Observable Proton Decay from Planck Scale Physics

In the Standard Model, no dim-5 $\Delta B \neq 0$ operators exist, so that Planck-scale-induced proton decay amplitudes are suppressed by at least $1/M^2_{P \ell}$. If the Standard Model is augmented by a light, color-non-singlet boson, then $O(1/M_{P \ell})$ 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 $K^+$.