Weak nuclear processes in the quest for elusive particles

Nuclear processes involving the weak interaction can be used to extract information on some elusive properties of particles. Remarkably useful to this goal is parity-violating elastic electron scattering off nuclei, which can be used to determine accurately the distribution of neutrons within the nucleus, including information on the neutron skin that can be related to the structure of neutron stars. It can also be used to determine the content of strange quark-antiquark virtual pairs in nucleons and can help in evaluating accurately Standard Model parameters or higher-order radiative corrections. To achieve these goals it is essential keeping under control the theoretical uncertainties that arise in modelling some confounding nuclear effects, such as isospin mixing or Coulomb distortion of electron wave functions. The paradigm of an evasive particle in current physics is dark matter. Sterile neutrinos are hypothetical dark matter candidates that could be produced in nuclear beta decays leaving a signal in the energy spectrum of the emitted charged lepton. They can also be coherently scattered by nuclei through an indirect weak neutral interaction, whose cross section can be written in terms of elastic electron scattering observables. We study the probability of these production and detection mechanisms using experimental and cosmological constraints on the sterile neutrino properties. The coherent scattering cross section off nuclei has also been analyzed for the Standard Model neutrinos, being a notably elusive process that has been recently measured for the first time and that can be used for Standard Model tests or for nuclear structure studies in ways analogous to parity-violating electron scattering