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We use diagrammatic many-body perturbation theory in combination withlow-momentum interactions derived from chiral effective field theory toconstruct effective shell-model transition operators for the neutrinolessdouble-beta decay of 76Ge and 82Se. We include all unfolded diagrams to first-and second-order in the interaction and all singly folded diagrams that can beconstructed from them. The resulting effective operator, which accounts forphysics outside the shell-model space, increases the nuclear matrix element byabout 20% in 76Ge and 30% in 82Se.

Effective double-beta-decay operator for 76Ge and 82Se