The contribution of light Majorana neutrinos to neutrinoless double beta decay and cosmology

Cosmology is making impressive progress and it is producing stringent bounds on the sum of the neutrino masses {\Sigma}, a parameter of great importance for the current laboratory experiments. In this letter, we exploit the potential relevance of the analysis of Palanque-Delabrouille et al. [JCAP 1502, 045 (2015)] to the neutrinoless double beta decay (0{\nu}{\beta}{\beta}) search. This analysis indicates small values for the lightest neutrino mass, since the authors find {\Sigma}<84 meV at 1{\sigma} C. L., and provides a 1{\sigma} preference for the normal hierarchy. The allowed values for the Majorana effective mass, probed by 0{\nu}{\beta}{\beta}, turn out to be<75meV at 3{\sigma}C.L. and lower down to less than 20meV at 1{\sigma}C.L.. If this indication is confirmed, the impact on the 0{\nu}{\beta}{\beta} experiments will be tremendous since the possibility of detecting a signal will be out of the reach of the next generation of experiments.


Introduction
Neutrinoless double beta decay (0νββ) [1] is a key tool to address some of the major outstanding issues in particle physics, such as lepton number conservation and the Majorana nature of neutrinos. Its discovery could also provide precious information on neutrino masses [2]. The 0νββ half-life can be factorized as: where G 0ν is the phase-space factor (PSF), M 0ν is the nuclear matrix element (NME) and f is due to the physics beyond the Standard Model. Many different mechanisms could generate the 0νββ decay. If the ordinary neutrino exchange dominates, the "Majorana effective mass": is a convenient parameter to study the process. U ei are the elements of the PMNS mixing matrix, m i are the masses of the individual ν i and m e is the electron mass. The knowledge of the oscillation parameters [3] allows to constrain m ββ . However, Majorana phases are unknown and cannot be probed by oscillations, thus they must be left free to vary in a conservative analysis of m ββ .

Bounds on the Majorana mass
An experimental limit on the 0νββ half-life can be translated into a limit on m ββ by reversing Eq. (1) and by using appropriate PSFs [4] and NMEs [12]. At present, the most recent and competitive bounds on 0νββ come from 130 Te, 76 Ge and 136 Xe (t  Fig. 1, where the allowed regions for m ββ are plotted as a function of the lightest neutrino mass for both the mass hierarchies [9,10]. However, the theoretical uncertainty on NMEs is very large. Present and future scenarios could actually be worse than what is depicted by the horizontal bands in the plot. As it appears from Fig. 2, the main reasons for this fact are not the differences among the available theoretical models (QRPA [11], IBM-2 [12], ISM [13], . . . ). Instead, the possible downward renormalization (i. e. reduction) of the value of the axial vector coupling constant g A in the nuclear medium has (potentially) a much higher impact, as highlighted in right panel of Fig. 2. In particular, a few cases should be considered for the value of g A , as shown in the figure and as discussed in Ref. [10].

Recent results from cosmology and implications for the 0νββ search
One of the most recent limits from cosmological surveys on the sum of the active neutrino masses (Σ) is so stringent, that it better agrees with the normal hierarchy (N H) spectrum, rather than with inverted (IH) one [14]. Similar results are obtained in newer and independent analyses (see Ref. [2] for further details). In particular, the limits reported in Ref. [14] imply: Σ < 84 meV (1σ C. L.) Σ < 146 meV (2σ C. L.) Σ < 208 meV (3σ C. L.).
Results on Σ from cosmological surveys have been somewhat controversial in the past and thus they have to be taken with due caution. However, the recent developments show constant improvements in the systematics evaluation. It is possible to combine the limit on Σ with the constraints on m ββ coming from oscillations, according to the procedure outlined in Ref. [15]. The result is shown in the right panel of Fig. 1, where it can be seen that the oscillation parameters induce only minor uncertainties on the  Figure 2. Uncertainty of the current m ββ bound from 136 Xe [8]. (Left) Dependence on the NME (QRPA [11], IBM-2 [12], ISM [13]). (Right) Dependence on the value of the axial vector coupling constant. See Ref. [2] for an extensive discussion.
expected value of m ββ . They are responsible for the widening of the allowed contours in the upper, lower and left sides of the picture. The boundaries in the rightmost regions are due to the information from cosmology and are cut at various confidence levels. It is notable that at 1σ, due to the exclusion of the IH, the set of plausible values of m ββ is highly restricted. The next generation of 0νββ experiments is expected to probe the upper values of the predicted IH region, with sensitivities for m ββ of a few tens of meV (assuming no quenching on g A ) [10].
In order to probe m ββ values compatible with the current tight bounds on Σ, assuming the correctness of the new cosmological analyses, multi-ton scale detectors are needed [15,16]. Nevertheless, a signal from the next generation of experiments will either imply a mechanism different from the light Majorana neutrino exchange as mediator for the 0νββ process, or it will disprove some assumptions of present cosmological models.