# Does the Higgs violate E=mc^2?

1. Mar 17, 2009

### franoisbelfor

The Higgs boson couples to all particles with mass. But even a photon has,
through E=mc^2, an equivalent mass. Therefore, the Higgs should also
couple to the photon. But every text says that it does not, because it is uncharged.

How can this paradox be solved?

François

2. Mar 17, 2009

### Staff: Mentor

When particle physicists talk about "mass", they always mean the "invariant mass" a.k.a. "rest mass" which is zero for a photon (as far as we know experimentally).

The coupling with the Higgs generates the particle's invariant mass.

3. Mar 17, 2009

### franoisbelfor

I know that. But in physics there is no effect that works with invariant mass but does not work also with energy; that is the meaning of mass-energy equivalence. The coupling to the Higgs would be the first effect in physics that distinguishes between rest mass and energy.
Maybe I miss something here.

4. Mar 18, 2009

### JustinLevy

The Higgs doesn't couple with the stress energy tensor indiscriminantly (it is not a graviton). Possibly where you are misunderstanding is that some popular science accounts say that Higgs is the "source of mass". More precisely though, it is interactions with the Higgs fields which we attribute to the invariant mass of many of the fundemental particles. This doesn't mean that the proton weighs what it does because of the Higgs (most of that energy is from QCD interactions, as well as electromagnetic interactions), or that the Higgs must couple to all energy, etc.

Does that help some?

5. Mar 21, 2009

### franoisbelfor

So you say that the rest mass is due to the interaction with the Higgs field. But everybody also says that this interaction is proportional to the mass. That would mean that the mass is defined *independently* of the interaction. Something is bizarre here. Either the mass is due to the interaction with the Higgs field; then the interaction cannot be proportional to the mass, because the mass *results* from the interaction.

Or the mass is there before, and then one asks why not all types of energy come into play.

I still find this all very bizarre...

FB

6. Mar 21, 2009

### malawi_glenn

The gauge bosons and fermions gets a mass term in the Lagrangian by including the Higgs field (this is HOW they do get mass).

The AMOUNT of mass (the size of the mass term) is determined by the parameter, each fermion and gauge boson has their own coupling constant to the higgs field (loose speaking).

So there is no bizzare paradox, if you know how the Higgs Mechanism works.

The mass term in the Lagrangian for fermion f is:

$$L_{\text{mass}} -G_f \, \phi_0 (\bar{f}_Lf_R + \bar{f}_Rf_L )$$

where \phi_0 is the vev (vacuum expectation value) of the higgs field. Without the Higgs field, there is no such term in the Standard Model Lagrangian.

Each fermion has their own parameter G_f, thus the greater the mass of the particle - the bigger the coupling (or vice verse, depending on how you look on it).

But if we put this logically, the correct thing to say is that the greater the coupling - the greater the mass, since the mass results from the interaction. But since we measure the mass (we dont measure the coupling, these are parameters) we often, sloppy, says that the greater the mass - the greater the interaction.

"But everybody also says that this interaction is proportional to the mass", you have to allow yourself to let go of that statement, "everybody" is a strong statement ;-)
You are in that sense arguing against a straw man, which yourself has built...

The same thing holds for your first post, "Therefore, the Higgs should also
couple to the photon. But every text says that it does not, because it is uncharged. "
First, have you read EVERY text on this? (I don't think so..) Why not instead say which text and where? The Z boson is also uncharged (electrically, but gets mass from the higgs field)

Last edited: Mar 21, 2009