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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?

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    $\begingroup$ Closely related if not a duplicate: What happens to matter in a standard model with zero Higgs VEV? $\endgroup$ – Alfred Centauri Jan 9 at 22:53
  • $\begingroup$ @Alfred Centauri very similar, in my question I leave the fermion masses turned on, so presumably atomic structure etc can still form $\endgroup$ – Craig Jan 9 at 23:19
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    $\begingroup$ 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. $\endgroup$ – Chiral Anomaly Jan 10 at 2:21
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    $\begingroup$ 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. $\endgroup$ – Chiral Anomaly Jan 10 at 2:24
  • $\begingroup$ 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. $\endgroup$ – Craig Jan 10 at 2:59

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