Quenching of nuclear matrix elements for $0\nu\beta\beta$ decay by chiral two-body currents

TL;DR

This paper investigates how chiral two-body currents affect nuclear matrix elements in neutrinoless double-beta decay, finding that three-body operators cause modest quenching, while two-body operators require renormalization due to divergences.

Contribution

It provides a detailed analysis of the effects of chiral two-body currents on decay matrix elements, highlighting the importance of three-body operators and the need for renormalization of two-body effects.

Findings

Three-body operators quench matrix elements by about 10%.

Two-body operators can cause larger quenching, but are divergent and need renormalization.

Large effects from two-body operators are mitigated when proper renormalization is applied.

Abstract

We examine the leading effects of two-body weak currents from chiral effective field theory on the matrix elements governing neutrinoless double-beta decay. In the closure approximation these effects are generated by the product of a one-body current with a two-body current, yielding both two- and three-body operators. When the three-body operators are considered without approximation, they quench matrix elements by about 10%, less than suggested by prior work, which neglected portions of the operators. The two-body operators, when treated in the standard way, can produce much larger quenching. In a consistent effective field theory, however, these large effects become divergent and must be renormalized by a contact operator, the coefficient of which we cannot determine at present.