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

TL;DR

This paper compares two decay path methods for calculating the nuclear matrix element of neutrinoless double-beta decay using QRPA, revealing their differences and proposing a modified approach for consistency.

Contribution

It introduces a modified QRPA method incorporating proton-neutron pairing to achieve consistent nuclear matrix elements across decay paths.

Findings

The two decay path methods yield inequivalent NMEs due to different many-body correlations.

Introducing proton-neutron pairing interaction aligns the NMEs from both methods.

The modified approach is validated as a consistent calculation method.

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.