Impact of the quenching of $g_A$ 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 $g_A$. The recent nuclear-model analyses of $\beta$ and $\beta \beta$ decays suggest that the value of $g_A$ could be dramatically quenched, reaching ratios of $g_A^{\mathrm{free}}/g_A\approx 4$, where $g_A^{\mathrm{free}}=1.27$ is the free, neutron-decay, value of $g_A$. The effects of this quenching appear devastating for the sensitivity of the present and future $0\nu \beta \beta$ experiments since the fourth 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 article 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, 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 $2\text{–}6$. This certainly has dramatic consequences for the potential to detect the $0\nu \beta \beta$ decay.

Figure 1

Effective values of $g_A$ in different theoretical approaches for the nuclear mass range $A=62\text{–}136$. For more information see the text.

Figure 2

Values of the $0\nu \beta \beta$ NME (3) as functions of $g_A$ for the decays of ${}^{76}\mathrm{Ge}$, ${}^{96}\mathrm{Zr}$, ${}^{100}\mathrm{Mo}$, ${}^{130}\mathrm{Te}$, and ${}^{136}\mathrm{Xe}$.

Figure 3

Values of the reduced half-lives $F^{\left(0\nu \right)}$ as functions of $g_A$ for the decays of ${}^{76}\mathrm{Ge}$, ${}^{96}\mathrm{Zr}$, ${}^{100}\mathrm{Mo}$, ${}^{130}\mathrm{Te}$, and ${}^{136}\mathrm{Xe}$.