Standard model physics and beyond in low energy neutrino scattering and parity violating electron interactions with nuclei

The object of my thesis work is the phenomenology of neutrino interactions at low energies, with special attention to the coherent elastic scattering of neutrinos off nuclei (CEvNS) and the elastic scattering of neutrinos off atomic electrons (vES). In the work, I discuss the many physical implications and applications of the measurement of the scattering cross sections for such neutrino scattering processes as precision tests of the standard model (SM) theory of particle physics and on new physics models. I discuss in detail the CEvNS process and the currently available experimental measurements from the COHERENT Collaboration and the Dresden-II one, together with a description of the data analysis techniques employed in my work. Moreover, I compare such a process with the vES process, highlighting its importance for some beyond the SM physics scenarios and direct dark matter detector data analysis. The main result discussed in my thesis is proof that performing combined analyses of different electroweak probes is a powerful tool to extract fully data-driven information. Indeed, I studied the physics of parity-violating electron scattering off nuclei and the atomic parity-violation process, which permit the extraction of complementary information to the one obtained by neutrino scattering processes. This technique has been applied to the extraction of the weak mixing angle at low energy, a key parameter of the SM theory and the determination of the nuclear neutron radius, which describes the distribution of neutrons inside the nucleus, which is a fundamental parameter of nuclear theory which gives insights on the inner structure of astrophysical objects such as neutron stars. Furthermore, I studied the implications of beyond the standard model scenarios that can be tested with the available CEvNS and vES measurements, in order to extract information on possible neutrino electromagnetic properties or possible light new boson mediators of a new kind of interactions.