# Why doesn't the photon have mass? The Higgs mechanism and pre-electroweak epoch

1) When electroweak separation occurred, 'why' wasn't the photon 'given' mass like the W and Z bosons? i.e why don't photos interact with the higg's field?

2a) How well is the higg's mechanism understood at the moment?

2b) Since the discovery of the higg's boson, is the process behind particles gaining mass something which is just accepted to have occured until we can explain it?

3) A slight abstract extension from this - before the electroweak epoch (i.e. in my understanding, the time before interactions with the higg's field occured to yield particles' mass) was the universe made up of a sea of massless particles? or at this very early stage, was the universe made up of pure energy rather than matter? (i know strictly speaking they are one and the same, but for the purpose of asking this question I am making a definition between the two.)

Thanks.

1. The $SU(2) \times U(1)$ electroweak gauge theory has 4 symmetry generators, of which the vacuum breaks only three -- corresponding to $W^+$, $W^-$ and $Z$. The vacuum is symmetric under the generator of electromagnetism, hence the photon cannot interact with the vacuum. Think of the vacuum as a medium -- if it was not symmetric under EM, then it could absorb a photon and transform into another state in the multiplet.

2. (a) We understand it very well. After all, we've known the theory for about 50 years now, and it is explained in a typical graduate text on QFT.

3. Yes, we expect the universe to have been made up of massless particles (I don't want to pedantically go into a bunch of possible deviations from that expectation -- your expectation is quite reasonable). It's unusual to refer to it as "energy rather than matter" -- at high energies one expects the Higgs field to have zero vev, and so fermions would have been massless -- but you'd still have Higgs and fermion quantum fields participating in the dynamics -- only their particles would be massless.

Could you explain question 2b more clearly?

• 2b was just me being unclear, your answer for 2 sorted that one out! Can you recommend any literature I can read? If possible, something edging on laymen's terms as I am engineering educated, not physics! Sep 6, 2014 at 14:18
• Might be a little too simplistic, but here's a blog post I wrote. If you understand what a "gauge-covariant derivative" is, you can make sense of the treatment in almost any textbook. You could (for eg) have a look at section IV.6 in Zee's book QFT in a nutshell, or almost any QFT notes you find online.
– Siva
Sep 6, 2014 at 16:56