Improved Lower Bounds on Partial Lifetimes for Nucleon Decay Modes

In the framework of a baryon-number-violating effective Lagrangian, we calculate improved lower bounds on partial lifetimes for proton and bound neutron decays, including $p to ell^+ ell^+ ell^-$, $n to bar u ell^+ ell^-$, $p to ell^+ ubar u$, and $n to bar u bar u u$, where $ell$ and $ell$ denote $e$ or $mu$, with both $ell = ell$ and $ell e ell$ cases. Our lower bounds are substantially stronger than the corresponding lower bounds from direct experimental searches. We also present lower bounds on $(tau/B)_{p to ell^+gamma}$, $(tau/B)_{n to bar u gamma}$, $(tau/B)_{p to ell^+ gammagamma}$, and $(tau/B)_{n to bar u gammagamma}$. Our method relies on relating the rates for these decay modes to the rates for decay modes of the form $p to ell^+ M$ and $n to bar u M$, where $M$ is a pseudoscalar or vector meson, and then using the experimental lower bounds on the partial lifetimes for these latter decays.