• Effective Field Theory
• Graphene
• Neutrinos mass
• Nuclear Physics
• PTOLEMY
• Relic neutrinos

The PTOLEMY experiment aims to detect the cosmic neutrino background (CnB) and measure the neutrino mass by studying the electron spectra emitted in the tritium beta decay, and neutrino capture, for tritium adsorbed on graphene layers.
This work presents a theoretical investigation of the effects arising from the interaction between tritium and Helium atoms with the graphene substrate, but at the same time performing a state-of-the-art treatment of the nuclear dynamics. In fact, the nuclear transition is studied within the framework of chiral effective field theory. To this end, we employ the most accurate nuclear interactions and weak nuclear transition current operators available in the literature, derived using chiral perturbation theory (ChPT). In the first part of the thesis, the ChPT is briefly discussed and the axial current at N3LO is explicitly
step-by-step rederived. Then, the trinucleon wave functions are computed using the (very accurate) Hyperspherical Harmonics expansion method, which are first used to reproduce the experimental tritium half-life. We then investigate the electron energy spectrum near the endpoint for polarized tritium, observing a preferential emission of electrons along the spin polarization axis. Finally, we introduce various nucleus-graphene interaction scenarios for the initial and final states (developed very recently in arxiv:2504.13259), including both free and trapped Helium atoms, in order to study their impact on the electron emission spectrum, with particular attention to the dependence on the neutrino mass.