Theoretical and computational studies of particle interactions for the CUORE+CUPID experiments.*

Tools from quantum field theory are our most powerful methods for the theoretical and computational analysis of elementary particle interactions. CUORE and its extension, CUPID, are part of a multinational collaboration dedicated to understanding the fundamental nature of neutrinos. The observation of 0νββ would confirm that neutrinos are Majorana particles, identical to their own antiparticle, challenging the Standard Model's current assumption of Dirac neutrinos, and providing new insight into the effective Majorana neutrino's mass and force us to reconsider the Standard Model's rule of lepton number conservation. Current theoretical and experimental methods employ the use of mathematical simulation toolkits such as Geant4 which takes care of the heavy-handed calculations for cross sections and decay rates via Monte Carlo methods. Our ability to utilize computational modeling tools has elucidated areas of background events in the CUORE+CUPID experiments to make it easier to distinguish an instance of 0νββ. This work continues to explore these principles for weak nuclear decays and utilizing Geant4 to model particle interactions for simple and complex geometries.