Effective Operator for Neutrinoless Double Beta Decay

After briefly discussing the importance of neutrinoless double-beta-decay searches to particle physics, I sketch the derivation of the relevant nuclear operator and review the nuclear-structure methods --- the shell-model and the QRPA --- used to evaluate its matrix element. I then consider a shell-model calculation of the matrix element in 82Se and show how to include corrections to the bare nuclear double-beta-decay operator through diagramatic perturbation theory. First I sum two-body ladders to obtain the effects of short-range correlations, and then evaluate the lowest-order corrections to the ladder sums. I argue that these corrections add QRPA-like physics to the shell model, and that a proper renormalization of the shell-model operator may bring the matrix elements closer to those of the QRPA.