Neutrinoless $\beta\beta$ decay nuclear matrix elements complete up to N$^2$LO in heavy nuclei
| Autor: | Castillo, Daniel, Jokiniemi, Lotta, Soriano, Pablo, Menéndez, Javier |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We evaluate all nuclear matrix elements (NMEs) up to next-to-next-to leading order (N$^2$LO) in chiral effective field theory ($\chi$EFT) for the neutrinoless double-beta ($0\nu\beta\beta$) decay of the nuclei most relevant for experiments, including $^{76}$Ge, $^{100}$Mo, and $^{136}$Xe. We use the proton-neutron quasiparticle random-phase approximation (pnQRPA) and the nuclear shell model to calculate the N$^2$LO NMEs from very low-momentum (ultrasoft) neutrinos and from loop diagrams usually neglected in $0\nu\beta\beta$ studies. Our results indicate that, separately, the new N$^2$LO NMEs can have up to a $15\%$ impact on the total NME, but cancellations lead to an overall N$^2$LO contribution centered around $-5\%$ for the shell model and $+10\%$ for the pnQRPA, with sizable uncertainties due to the short-range nature of the loop NMEs. The sign discrepancy between many-body methods is common to all studied nuclei and points to the different behaviour of the intermediate states of the $0\nu\beta\beta$ decay. In addition, our results support the $\chi$EFT prediction that the ultrasoft NME is closely related to contributions usually referred to as ``beyond the closure approximation''. Comment: 10 pages, 4 figures, and 2 tables |
| Databáze: | arXiv |
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