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M ay 2 00 2 MADPH-02-1273 UPR-0994 T No-go for detecting CP violation via neutrinoless double beta decay

We present a necessary condition on the solar oscillation amplitude for CP violation to be detectable through neutrinoless double beta (0νββ) decay. It depends only on the fractional uncertainty in the νe–νe element of the neutrino mass matrix. We demonstrate that even under very optimistic assumptions about the sensitivity of future experiments to the absolute neutrino mass scale, and on the precision with which nuclear matrix elements that contribute to 0νββ decay are calculable, it will be impossible to detect neutrino CP violation arising from Majorana phases. If neutrinos are Majorana, the potentiality of detecting CP violation using neutrinoless double beta decay exists [1]. We consider this in a scenario wherein there are exactly three left-handed neutrino states with Majorana masses. We derive a necessary condition that involves the solar oscillation amplitude and the uncertainty in the νe–νe element of the neutrino mass matrix that must be satisfied for CP violation to be detectable. Assuming that this condition is satisfied and allowing for experimental and theoretical uncertainties that are unrealistically small in some cases, we show that it will not be possible to detect neutrino CP violation through this process. The charged-current eigenstates are related to the mass eigenstates by a unitary transformation