Nucleon decays into three leptons: noncontact contributions

TL;DR

This work systematically analyzes noncontact contributions from dimension-6 baryon-number-violating operators in the LEFT framework to nucleon decays into three leptons with $ΔF_L=1$. By matching quark-level operators to chiral perturbation theory and computing leading-order diagrams, the authors derive decay widths and robust bounds on partial lifetimes using existing two-body decay limits and meson-lepton branching ratios. They find strong, operator-dependent bounds, with photon- and four-fermion-mediated channels typically yielding lifetimes far beyond current experimental reach, while certain resonance-enhanced meson channels with muons can approach present limits. The results significantly improve prior estimates and guide future exploration of higher-dimension (e.g., dim-9) contact contributions.

Abstract

We investigate baryon number violating (BNV) nucleon decays into three leptons from noncontact contributions that are induced by dimension-6 (dim-6) BNV operators in low-energy effective field theory (LEFT) with an exchange of a baryon, meson, lepton, or photon field. We systematically classify all these processes that change lepton flavor by one unit and formulate their decay widths in terms of the dim-6 LEFT Wilson coefficients. By applying constraints on these Wilson coefficients derived from current experimental limits on BNV two-body nucleon decays, we obtain stringent and robust bounds on the rates of these triple-lepton modes. These bounds vary significantly from one dim-6 operator to another under consideration. Our results for the $Δ(B-L)=0$ modes differ by several orders of magnitude from previous phase-space estimates in the literature, thereby providing a more reliable assessment of their potential occurrence. In addition, we provide improved bounds on $Δ(B+L)=0$ modes compared to the existing experimental limits.