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If the W's and Z bosons were massless at low energies (i.e. no Higgs interaction), what would the universe look like? Would there be "weak bound states" ? How would electromagnetic theory differ with there being charged yet massless W's? Would the electroweak unification be natural, or impossible?

Craig
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    Closely related if not a duplicate: What happens to matter in a standard model with zero Higgs VEV? – Alfred Centauri Jan 09 '19 at 22:53
  • @Alfred Centauri very similar, in my question I leave the fermion masses turned on, so presumably atomic structure etc can still form – Craig Jan 09 '19 at 23:19
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    I'm not sure that saying that the W's and Z's are massless (and that the fermions remain massive) is enough info to specify the model. For example, if we delete the Higgs field and keep the $SU(2)_L\times U(1)_Y$ gauge structure, then we can't have Dirac mass terms for the fermions, because those terms would not be gauge invariant and the model would be ill-defined. (A Dirac mass term is a product of left- and right-handed fermion components, which transform differently under the gauge group.) So I think the model needs to be specified more carefully before the question is answerable. – Chiral Anomaly Jan 10 '19 at 02:21
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    This is presumably why @AlfredCentauri compared this to the zero-Higgs-VEV post, because that's a way of eliminating the gauge boson mass terms while keeping the model well-defined -- but then the fermion mass terms also disappear, as you noted. – Chiral Anomaly Jan 10 '19 at 02:24
  • Could we use the non trivial QCD vacuum (Pion condensation I believe is the name), which also breaks electro-weak symmetry? The fermion masses would be small, but not 0. – Craig Jan 10 '19 at 02:59
  • @DanYand "if we delete the Higgs field and keep the SU(2)L×U(1)Y gauge structure" - What if we delete both? And also keep Z and W massive. Would this work? In other words, is the Higgs idea just to fix the electroweak gauge invariance? What if we just get rid of the electroweak unification and keep the electromagnetic and weak interactions separate? Is this possible? – safesphere Jan 10 '19 at 03:27
  • @safesphere Probably, yes. The option I described is just one (maybe the simplest one) of many options that we could consider, although we'd need to check any given option to make sure it's gauge-invariant and free of chiral anomalies, at least. More importantly, if we abandon the $SU(2)\times U(1)$ structure, then in what ways would it still be "similar to the Standard Model"? We could consider a variety of little toy models, each one with different similarities to the SM, to build some general intuition, which I assume is really what the OP wants. But then it's a very broad question. – Chiral Anomaly Jan 10 '19 at 03:52
  • @Craig I hadn't thought about that. That's exceeding the boundaries of my current understanding, so I don't have any insight to offer. I'll think about it, but I'm a pretty slow thinker... – Chiral Anomaly Jan 10 '19 at 03:58
  • @DanYand Thanks for responding. My intuition is against inventing unobserved things only to justify theories that otherwise would not work. Examples include luminiferous aether, phlogiston, dark energy, dark matter, Higgs boson, etc. I believe theories should explain observations, not to invent what observations fail to detect. So I'm not concerned with saving the Standard Model. If observations can be explained without the electroweak interactions and Higgs boson, then I think this may be a good avenue to explore. Sorry for the rant :) – safesphere Jan 10 '19 at 04:09
  • @safesphere No apology needed. I think we agree. I didn't mean to glorify the Standard Model; I was only assuming that the goal was to build intuition about how the Standard Model's predictions would change (that is, in what ways would the predictions become unrealistic) if we modified it in such-and-such a way. I was viewing it as an intuition-building exercise, kind of like asking how orbitology would change if gravity were $1/r^3$ instead of $1/r^2$. That's different than asking what alternative models would agree with the experimental facts. As you said, saving the SM isn't the goal. – Chiral Anomaly Jan 10 '19 at 04:29
  • @Safesphere I agree the standard model is not the prettiest, but the Higgs is an observable, and a (so far) correct prediction of the theory. You can consider the necessity of the Higgs a failure of the preceding theory, but you cannot say that you wish to do away with it without also explaining the incredibly likely detection of a spin 0 boson with mass of 125 GeV. It is not like dark matter or energy, it is a prediction, not purely an observation – Craig Jan 10 '19 at 13:30
  • @Craig Is there any convincing evidence that the particle they've found is if fact the Higgs boson? "Incredibly likely" referred to the detection of some particle, not the that particle being the Higgs boson. The Higgs interaction has not been observed, has it? – safesphere Jan 10 '19 at 14:09

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