Two decay paths for calculation of nuclear matrix element of neutrinoless double-beta decay using quasiparticle random-phase approximation

Abstract

It is possible to employ virtual decay paths, including two-particle transfer, to calculate the nuclear matrix element of neutrinoless double-beta decay under the closure approximation, in addition to the true double-beta path. In the quasiparticle random-phase approximation (QRPA) approach, it is necessary to introduce the product wave functions of the like-particle and proton-neutron QRPA ground states, for achieving consistency between the calculations of the true and virtual paths. Using these different paths, the problem of whether or not these two methods give equivalent nuclear matrix elements (NME) is investigated. It is found that the two results are inequivalent, resulting from the different many-body correlations included in the two QRPA methods, i.e., the use of the product wave functions alone is not sufficient. The author proposes introduction of the proton-neutron pairing interaction with an adequate strength in the double-beta-path method, which carries less many-body correlations without this supplemental interaction, for obtaining the NME equivalent to that of the two-particle-transfer-path method. The validity of the proposed modified approach is examined.

16 pages, 4 figures

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Cited by in corpus (7)

• Status and Future of Nuclear Matrix Elements for Neutrinoless Double-Beta Decay: A Review
• Neutrinoless double beta decay and neutrino mass
• Precision Analysis of the ${}^{136}$Xe Two-Neutrino $\beta \beta$ Spectrum in KamLAND-Zen and Its Impact on the Quenching of Nuclear Matrix Elements
• Physical features of strength of isoscalar pairing interaction determined by relation between double charge change and double pair transfer
• Isoscalar pairing interaction for the quasiparticle random-phase approximation approach to double-$\beta$ and $\beta$ decays
• Examinations of the consistency of the quasiparticle random-phase approximation approach to double-$\beta$ decay of ${}^{48}$Ca
• Investigation of the cause of the discrepancies between calculated running sums for nuclear matrix elements of two-neutrino double-$\beta$ decay