I understand that in the early universe there was a time when particles did not have mass yet. I'm wonder in what cosmological era did particles get their mass. Was this in the electroweak era < 10-32 seconds or afterwards? And is it true that then afterwards the higgs field acquired a vacuum expectation value so that particle fields could couple to the higgs field and gain mass?
My suspicion is that there may have been a time that the higgs field was so energetic and fluctuating so wildly that particle fields could not couple to it. How can there be a coupling "constant" between fields that are fluctuating to rapidly? This perspective allows me to understand that it may have been the heavier particles that coupled to the higgs field first (because their frequencies were higher than the higgs fluctuations and so would appear more stable wrt these higher mass, higher frequency particles). And then after the higgs field cooled down and fluctuation were not so energetic, the lower mass particles could couple to the higgs field and gain mass too. This would seem to be consistent with the strong force freezing out of the unified field first because it has higher mass particles with higher frequency (compared to the higgs fluctuations). And then the electromagnetic and weak forces froze out latter because they have lower mass particles. Is this the right picture of things?
My suspicion is that there may have been a time that the higgs field was so energetic and fluctuating so wildly that particle fields could not couple to it. How can there be a coupling "constant" between fields that are fluctuating to rapidly? This perspective allows me to understand that it may have been the heavier particles that coupled to the higgs field first (because their frequencies were higher than the higgs fluctuations and so would appear more stable wrt these higher mass, higher frequency particles). And then after the higgs field cooled down and fluctuation were not so energetic, the lower mass particles could couple to the higgs field and gain mass too. This would seem to be consistent with the strong force freezing out of the unified field first because it has higher mass particles with higher frequency (compared to the higgs fluctuations). And then the electromagnetic and weak forces froze out latter because they have lower mass particles. Is this the right picture of things?
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+Stam Nicolis
Thank you, Stam. It is generous of you to reply. And I appreciate it.
When you write, "This breaking would involve additional, hitherto unkown, Higgs bosons." ... for the strong force, did you actually mean another type of "higgs boson" because I've heard that some are looking for multiple kinds of higgs bosons. Or did you simply mean some other kind of (or similar to) mechanism that breaks that symmetry?Nov 11, 2015
Stam NicolisModeratorIndeed, these would be the Higgs bosons, that are involved in breaking the symmetry group of the ``Grand Unified Theory'' to that of the Standard Model, not to be confused with the, also, to date, putative Higgs bosons that would be involved in supersymmetric extensions of the Standard Model.Nov 11, 2015- +Stam Nicolis
I wonder if supersymmetry is needed if the fermions are just as massless as the bosons (before the higgs mechanism breaks the symmetry)? How else would you tell them apart (probably a stupid question)?Nov 11, 2015 - Stam NicolisModeratorYou can tell them apart by the fact that you have to impose that the state of many identical fermions is antisymmetric when you permute them, while that of many identical bosons is symmetric. This then has consequences for the quantum corrections their mass can receive. Fermions have a symmetry, known as chiral symmetry, that implies that corrections to their mass, due to interactions with other particles, are proportional to the logarithm of the energy scale one is looking at; the same holds for gauge bosons, due to a symmetry called gauge invariance-here, absent their interactions with the Higgs, they would be massless, as would the fermions, such as the charged leptons, that require the interaction with the Higgs to acquire their mass, in the first place. However the mass of the Higgs itself and its vev, also are subject to corrections, due to the interactions of the Higgs with the other particles-and there's no symmetry that protects the corrections from leading to a mass or vev that would be arbitrarily
large much faster, as the square of the energy scale one is looking at, and this would lead to observable consequences. One way to describe the fact that such a sensitivity isn't observed, is to imagine the existence of, hitherto, unknown particles, whose contributions to the corrections to the mass and vev of the Higgs, partially, cancel the corrections from the known particles. If one then tries to organize this calculation, one finds that the new particles are related to the known particles by the fact that they have spin that differs by 1/2, so the new particles behave as fermions, if the known particles were bosons and vice versa. This is called supersymmetry, that would imply that the ``partners'', though of different spin, would have the same mass-there would be a particle of spin 0, but of charge and mass equal to that of the electron, for instance, whose contribution to the corrections to the mass and vev of the Higgs would cancel that of the electron; and so on. Since such a particle doesn't exist with such properties, its mass must be different, supersymmetry must be broken. How isn't known and must be parametrized. And that's what's being done.
In addition, while we're on the subject, it's interesting to remark that all, hitherto known, particles that describe matter, the quarks and leptons, are fermions, while all particles that describe forces, the photon, the W and Z bosons and the gluons (and the graviton, too) are bosons. The Higgs, in fact, is the first particle that describes bosonic matter.So it's natural to imagine a situation, where matter is described by bosons and forces are described by fermions, which is another way one is led to introduce supersymmetry. Nov 11, 2015 - Stam NicolisModerator+Malik Matwi Some of the statements are incorrect: the mass and spin of particles are Poincaré invariants, for instance. In quantum field theory the number of particles isn't fixed-it's known that it isn't possible to describe the dynamics of a fixed number of particles, in a relativistically invariant way, unless the particles, in fact, don't interact. So one should be careful. It is known how to describe quantum fields in general, and quarks in particular, at finite temperature. Look here: http://web.mit.edu/redingtn/www/netadv/XthermalFT.htmlNov 14, 2015
- Stam NicolisModerator+Malik Matwi But not for the reasons stated. This is standard material of a quantum field theory course, so it's useful to go beyond the background knowledge, as presented, for instance, in the links provided.Nov 14, 2015
