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Physics
Beyond the Standard Models
Masses of Fermions, string theory, Higgs mechanism
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[QUOTE="mitchell porter, post: 6058732, member: 103130"] First let's just think in terms of field theory. I don't know if you thought of this yourself, but this kind of idea has been around for a while. It can be expressed in terms of self-energy, e.g. the neutrino mass as arising from weak-interaction self-energy, the electron mass as arising from electromagnetic self-energy, the up and down quark masses as arising from chromodynamic as well as electromagnetic self-energy. What standard physics says, is that the mass of these particles has a nonzero contribution from other factors (e.g. seesaw mechanism for the neutrino, Higgs mechanism for the others), but does indeed have a substantial component coming from the self-energy. [URL='http://physics.stackexchange.com/questions/426153/mass-of-the-electron']Here's a brief discussion.[/URL] I quote Polchinski as saying that roughly 20% of the electron mass comes from self-energy; in the next sentence he says, "for quarks the effect is larger due to the larger SU(3) coupling, so that the self-energy is of order the mass itself". But in our current understanding, the mass scales of electron, up, and down are set fundamentally by yukawa couplings to the Higgs (and in the case of the neutrino, by unknown physics such as a seesaw with a heavy right-handed neutrino). The number of forces does not determine the mass even qualitatively, and even in the realm of the self-energy contribution, the strength of the individual forces counts for more than the overall number. Nonetheless: in another thread, we have extensively discussed [USER=81]@arivero[/USER]'s [URL='http://arxiv.org/abs/1111.7232']2011 generalization of the Koide formula[/URL], and it comes in two forms, an "unperturbed" version in which electron and up masses are zero, and a slightly "perturbed" version which is the realistic one. Could the "perturbation" come from the self-energy? It's a logical idea, but lacking a genuine model, it's just an idea. As for string theory, the string theory account of mass is exactly as in field theory: as free particles, the chiral fermions are massless, they pick up a mass by yukawa coupling to the Higgs, and then the mass runs due to the self-energy. The only difference is that string theory has to provide extra details. Field theory just says it's "massless fermions interacting with a Higgs vev", with yukawa couplings and gauge couplings as free parameters. In string theory, this will correspond to strings and branes interacting in some specific way (there are many ways to do it), and the values of the couplings will be determined by the geometric details rather than being free parameters. So in string phenomenology, one normally supposes that even in the first generation of fermions, there's a nonzero yukawa coupling that contributes to the mass, and the self-energy is just a correction rather than the whole contribution. It's certainly mathematically possible to obtain "rank one mass matrices" in which only the third-generation yukawas are nonzero. There are somewhat contrived field-theory models in which the first and second generations then get their masses from virtual top quarks. The possibility that string theory can do it better is at least worth some attention. [/QUOTE]
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Beyond the Standard Models
Masses of Fermions, string theory, Higgs mechanism
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