Abstract
We re-analyze the compatibility of the claimed observation of neutrinoless double beta decay ($0\nu\beta\beta$) in $^{76}$Ge with the new limits on the half-life of $^{136}$Xe from EXO-200 and KamLAND-Zen. Including recent calculations of the nuclear matrix elements (NMEs), we show that while the claim in $^{76}$Ge is still compatible with the individual limits from $^{136}$Xe, it is inconsistent with the KamLAND-Zen+EXO-200 combined limit for all but one NME calculations. After imposing the most stringent upper limit on the sum of light neutrino masses from Planck, we find that the canonical light neutrino contribution cannot satisfy the claimed $0\nu\beta\beta$ signature or saturate the current limit, irrespective of the NME uncertainties. However, inclusion of the heavy neutrino contributions, arising naturally in TeV-scale Left-Right symmetric models, can saturate the current limit of $0\nu\beta\beta$. In a type-II seesaw framework, this imposes a lower limit on the lightest neutrino mass. Depending on the mass hierarchy, we obtain this limit to be in the range of 0.07 - 4 meV for a typical choice of the right-handed (RH) gauge boson and RH neutrino masses relevant for their collider searches. Using the $0\nu\beta\beta$ bounds, we also derive correlated constraints in the RH sector, complimentary to those from the LHC.
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