# Why do people say that the Higgs mechanism gives mass to the gauge bosons without mentioning the fermions?

Many presentations of the Higgs mechanism only explain it as giving mass to the $W$ and $Z$ gauge bosons, but don't mention the quarks or charged leptons. For example:

But it is equally responsible for the generation of the fermion mass terms via the Yukawa coupling of the fermion fields to the pre-symmetry-breaking Higgs field becoming a fermion mass term plus a new Yukawa coupling to the post-symmetry breaking Higgs field, correct? So, for example, I believe that during the electroweak epoch when the universe was hotter than 100 GeV and electroweak symmetry had not yet been broken, all fermions were completely massless.

I know that historically, Higgs et al were originally only trying to explain the masses of the gauge bosons, not fermions. Is the emphasis on the Higgs mechanism's granting mass to the gauge bosons just a historical relic?

• 1. I'm not sure where the physics question is here, it seems to be more about personal idiosynracies in the presentation of the Higgs mechanism. 2. You have to be careful when talking about "pre-symmetry-breaking". In vacuum field theory at zero temperature (i.e. what is usually done when introducing Higgs), the theory is never unbroken, the breaking just becomes neglegible. You need thermal field theory to actually consider a "broken" and "unbroken" phase. May 3, 2016 at 19:22
• en.wikipedia.org/wiki/Higgs_mechanism#Consequences_for_fermions Like this? Both the wikipedia and scholarpedia articles mention the Yukawa terms/fermion masses. Beyond that, you can have massive spin-half particles without the Higgs mechanism, but you can't have massive spin-one particles without the Higgs mechanism. May 3, 2016 at 19:22
• @ACuriousMind 1. That is my question - is the presentation just a personal idiosyncrasy, or is there a fundamental difference that I'm not getting? 2. I know - by "pre-symmetry breaking" I simply meant expressing the Lagrangian in terms of the field where the symmetry is manifest, even if that field configuration isn't the physical ground state. I mentioned having to go to ~100 GeV temperatures to actually have the symmetry unbroken May 3, 2016 at 19:32
• @LukePritchett I'm just wondering whether there's any important physically reason why they mention the gauge boson masses in the intro sentence but relegate the fermion masses to a subsection May 3, 2016 at 19:34
• @tparker Here's my best guess: If you want a theory with massive spin-one particles you need the Higgs mechanism.* If you want a theory with massive spin-half particles you don't need the Higgs mechanism. In the SM you already know that your fermions have gauge quantum numbers, so you do need SSB for the mass, but you don't in general models of fermions. (* Not precisely true; there are other tricky ways to get spin-one massive states) May 4, 2016 at 1:01