Lepton-number-violating pion decay and 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-I seesaw mechanism. The type-I seesaw mechanism leads to the Dirac and Majorana mass terms of neutrinos by introducing the gauge-singlet right-handed neutrinos, which are often called sterile neutrinos. Applying the chiral perturbation theory, we calculate the transition amplitudes for light and heavy sterile neutrinos up to $ \mathcal{O}(Q^2/\Lambda^2_\chi) $ , where Qis 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.