Baryon-number-violating nucleon decays into a dark photon particle

Baryon-number-violating (BNV) nucleon decays into a light new particle represent an exciting yet experimentally unexplored frontier. In this work, we systematically study nucleon decays into a dark photon using a low-energy effective field theory extended with a dark photon $X$, referred to as $X$LEFT. We first construct a complete set of leading-order BNV $X$LEFT operators and then perform a systematic matching onto the chiral perturbation theory for operators involving light $u,d,s$ quarks that dominantly contribute to nucleon decays. Within the chiral framework, we derive general expressions for the decay widths of both two- and three-body nucleon decays and analyze the momentum distributions in the latter. Finally, we thoroughly reinterpret the existing experimental data on conventional two-body modes (into a lepton and a meson) to set lower bounds on partial lifetimes of the corresponding three-body modes involving an additional dark photon. These bounds allow us to further set stringent constraints on the $X$LEFT operators and other correlated decay modes. Our results provide a toolkit for future experimental and theoretical studies of these exotic nucleon decays.