High-precision Q-value measurement and evaluation of nuclear matrix elements for ¹²²Sn and ¹²⁴Sn neutrinoless double beta decays

We have determined the decay energy ( Q value) of the double beta decay of ¹²² 122 Sn with the JYFLTRAP double Penning trap mass spectrometer using the Phase-Imaging Ion Cyclotron Resonance technique. Our new Q value, 373.58(12) keV, agrees with the literature value but is 20 times more precise. We also measured the Q value for the double beta decay of ¹²⁴ 124 Sn with unprecedented precision, 2293.542(83) keV. The Q values of ¹²² 122 Sn and ¹²⁴ 124 Sn were used to calculate precisely the phase-space factors for the neutrinoless double beta ( 0ν β β 0 ν β β ) decay mode of these nuclei. With the phase-space factor and our computed nuclear matrix elements (NMEs) we predict the 0ν β β 0 ν β β -decay half-life of ¹²² 122 Sn based on the recently extracted upper limit of the effective neutrino mass by the KamLAND-Zen experiment. We used three nuclear-structure frameworks to compute the NMEs, namely the proton-neutron quasiparticle random-phase approximation (pnQRPA), the microscopic interacting boson model (IBM-2), and a hybrid model exploiting both the pnQRPA and the nuclear shell model (NSM). We find that including the short-range components enhances the total NME in the IBM-2 model, making it significantly larger than the NMEs calculated with the pnQRPA and hybrid models. Nevertheless, for all models, the obtained half-lives are very long for ¹²² 122 Sn ( ≈ 10²⁷ ≈ 10 27 – 10²⁹ 10 29 years), making the observation of 0ν β β 0 ν β β decay of ¹²² 122 Sn experimentally challenging. On the other hand, the hybrid-model calculated value of the NME for ¹²⁴ 124 Sn goes, interestingly enough, toward those previously computed by the NSM and the ab initio model.