Why doesn't the Higgs field give photons mass?
b/c it is constructed such that it couples to the SU(2) triplet, not to the U(1) gauge field
Ask the LHC guys :-)ok, thank you. but how likely can the Higgs be found? and what happens if there is no higgs, where does the mass come from?
The Higgs boson is the oscillation of the Higgs field around its vacuum. Its like any other quantum field and the corresponding relation between field and particle in QFR - excpet for the fact that its vev is nonzero.
The fermion masses are subtle. Usually one is allowed to introduce standard mass terms. But due to the chiral structure of the electro-weak interaction this would violate a local gauge symmetry and one must therefore find a new mechanism to introduce these masses.
Again this is ad-hoc: instead of introducing a mass mf for each fermion f one introduces a coupling constant gf which couples the fermion to the Higgs. The mass is related to gf and to the vev of teh Higgs. So the arbitrary masses are replaced by arbitrary coupling constants (ugly!). If there are massless fermions on is allowed to set this coupling to zero.
It has to do with the spontaneous symmetry breaking of [tex] SU(2) x U(1)[/tex], the photon essentially doesn't couple to the Higgs Field.
"The simplest implementation of the mechanism adds an extra Higgs field to the gauge theory. The spontaneous symmetry breaking of a local symmetry causes this Higgs field to interact with (at least some of) the other fields in the theory, in a manner producing mass terms for (at least some of) the gauge bosons. The symmetry breaking can also produce elementary scalar (spin-0) particles, known as Higgs bosons." - Wikipedia
Yes, this is one example of a Higgs-less model, but afaik it does not account for all masses but only for special particles.