The lepton-number-violating pion decay and the type-I seesaw mechanism in chiral perturbation theory

Abstract

We investigate the process of lepton-number-violating pion decay, which dominates the nuclear neutrinoless double beta decay induced by the short-range operator, within the type-\uppercase\expandafter{\romannumeral1} seesaw mechanism. The type-\uppercase\expandafter{\romannumeral1} seesaw mechanism gives rise to the Dirac and Majorana mass terms of neutrinos by introducing the gauge-singlet right-handed neutrinos, which are usually called sterile neutrinos. Using chiral perturbation theory, the transition amplitudes in the case of the light and heavy sterile neutrinos are calculated up to $\mathcal{O}(Q^2/\Lambda^2_\chi)$ respectively, where $Q$ is the typical low-energy scale in this process and $\Lambda_\chi$ the chiral symmetry breaking scale. We then adopt a naive interpolation formula of mass dependence to obtain the amplitude in the full mass range and briefly discuss its validity.