"In this picture, we discover that Mp ∝ mt2/27: despite the negligible population of virtual top-antitop pairs in the nucleon, the top-quark mass influences the proton mass."
This is not some wild-eyed vixra prophet of numerology speaking, but Chris Quigg, who has had a long and very respectable career, working especially on hadrons.
Koide-ologists ought to take a keen interest in this claim, for several reasons.
First, the "Brannen phases" for the triples u-c-t, d-s-b, e-mu-tau, are all multiples of 2/27.
Second, the centrality of the top is consistent with Rivero-ist ideas such as the waterfall (in which the quark masses can be understood as arising from a chain of Koide triplets starting with t-b-c) and the sbootstrap (in which all the SM fermions are superpartners of quark-(anti)quark composites of the 5 "light" quarks, i.e. everything but the top) and even "84"-ism.
Third, it legitimizes, in a new way, the appearance of QCD scales as "Brannen mass scales" for e-mu-tau and s-c-b.
I'm confused. The mass of the top quark is about 173,200 MeV. The (mass of the top quark)^2/27 is numerically about 2.44 Mev^2/27 which isn't in the same units as the proton 938 MeV and isn't anywhere particularly close in magnitude of the proton.
ReplyDeleteThe relationship also isn't independent of the units used. If you use 173.2 GeV insted of 173,200 MeV, you get 1.465 as the 2/27th power instead of 2.44. If you use 173,200,000,000 eV, you get 5.73333333.
The proton mass is 0.938 GeV, 938 MeV and 938,000,000 eV. Any genuine physical relationship would have to hold for all units expressing the relationship.
See equation 3.4 and following sentence, and then reference 24. Looks to me like, if you divide out by a different unit of mass, there will be an extra numerical factor in the constant of proportionality. The deeper fact is the big formula relating proton mass to quark masses via RG flow.
Delete