Majorana neutrino mass

We treat 0+ → 2+ 0νββ decays taking into account recoil corrections to the nuclear currents. The decay probability can be written as a quadratic form of the effective coupling constants of the right-handed leptonic currents and the effective neutrino mass. We calculate the nuclear matrix elements for the 0+ → 21 0νββ decays of 76Ge and 100Mo, and demonstrate that the relative sensitivities of 0+ → 2+ decays to the neutrino mass and the right-handed currents are comparable to those of 0+ → 0+ decays. The neutrinoless double beta (0νββ) decay can take place through an exchange of neutrino between two quarks in nulei if the electron neutrino is a Majorana particle and has a nonvanishing mass and/or right-handed couplings [1–3]. There may be other possible mechanisms such as those involving supersymmetric particles which also cause the decay of two neutrons into two protons and two electrons [4–6]. In the present work, however, we restrict ourselves to the conventional two-nucleon and ∆ mechanisms of 0νββ decay through light Majorana neutrino exchange. From the analises of experimental data on 0 → 0 0νββ decays, stringent limits on the effective neutrino mass and the effective coupling constants of the right-handed leptonic currents have been deduced (see e.g. [3,7] and the references quoted therein). On the other hand it still seems to be believed widely that 0 → 2 0νββ decays are sensitive only to the right-handed currents. In view of the theorem that the electron neutrino should have a nonvanishing Majorana mass if 0νββ decay occurs anyway [8–10], an observation of 0νββ decay due to right-handed interactions would certainly mean also a nonvanishing Majorana mass of the electron neutrino. The purpose of the present work is, however, not to investigate the role of the 1 E-mail: [email protected] Preprint submitted to Elsevier Preprint 1 February 2008 Majorana neutrino mass in such a sense, but to demonstrate that it causes 0 → 2 0νββ decays directly. A direct contribution of the neutrino mass to 0 → 2 0νββ decays was considered in [3] taking into account the nuclear recoil currents, and the inverse half-life was given as [τ 0ν 1/2(0 + → 2+)]−1 =F1+(Z1+) + F1−(Z1−) + F2+(Z2+) + F2−(Z2−) , (1) where Fj± (j = 1, 2) are the phase space integrals and Z1± =Mλ〈λ〉 −Mη〈η〉 ±Mm 〈mν〉 me , Z2± =M ′ η〈η〉 ±Mm 〈mν〉 me , (2) with the electron mass me and