Updated constraints on the light-neutrino exchange mechanisms of the 0νββ-decay

The neutrinoless double-beta (0 nu beta beta) decay associated with light neutrino exchange mechanisms, which are due to both left-handed V-A and right-handed V+A leptonic and hadronic currents, is discussed by using the recent progress achieved by the GERDA, EXO and KamlandZen experiments. The upper limits for effective neutrino mass m beta beta and the parameters <lambda > and <eta > characterizing the right handed current mechanisms are deduced from the data on the 0 nu beta beta-decay of Ge-76 and Xe-136 using nuclear matrix elements calculated within the nuclear shell model and quasiparticle random phase approximation and phase-space factors calculated with exact Dirac wave functions with finite nuclear size and electron screening. The careful analysis of upper constraints on effective lepton number violating parameters assumes a competition of the above mechanisms and arbitrary values of involved CP violating phases.