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 (0\nu\beta\beta) decay. It depends only on the fractional uncertainty in the \nu_e-\nu_e 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 0\nu\beta\beta decay are calculable, it will be impossible to detect neutrino CP violation arising from Majorana phases.