Observable Proton Decay from Planck Scale Physics

In the Standard Model, no dim-5 $\mathrm{\Delta }B\mathrm{\ne }0$ operators exist, so that Planck-scale-induced proton decay amplitudes are suppressed by at least $1\mathrm{/}{M}_{P\mathrm{\ell }}^2$. If the Standard Model is augmented by a light, color-non-singlet boson, then $O(1\mathrm{/}{M}_{P\mathrm{\ell }})$ proton-decay amplitudes are possible. These always conserve $B+L$, so that the dominant decay modes are $p \rightarrow \Pi^+ \nu$and$p \rightarrow \Pi^+ \Pi^+ \ell^-$,where$\Pi^+ = \pi^+$or$K^+$.