Nuclear Matrix Elements for β and ββ Decays and Quenching of the Weak Coupling gA in QRPA

Nuclear matrix elements (NMEs) for double beta decays (DBDs) are crucial for studying neutrino mass and neutrino properties of particle physics interest. The major components of the DBD NMEs are axial-vector NMEs associated with spin isospin transition operators. In this work it is discussed how absolute values for the NMEs are reduced (quenched) with respect to those for the model NMEs. The reduction is discussed in terms of the renormalized (quenched) axial-vector coupling gAeff in unit of gA for free nucleon. Recent experimental studies at RCNP on single and double β NMEs relevant to DBDs are briefly discussed. The axial-vector single β NMEs are shown to be reduced by the renormalization (quenching factor) factor gAeff/gA≈ 0.5–0.6 with respect to the QRPA (Quasi particle Random Phase Approximation) model NMEs due to non-nucleonic and nuclear medium effects which are not explicitly included in the model. Two-neutrino axial-vector DBD NMEs are reduced much with respect to the QP (Quasi Particle) NMEs, and are reproduced by the FSQP (Fermi Surface Quasi Particle) model NMEs. Impact of the reduction of the axial-vector NMEs on the DBD NMEs and the DBD experiments is briefly discussed.