Vertex correction to nuclear matrix elements of double-β decays

The predicted neutrinoless double-β (0νββ) 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 0νββ decay is an important theoretical quantity to determine the effective neutrino mass and help the detector design for the next generation of the 0νββ 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 0νββ and the 2νββ NME of ¹³⁶Xe in the framework of the hybrid application of the quantum field theory to the leptons and the Rayleigh-Schr\"{o}dinger perturbation to the nucleus. The unperturbed nuclear states are obtained by the quasiparticle random-phase approximation. These corrections reduce the 0νββ 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 0νββ NME is not quite different from that for the 2νββ NME; the difference is only 10%. This indicates the possibility that the phenomenological effective gA to reproduce the experimental half-life of the 2νββ decay can be approximately used for the calculation of the 0νββ NME.