This paper is addressed to the analysis of the set of observables of the bound-state beta-decay, which can be used for the experimental investigation of contributions of i) interactions beyond the Standard Model (SM) and of ii) the left-handed polari
sation state of antineutrinos. For this aim we calculate the branching ratio, probabilities and angular distributions of probabilities of hydrogen in the hyperfine states and of the proton-electron pair in different spinorial states, induced by left-handed and right-handed hadronic and leptonic currents. The branching ratio of the bound-state beta-decay is calculated by taking into account radiative corrections. We show that the probabilities of the bound-state beta-decay can be good observables for experimental investigations of contributions of interactions beyond the SM, whereas the angular distributions of probabilities are good observables for experimental searches of contributions of the left-handed polarisation state of antineutrinos.
We calculate the continuum- and bound-state l^- decay rates of pionic and kaonic hydrogen in the ground state, where l^- is either the electron or the muon.
We calculate the decay rates lambda_(beta^-_c) and lambda_(beta^-_b) of the continuum- and bound-state beta^- decays for bare 205Hg80+ and 207Tl81+ ions. For the ratio of the decay rates R_(b/c) = lambda_(beta^-_b)/lambda_(beta^-_c) we obtain the val
ues R_(b/c) = 0.161 and R_(b/c) = 0.190 for bare 205Hg80+ and 207Tl81+ ions, respectively. The theoretical value of the ratio R_(b/c) = 0.190 for the decays of 207Tl81+ agrees within 1% of accuracy with the experimental data R^exp_(b/c) = 0.188(18), obtained at GSI. The theoretical ratio R_(b/c) = 0.161 for 205Hg80+ is about 20% smaller than the experimental value R^exp_(b/c) = 0.20(2), measured recently at GSI.
