Vertex correction to nuclear matrix elements of double- decays

The predicted neutrinoless double- (0) decay is the crucial phenomenon to prove the existence of the Majorana neutrino, which gives a foundation to leptogenesis to explain the matter prevalence of the universe. The nuclear matrix element (NME) of 0 decay is an important theoretical quantity to determine the effective neutrino mass and help the detector design for the next generation of the 0 decay search. Reliable calculation of this NME is a long-standing problem because of the diversity of the predicted values of the NME. The main reason for this difficulty is that the effective strength of the Gamow-Teller transition operator gA for this decay is unknown. I will show the lowest-order vertex corrections for the 0 and the 2 NME of ^136Xe in the framework of the hybrid application of the quantum field theory to the leptons and the Rayleigh-Schr\"odinger perturbation to the nucleus. The unperturbed nuclear states are obtained by the quasiparticle random-phase approximation. These corrections reduce the 0 NME by 30%. The effective gA referring to this reduced NME is also obtained, and it is shown for the first time that the effective gA for the 0 NME is not quite different from that for the 2 NME; the difference is only 10%. This indicates the possibility that the phenomenological effective gA to reproduce the experimental half-life of the 2 decay can be approximately used for the calculation of the 0 NME.