Proton Decay into Charged Leptons

We discuss proton and neutron decays involving three leptons in the final state. Some of these modes could constitute the dominant decay channel because they conserve lepton-flavor symmetries that are broken in all usually considered channels. This includes the particularly interesting and rarely discussed $p\to e^{+}{e}^{+}{\mu }^{-}$ and $p\to {\mu }^{+}{\mu }^{+}{e}^{-}$ modes. As the relevant effective operators arise at dimension 9 or 10, observation of a three-lepton mode would probe energy scales of order 100 TeV. This allows us to connect proton decay to other probes such as rare meson decays or collider physics. UV completions of this scenario involving leptoquarks unavoidably violate lepton-flavor universality and could provide an explanation to the recent $b\to s\mu \mu$ anomalies observed in $B$-meson decays.

Figure 1

Topologies (a) and (b) relevant for nucleon decay into three leptons. The external lines are labeled by three quarks and three leptons, which fixes the $SU(3)\times U(1{)}_{\mathrm{EM}}$ charges of the internal scalars $S_j$ and fermion $F$.

Figure 2

Diagram for $p\to {\mu }^{+}{\mu }^{+}{e}^{-}$ with the LQs of Eq. (8), taking all fermions as incoming.