Impact of the quenching of $g_{\rm A}$ on the sensitivity of $0νββ$ experiments

Abstract

Detection of the neutrinoless $ββ$ ($0νββ$) decay is of high priority in the particle- and neutrino-physics communities. The detectability of this decay mode is strongly influenced by the value of the weak axial-vector coupling constant $g_{\rm A}$. The recent nuclear-model analyses of $β$ and $ββ$ decays suggest that the value of $g_{\rm A}$ could be dramatically quenched, reaching ratios of $g^{\rm free}_{\rm A}/g_{\rm A}\approx 4$, where $g^{\rm free}_{\rm A}=1.27$ is the free, neutron-decay, value of $g_{\rm A}$. The effects of this quenching appear devastating for the sensitivity of the present and future $0νββ$ experiments since the 4$th$ power of this ratio scales the $0νββ$ half-lives. This, in turn, could lead to some two orders of magnitude less sensitivity for the $0νββ$ experiments. In the present Letter it is shown that by using a consistent approach to both the two-neutrino $ββ$ and $0νββ$ decays by the proton-neutron quasiparticle random-phase approximation (pnQRPA), the feared two-orders-of-magnitude reduction in the sensitivity of the $0νββ$ experiments actually shrinks to a reduction by factors in the range $2-6$. This certainly has dramatic consequences for the potential to detect the $0νββ$ decay.