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 $p\to {\mathrm{\ell }}^{+}{\mathrm{\ell }}^{\mathrm{\prime }+}{\mathrm{\ell }}^{\mathrm{\prime }-}$, $n \to \bar\nu \ell^+ \ell’^-$,$p \to \ell^+ \nu\bar\nu$,and$n \to \bar\nu \bar\nu \nu$,where$\ell$and$\ell’$denote$e$or$\mu$,withboth$\ell = \ell’$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 $(\tau \mathrm{/}B{)}_{p\to {\mathrm{\ell }}^{+}\gamma }$, $(\tau/B){n \to \bar\nu \gamma}$,$(\tau/B){p \to \ell^+ \gamma\gamma}$,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 $p\to {\mathrm{\ell }}^{+}M$ 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.