Lepton-number conservation and the double-βdecay ofTe128andTe130

Abstract

We consider the classic argument of Pontecorvo that the ratio of $\beta \beta$-decay half-lives for ${}_{}{}^{130}{}_{}{}^{}\mathrm{Te}$ and ${}_{}{}^{128}{}_{}{}^{}\mathrm{Te}$ may indicate violation of lepton number. We believe that the theoretical support for the assumption underlying this argument, equality of the nuclear matrix elements mediating the $2\nu$ $\beta \beta$ decay of these isotopes, is weak due to a significant disparity between the calculated and geochemical absolute rates. If one ignores this inconsistency and attributes the breaking of the ${\gamma }_5$ invariance of the weak leptonic current to a Majorana mass, faithful treatment of the radial dependence of the $0\nu -\beta \beta$-decay operators yields ${〈m^{\mathrm{Maj}}〉}_{\nu }\cong 10$ eV.