Majorana phases beyond neutrinoless double beta decay

The ν_M SM is defined as the SM extended to include dimension-5 operators. In this model neutrino masses violate lepton number, and two parameters of the lepton mixing matrix, the Majorana phases, are yet to be constrained. One combination of these phases and the neutrino masses, often denoted by m_ee, is probed by neutrinoless double beta decays (0νββ). We explore what information may be obtained beyond 0νββ, and how it depends on the lightest neutrino mass. We point out that with current central values of the mixing parameters, ∆L_e = 2 and ∆L_e = ∆L_μ = 1 (or ∆L_e = 2 and ∆L_μ = 2) processes cannot simultaneously vanish, providing a no-lose theorem, in principle, for excluding the ν_M SM, even in the case of normal mass ordering.