Corrections to the Neutrinoless Double-Beta-Decay Operator in the Shell Model

TL;DR

This paper develops an effective shell-model operator for neutrinoless double-beta decay in 82Se, incorporating short- and long-range correlations through diagrammatic perturbation theory, revealing significant cancellations that impact decay matrix elements.

Contribution

It introduces a systematic perturbative approach to correct the decay operator, highlighting the importance of nonperturbative effects in accurate nuclear matrix element calculations.

Findings

High-energy ladder diagrams suppress short-distance matrix elements.

Long-range corrections are large but tend to cancel each other.

The corrected matrix element is similar to the bare operator due to cancellations.

Abstract

We use diagrammatic perturbation theory to construct an effective shell-model operator for the neutrinoless double-beta decay of 82Se. The starting point is the same Bonn-C nucleon-nucleon interaction that is used to generate the Hamiltonian for recent shell-model calculations of double-beta decay. After first summing high-energy ladder diagrams that account for short-range correlations and then adding diagrams of low order in the G matrix to account for longer-range correlations, we fold the two-body matrix elements of the resulting effective operator with transition densities from the recent shell-model calculation to obtain the overall nuclear matrix element that governs the decay. Although the high-energy ladder diagrams suppress this matrix element at very short distances as expected, they enhance it at distances between one and two fermis, so that their overall effect is small. The corrections due to longer-range physics are large, but cancel one another so that the fully corrected matrix element is comparable to that produced by the bare operator. This cancellation between large and physically distinct low-order terms indicates the importance of a reliable nonperturbative calculation.