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

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.