Double beta decay versus cosmology: Majorana CP phases and nuclear matrix elements

We discuss the relation between the absolute neutrino mass scale, the effective mass measured in neutrinoless double beta decay, and the Majorana CP phases. Emphasis is placed on estimating the upper bound on the nuclear matrix element entering calculations of the double beta decay half life. Consequently, one of the Majorana CP phases can be constrained when combining the claimed evidence for neutrinoless double beta decay with the neutrino mass bound from cosmology. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] 1 Over the past years much effort has been invested to probe leptonic mixing with increasing accuracy, and, in fact, a unique picture is evolving from the precise measurements of neutrino oscillation probabilities. For a full construction of the mixing matrix, however, knowledge about CP violating phases is necessary. To describe leptonic mixing one can always work in a basis where the charged lepton Yukawa matrix is diagonal. In this case the neutrino mass matrix m can be written in the flavor basis as m = UmU , (1) with m = diag(m1, m2, m3), and the Maki-Nakagawa-Sakata (MNS) matrix U , which contains three mixing angles and one CP violating Dirac phase. The determination of the mixing angles is subject to neutrino oscillation experiments, as is (at least in principle) the determination of the Dirac phase the leptonic analogue of the CKM phase in the quark sector. Three of the mixing angles can be identified with the maximal, large and small observables measured in atmospheric, solar and reactor neutrino oscillations, respectively [1]. Important information on the Dirac phase can be expected from a combination of future long-baseline experiments [2], and ultimately, from a neutrino factory [3]. If the neutrino is of Majorana type, two more phases enter, though. The determination of these Majorana phases is, in fact, the most challenging task in the reconstruction of the fundamental parameters of the Standard Model particle content. In general, U can be written as U = V · diag(1, e12, e23), (2) where V is parametrized in the standard CKM form,