Rescattering effects in nucleon-to-meson form factors and application to tau-lepton-induced proton decay

Nucleon decays put extremely stringent bounds on baryon-number-violating interactions. However, in case the corresponding operators involve only τ leptons, the direct two-body decays, e.g., p→π0τ+, are kinematically not allowed and nucleon decay can only proceed via an off-shell τ, leading to p→π0ℓ+νℓν¯τ. To calculate such processes, the momentum dependence of the form factors for nucleon-to-meson transitions, which describe the hadronization of the underlying process at the quark level, is needed. In this work, we point out new isospin and Fierz relations among such proton–kaon matrix elements and calculate the momentum dependence of the nucleon-to-meson form factors from the universal final-state interactions in terms of pion–nucleon or kaon–nucleon scattering phase shifts. We use these results to derive novel limits on the Wilson coefficients of the baryon-number-violating dimension-6 operators involving a τ lepton, which were previously unconstrained.