Half-life of $^{136}$Xe for neutrinoless double-$β$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$β$ decay modes
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915485191241728 |
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| author | Terasaki, J. Civitarese, O. |
| author_facet | Terasaki, J. Civitarese, O. |
| contents | The upper limit on the mass of the Majorana neutrino, extracted from the limits on the nonobservation of the neutrinoless double-$β$ ($0νββ$) decay, is hampered by uncertainties in the matrix elements of the transition operators. Recently, we have shown that the values of the effective axial-vector current coupling constants ($g_A^\textrm{eff}$) for the $0νββ$ and the two-neutrino double-$β$ decays are close. This striking result was obtained for the first time by including vertex corrections and two-body currents in these matrix elements. In this letter, we calculate the half-life for the $0νββ$ decay ($T_{1/2}^{0ν}$) of $^{136}$Xe using this closeness and show the convergence of the half-life with respect to the variation of the method to determine $g_A^\textrm{eff}$. The closeness of the $g_A^\textrm{eff}$ of the two decay modes plays a decisive role in predicting $T_{1/2}^{0ν}$. The appropriate value of $g_A^\textrm{eff}$ depends on the assumptions made for the sectors of the nuclear structure and transition operators of the calculations within the perturbation scheme. The value $g_A^\textrm{eff}\approx 1$ is obtained when the SkM$^\ast$ is used to describe the nuclear structure component, while a smaller value of $g_A^\textrm{eff}$ is obtained by applying a less realistic interaction like the SGII one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_23239 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Half-life of $^{136}$Xe for neutrinoless double-$β$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$β$ decay modes Terasaki, J. Civitarese, O. Nuclear Theory Nuclear Experiment The upper limit on the mass of the Majorana neutrino, extracted from the limits on the nonobservation of the neutrinoless double-$β$ ($0νββ$) decay, is hampered by uncertainties in the matrix elements of the transition operators. Recently, we have shown that the values of the effective axial-vector current coupling constants ($g_A^\textrm{eff}$) for the $0νββ$ and the two-neutrino double-$β$ decays are close. This striking result was obtained for the first time by including vertex corrections and two-body currents in these matrix elements. In this letter, we calculate the half-life for the $0νββ$ decay ($T_{1/2}^{0ν}$) of $^{136}$Xe using this closeness and show the convergence of the half-life with respect to the variation of the method to determine $g_A^\textrm{eff}$. The closeness of the $g_A^\textrm{eff}$ of the two decay modes plays a decisive role in predicting $T_{1/2}^{0ν}$. The appropriate value of $g_A^\textrm{eff}$ depends on the assumptions made for the sectors of the nuclear structure and transition operators of the calculations within the perturbation scheme. The value $g_A^\textrm{eff}\approx 1$ is obtained when the SkM$^\ast$ is used to describe the nuclear structure component, while a smaller value of $g_A^\textrm{eff}$ is obtained by applying a less realistic interaction like the SGII one. |
| title | Half-life of $^{136}$Xe for neutrinoless double-$β$ decay calculated with effective axial-vector current coupling unified for two-neurtino and neutrinoless double-$β$ decay modes |
| topic | Nuclear Theory Nuclear Experiment |
| url | https://arxiv.org/abs/2506.23239 |