Sprecher
Beschreibung
The determination of the absolute neutrino mass scale remains one of the most pressing open challenges in modern physics. Although the Standard Model assumes massless neutrinos, flavor oscillations unequivocally prove the existence of massive, non-degenerate eigenstates. State-of-the-art experiments like KATRIN are currently pushing the sensitivity limits of tritium $\beta$-decay spectroscopy, while upcoming projects such as PTOLEMY aim to further expand this frontier, including the long-term goal of detecting the Cosmic Neutrino Background. The method relies on the analysis of the kinematic distortion at the endpoint of the energy spectrum; however, the extreme statistical and systematic precision required by these measurements makes standard theoretical approximations insufficient.The present work focuses on the rigorous advancement of the formalism for describing the $\beta$ spectrum. Starting from the $V-A$ theory of the weak interaction, the study extends the treatment into a complete Quantum Field Theory (QFT) framework. This approach allows the calculation of the decay rate by overcoming the traditional factorization approximation of the leptonic wave functions and exactly integrating the solutions of the Dirac equation. Particular attention will be devoted to the evaluation of radiative and nuclear corrections within this new framework.While this theoretical framework has already proven its validity in low-energy neutrino physics—offering, for instance, an interpretation for the so-called "gallium anomaly" [1] through the redetermination of absorption rates—the talk will specifically focus on the application of this formalism to tritium decay. It will be shown how theoretical control at the QFT level is essential to extract the neutrino mass parameter by minimizing theoretical systematics at the kinematic endpoints.