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 $p \to \ell^+ \ell'^+ \ell'^-$, $n \to \bar\nu \ell^+ \ell'^-$, $p \to \ell^+ \nu\bar\nu$, and $n \to \bar\nu \bar\nu \nu$, where $\ell$ and $\ell'$ denote $e$ or $\mu$, with both $\ell = \ell'$ and $\ell \ne \ell'$ cases. Our lower bounds are substantially stronger than the corresponding lower bounds from direct experimental searches. We also present lower bounds on $(\tau/B)_{p \to \ell^+\gamma}$, $(\tau/B)_{n \to \bar\nu \gamma}$, $(\tau/B)_{p \to \ell^+ \gamma\gamma}$, and $(\tau/B)_{n \to \bar\nu \gamma\gamma}$. 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 $n \to \bar\nu M$, where $M$ is a pseudoscalar or vector meson, and then using the experimental lower bounds on the partial lifetimes for these latter decays.