Impact of the quenching of $g_{\mathrm{A}}$ on the sensitivity of $0\nu \beta \beta$ experiments

Detection of the neutrinoless $\beta \beta$ ($0\nu \beta \beta$) 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 $g_{\mathrm{A}}$. The recent nuclear-model analyses of $\beta$ and $\beta \beta$ decays suggest that the value of $g_{\rm A}$couldbedramaticallyquenched,reachingratiosof$g^{\rm free}{\rm A}/g{\rm A}\approx 4$,where$g^{\rm free}_{\rm A}=1.27$ is the free, neutron-decay, value of $g_{\mathrm{A}}$. The effects of this quenching appear devastating for the sensitivity of the present and future $0\nu \beta \beta$ experiments since the 4$th$ power of this ratio scales the $0\nu \beta \beta$ half-lives. This, in turn, could lead to some two orders of magnitude less sensitivity for the $0\nu \beta \beta$ experiments. In the present Letter it is shown that by using a consistent approach to both the two-neutrino $\beta \beta$ and $0\nu \beta \beta$ decays by the proton-neutron quasiparticle random-phase approximation (pnQRPA), the feared two-orders-of-magnitude reduction in the sensitivity of the $0\nu \beta \beta$ experiments actually shrinks to a reduction by factors in the range $2-6$. This certainly has dramatic consequences for the potential to detect the $0\nu \beta \beta$ decay.