Physics Asked on March 12, 2021
Grand unification theories (GUT), such as $SU(5)$/$SO(10)$/SUSY variants, suggest proton decay. The lack of observational evidence for proton decay is supposed to rule out basic GUTs, at least for the basic $SU(5)$ GUT.
But does the lack of evidence for proton decay really rules out the basic grand unification theories?
The GUT’s prediction of proton half-life is based on the assumption that the primary channel of proton decay in GUTs is usually "proton to electron/positron and meson", which is actually predicated on the assumption of $(e, nu_e, u, d)$ being in the same generation.
However, 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. The standard generation assignment
$$
(e, nu_e, u, d)
(mu, nu_mu, c, s)
(tau, nu_tau, t, b)
$$
is essentially arbitrary: the only rational of the above generation assignment is the relative magnitudes of masses.
If we adopt an alternative generation assignment, say
$$
(mu, nu_mu,u, d)
(tau, nu_tau, c, s)
(e, nu_e, t, b)
$$
the standard model is still working fine as usual.
If the alternative generation assignment is true, and assuming that GUT transition processes involving GUT gauge interactions are generation preserving (meaning not changing between different particle families), then proton should decay into antimuon, rather than positron. And this means that the proton half-life is longer than envisioned before, since muons are much heavier than electrons.
If this is the case, does it mean that the lack of observational evidence for proton decay might NOT disprove simple GUTs?
There are two kinds of counter arguments to the reasoning above:
My guess to your title answer is "yes", to the extent that the conventional-case phase space for $pto pi^0 ~ e^+$ is 1-0.135- 0.0005 ~ 0.865 GeV which is not dramatically larger than that for a $pto pi^0 ~ mu^+$ decay, 1-0.135- 0.106 ~ 0.759 GeV. So if your alternate theory had your gauge boson X decay to $mu^+ bar{d}$ instead of $e^+ bar{d}$, you'd get a comparable rate excluded, as the $pi^0to 2gamma$ has been excluded to minuscule limits... But I have not fussed those in the PDG compilation... For example, Super-Kamiokande excluded Cherenkov rings, such as
which wouldn't be dramatically different than the muon Ersatz.
Correct answer by Cosmas Zachos on March 12, 2021
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