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

Abstract

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 $g_{\mathrm{A}}$ could be dramatically quenched, reaching ratios of $g_{\mathrm{A}}^{\mathrm{free}}/g_{\mathrm{A}}\approx 4$, where $g_{\mathrm{A}}^{\mathrm{free}}=1.27$ 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.

5 pages, 3 figures, published in PRC

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• Perturbative Approach to Effective Shell-Model Hamiltonians and Operators
• $\mathcal{F}t$ values of the mirror $\beta$ transitions and the weak magnetism induced current in allowed nuclear $\beta$ decay
• Nuclear matrix elements for neutrinoless double beta decays and spin-dipole giant resonances
• Quenching of Gamow-Teller strengths and two particle -- two hole configurations
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• The Majorana Demonstrator's Search for Double-Beta Decay of ${}^{76}$Ge to Excited States of ${}^{76}$Se
• $g_{\mathrm{A}}$-sensitive $\beta$ spectral shapes in the mass $A=86-99$ region assessed by the nuclear shell model
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• The MONUMENT Experiment: Ordinary Muon Capture studies for 0$\nu \beta \beta$ decay
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• Systematic shell-model analysis of $2\nu \beta \beta$ decay of ${}^{76}$Ge and ${}^{96}$Zr to the ground and excited states of ${}^{76}$Se and ${}^{96}$Mo