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Two-neutrino $ββ$ decay to excited states at next-to-leading order

Daniel Castillo, Dorian Frycz, Beatriz Benavente, Javier Menéndez

Abstract

We study two-neutrino double-beta decay ($2νββ$) into first-excited $0^+_2$ states of nuclei used in $ββ$ decay experiments, including $^{76}$Ge, $^{82}$Se, $^{130}$Te, and $^{136}$Xe. We calculate the corresponding nuclear matrix elements (NMEs) within the nuclear shell model, using various Hamiltonians that describe well the spectroscopy of the initial and final nuclei. We evaluate the next-to-leading order (NLO) long-range NMEs recently introduced within chiral effective field theory, keeping three terms in the expansion of the energy denominator. In most cases, NLO contributions to the half-life are below 5%, but they can significantly increase due to cancellations in the leading-order Gamow-Teller NME. A detailed analysis in terms of nuclear deformation, including triaxiality, indicates that larger deformation differences between the initial and final states generally lead to smaller NMEs, but the seniority structure of the states also plays a relevant role. The lower range of our predicted half-lives, with uncertainties dominated by the nuclear Hamiltonian used, are slightly longer than the current experimental limit in $^{76}$Ge and consistent with the very recent half-life indication in $^{82}$Se.

Two-neutrino $ββ$ decay to excited states at next-to-leading order

Abstract

We study two-neutrino double-beta decay () into first-excited states of nuclei used in decay experiments, including Ge, Se, Te, and Xe. We calculate the corresponding nuclear matrix elements (NMEs) within the nuclear shell model, using various Hamiltonians that describe well the spectroscopy of the initial and final nuclei. We evaluate the next-to-leading order (NLO) long-range NMEs recently introduced within chiral effective field theory, keeping three terms in the expansion of the energy denominator. In most cases, NLO contributions to the half-life are below 5%, but they can significantly increase due to cancellations in the leading-order Gamow-Teller NME. A detailed analysis in terms of nuclear deformation, including triaxiality, indicates that larger deformation differences between the initial and final states generally lead to smaller NMEs, but the seniority structure of the states also plays a relevant role. The lower range of our predicted half-lives, with uncertainties dominated by the nuclear Hamiltonian used, are slightly longer than the current experimental limit in Ge and consistent with the very recent half-life indication in Se.

Paper Structure

This paper contains 8 sections, 11 equations, 3 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Two-neutrino $\beta\beta$ decay
  3. Nuclear Shell Model
  4. Results and Discussions
  5. $2\nu\beta\beta$ decay half-lives
  6. $2\nu\beta\beta$, deformation and nuclear structure
  7. Lepton expansion and NLO contributions
  8. Summary

Figures (3)

  • Figure 1: $2\nu\beta\beta$ half-lives for all $0^+_{\rm gs}\xrightarrow[]{}0^+_{2}$ decays studied in this work, besides $0^+_{\rm gs}\xrightarrow[]{}0^+_{\rm gs}$ for $^{124}$Sn. We use various nuclear interactions (indicated by bars with different colors) in each mass region. The associated uncertainties span the results obtained with bare and effective GT operators and the range of quenching factors $q_{\beta}-q_{\beta\beta}$ ($1-q_{\beta\beta}$) for the bare (effective) operator (see text). The total uncertainty (black bars) encompasses all our predictions. They are compared to 90% confidence level experimental limits Arnquist24Arnold20Adams21DAWSON2008167AlKharusi_2023ASAKURA2016171PANDAX-4TBakalyarov:2002wu (horizontal bars with arrows), the $^{82}$Se measurement indication at 1$\sigma$Barabash:2025bxa (wide band), and other NSM predictions Coraggio24PhysRevC.87.014320gerda_collaboration_2_2015horoi_shell_2016Jokiniemi:2022yfr (brown bars). Limits for $^{48}$Ca, $^{124}$Sn are below the scale.
  • Figure 2: Deformation parameters $\beta_2,\gamma$ (circles) with 1$\sigma$ fluctuations (ellipses) for $2\nu\beta\beta$$0^+_{\rm gs}\xrightarrow[]{}0^+_{2}$ initial (red) and final (blue) states. Top panels: results for the shell-model interactions giving the longest (RG) and shortest (GCN2850) $^{76}$Ge half-life. Bottom panels: results for the interactions giving shortest (JUN45) and longest (JJ4BB) $^{82}$Se half-life.
  • Figure 3: Leading-order $2\nu\beta\beta$ NSM NMEs as a function of the difference of deformation ($\delta_\text{def}$) for the $0^+_{\rm gs}\rightarrow0^+_{2}$ decays of $^{76}$Ge (blue) and $^{82}$Se (red). Results for the GCN2850 (squares), JUN45 (circles), JJ4BB (up triangles), and RG (down triangles) shell-model Hamiltonians. The error bars cover all our results with bare and effective GT operators.