Abstract: The study of two-neutrino double-beta decay ($2\nu\beta\beta$), an allowed process within the Standard Model in which two neutrons convert into two protons with the emission of two electrons and two antineutrinos, provides a unique window into nuclear structure and plays a crucial role in constraining theoretical descriptions of double-beta decay [1]. In particular, it offers valuable benchmarks for the nuclear matrix elements (NMEs) that also govern neutrinoless double-beta decay ($0\nu\beta\beta$), a hypothetical process beyond the Standard Model of particle physics (BSM) in which no antineutrinos are emitted. The observation of $0\nu\beta\beta$ would have important implications for particle physics, shedding light on open questions such as the origin of neutrino masses and the matter–antimatter asymmetry of the Universe [2].

In this talk, we present new predictions for $2\nu\beta\beta$ decay half-lives to the first excited $0_2^+$ states in nuclei of experimental interest, including $^{76}$Ge, $^{82}$Se, $^{130}$Te, and $^{136}$Xe. A major source of theoretical uncertainty in these calculations arises from the NMEs, on which the decay half-lives depend quadratically. We compute the NMEs within the nuclear shell-model framework, including contributions up to next-to-leading order in chiral effective field theory [3] and incorporating important corrections from the lepton energy expansion [4]. Finally, we discuss how uncertainties in the NMEs are connected to key features of nuclear structure, such as nuclear deformation [5]. We show that larger deformation differences between the initial and final states yield to smaller NMEs. 

References:

[1] J. Engel, J. Menéndez, Rep. Prog. Phys. 80 (2017) 046301. 

[2] M. Agostini, G. Benato, J. A. Detwiler, J. Menéndez, F. Vissani, Rev. Mod. Phys. 95 (2023) 025002. 

[3] S. el Morabit, R. Bouabid, V. Cirigliano, J. de Vries, L. Gráf, E. Mereghetti, J. High Ener. Phys. 06 (2025).

[4] F. Simkovic, R. Dvornický, D. Stefánik, A. Faessler, Phys. Rev. C 97 (2018) 034315. 

[5] T. R. Rodríguez, G. Martínez-Pinedo, Phys. Rev. Lett. 105 (2010) 252503.