Many-body correlations of quasiparticle random-phase approximation in nuclear matrix element of neutrinoless double-beta decay

We show that the correlations of the quasiparticle random-phase approximation (QRPA) significantly reduce the nuclear matrix element (NME) of neutrinoless double-beta decay by a new mechanism in the calculation for $^{150}$Nd $\rightarrow$ $^{150}$Sm. This effect is due mainly to the normalization factors of the QRPA ground states included in the overlap of intermediate states, to which the QRPA states based on the initial and final ground states are applied. These normalization factors arise according to the definition of the QRPA ground state as the vacuum of quasibosons. Our NME is close to those of other groups in spite of this new reduction effect because we do not use the proton-neutron pairing interaction usually used for reproducing the experimental NME of the two-neutrino double-beta ($2\nu\beta\beta$) decay. Our method can repeoduce the experimental $2\nu\beta\beta$ NME for $^{150}$Nd $\rightarrow$ $^{150}$Sm with the quenching axial-vector current coupling without approacing the breaking point of the QRPA. The consistency of QRPA approaches taking different virtual paths under the closure approximation is also discussed, and an extension of the QRPA ground state is proposed.