Ordinary muon capture, a perfect probe of the 0νββ decay

Experimental and theoretical studies of neutrinoless double beta (0νββ ) decay are in the forefront of the present particle and nuclear physics. There is an expanding interest in computing the values of the associated nuclear matrix elements (NMEs) since this is crucial for extraction of neutrino properties from the potential discoveries of the running and future underground experiments. In addition, one needs to access the effective value of the weak axial-vector coupling g_A since it has a strong effect on the 0νββ half-lives. The quenching of g_A has thus far been studied through allowed Gamow-Teller β decays, first- and higher-forbidden unique and non-unique β decays, and two-neutrino ββ decays. All these studies probe the value of g_A at low momentum exchanges, whereas for high momentum exchanges, in the range of 100 MeV/c, relevant for 0νββ decay, a new probe, the ordinary muon capture (OMC), can be engaged. New muon-producing facilities have been launched and presently an increasing number of measurements of the OMC properties can be carried out. In this article the OMC as a tool to probe the value of g_A and wave functions of the 0νββ intermediate nucleus is reviewed.