting for a low-energy determination of the weak mixing angle and for the study of new physics leading to spectral distortions at low momentum transfer. Using two hypotheses for the quenching factor, we study the impact of the data on: (i) The weak mixing angle at a renormalization scale of similar to 10 MeV, (ii) neutrino generalized interactions with light mediators, (iii) the sterile neutrino dipole portal. The results for the weak mixing angle show a strong dependence on the quenching factor choice. Although still with large uncertainties, the Dresden-II data provide for the first time a determination of sin(2)theta(W) at such scale using coherent elastic neutrino-nucleus scattering data. Tight upper limits are placed on the light vector, scalar and tensor mediator scenarios. Kinematic constraints implied by the reactor anti-neutrino flux and the ionization energy threshold allow the sterile neutrino dipole portal to produce up-scattering events with sterile neutrino masses up to similar to 8 MeV. In this context, we find that limits are also sensitive to the quenching factor choice, but in both cases competitive with those derived from XENON1T data and more stringent that those derived with COHERENT data, in the same sterile neutrino mass range.