Constraining neutrino mass from neutrinoless double beta decay

We study the implications of the recent results on neutrinoless double beta decay ($0\nu \beta \beta$) from GERDA-I (${}^{76}\mathrm{Ge}$) and $\mathrm{KamLAND}\mathrm{\text{−}}\mathrm{Zen}+\mathrm{EXO}\mathrm{\text{−}}200$ (${}^{136}\mathrm{Xe}$) and the upper limit on the sum of light neutrino masses from Planck. We show that the upper limits on the effective neutrino mass from ${}^{136}\mathrm{Xe}$ are stronger than those from ${}^{76}\mathrm{Ge}$ for most of the recent calculations of the nuclear matrix elements (NMEs). We also analyze the compatibility of these limits with the claimed observation in ${}^{76}\mathrm{Ge}$ and show that while the updated claim value is still compatible with the recent GERDA limit as well as the individual ${}^{136}\mathrm{Xe}$ limits for a few NME calculations, it is inconsistent with the combined ${}^{136}\mathrm{Xe}$ limit for all but one NME. Imposing the most stringent limit from Planck, we find that the canonical light neutrino contribution cannot saturate the current limit, irrespective of the NME uncertainties. Saturation can be reached by inclusion of the right-handed (RH) neutrino contributions in TeV-scale left-right symmetric models with type-II seesaw. This imposes a lower limit on the lightest neutrino mass. Using the $0\nu \beta \beta$ bounds, we also derive correlated constraints in the RH sector, complimentary to those from direct searches at the LHC.

Figure 1

$0\nu \beta \beta$ predictions in ${}^{76}\mathrm{Ge}$ (left) and ${}^{136}\mathrm{Xe}$ (right) due to light neutrino exchange. See text for details.

Figure 2

The $\mathrm{\text{light}}+\mathrm{\text{heavy}}$ neutrino contribution to $0\nu \beta \beta$ in ${}^{76}\mathrm{Ge}$ (left) and ${}^{136}\mathrm{Xe}$ (right) for both NH and IH, and with type-II seesaw dominance. Here $(M_{W_R},M_{N_{>}})=(3,1)\mathrm{TeV}$. The vertical and horizontal lines are the same as in Fig. 1.

Figure 3

The $0\nu \beta \beta$ constraints in the $M_{W_R}\mathrm{\text{−}}{M}_{N_{<}}$ plane, along with the direct search limits from CMS and ATLAS. The brown (dashed) region saturates the $\mathrm{KLZ}+\mathrm{EXO}$ combined limit, and the grey (white) region is excluded (allowed).