Why should proton decay into positron rather than antimuon?

Grand unification theories, such as $$SU(5)$$/$$SO(10)$$/SUSY variants, suggest proton decay. The lack of observational evidence for proton decay rules out simple GUTs.

But wait a minute! The GUT's prediction of proton half-life is based on the assumption that proton decays into positron (along with a neutral pion). According to Cosmas Zachos's comment on another PSE post, there is NO established generational linkage between up/down quarks (making up the proton) and electron/position. We might as well assume up/down quarks and muon/antimuon are in the same generation (as suggested here, whereas electrons and, say, top/bottom quarks are in the same generation). Hence proton should decay into antimuon, rather than positron (assuming GUT vertices involving X bosons are generation preserving).

If this is the case, the proton half-life is much longer than envisioned before, since muons are heavier than electrons. Therefore, the lack of observational evidence for proton decay does NOT disprove simple GUTs at all.

• Respective partial lifetime channels in Nishino et al 2012. – Cosmas Zachos Sep 28 '18 at 16:21
• Yes, that's why it's important to search all channels. In fact in general we probably have some linear superposition of leptons that are to be associated with the up/down pair. It's also possible that certain flavor symmetries are unbroken. See this interesting talk about this at Neutrino 2018: doi.org/10.5281/zenodo.1286980 – Lukas Berns Sep 29 '18 at 0:57
• – rob Oct 5 '18 at 20:35
• I don't see how there can be any reliable answers to a question based upon such speculative physics theories. We know that proton decay is excluded experimentally to a very extreme level. There is a Standard Model reason that this is true. There is not any theory with experimental support that reaches any other conclusion. – ohwilleke Oct 5 '18 at 20:51

In more detail: we already know that lepton number is violated, which means that if the decay $$p \to \mu^+ \pi_0$$ is allowed, so is $$p \to e^+ \pi_0$$. From an effective field theory point of view, the fact that one of these process is allowed "directly" by an exchange of a GUT X or Y-boson, while the other requires "extra" violations, doesn't really matter. Both are described by dimension 6 operators consistent with the symmetries, so both must happen at comparable rates, suppressed by $$1/\Lambda_{\text{GUT}}^2$$.