Higgs boson sources

Question

Every fundamental interaction in Physics comes from "some bosonic field" or "force carrier", according to QFT. We have 4 fundamental interactions(force carriers):

Gravity (Gravitons)
Electromagnetism (photons)
Weak nuclear force.(W, Z)
Strong nuclear force (gluons).

Every field has a source:

Gravity's source: mass (or more generally energy-momentum in general relativity).
Electromagnetism: electric charge (also magnetic charges if we include magnetic monopoles or their generalizations in the picture).
Weak nuclear force: "weak charge" (we could undertand it as "flavor exchange" at the level of the electroweak theory at energies around 80-90GeV).
Strong nuclear force: "color charge".

With the discovery of the Higgs field, one question naturally arises:

What is the "source"/characteristic of the Higgs boson field? Is the Higgs field "universal" like gravity or it is more like the electroweak or strong fields?

possible duplicate http://physics.stackexchange.com/q/17944/ — anna v, Jul 19 '13 at 17:41
Possible duplicate: http://physics.stackexchange.com/q/1080/2451 — Qmechanic, Jul 19 '13 at 17:59
There is no answer or question in those questions to what the Higgs field "characteristic" would be... — riemannium, Jul 19 '13 at 18:03
The Higgs is not a gauge field so you can't interpret it's couplings as "charges" in the usual sense. That is, it isn't coupled to a conserved current. — Michael, Jul 20 '13 at 08:56
Then, if the Higgs is not gauge invariant in the usual sense, is it fundamental or not? — riemannium, Jul 20 '13 at 11:31
I had not remembered that cool remark, Michael. The Higgs field is not really a "gauge" field...Therefore, could it be a hint of its compositeness? After all, there is no symmetry to guarantee its mass so low as 126GeV in the SM. We can advocate SUSY, but LHC data are more and more stringent. Technicolor? ETC? I think this question is not naive. Michael, do you know if there are some theory making the Higgs "gauge invariant" somehow? Just curious! — riemannium, Jul 20 '13 at 11:59
@riemannium, the notions of "gauge field" and "gauge invariant" are distinctly different. Michael wrote "the Higgs field is not a gauge field". You replied "if the Higgs is not gauge invariant..." but that's not what Michael wrote nor, I think, what he meant. — Alfred Centauri, Jul 20 '13 at 19:36
Alfred, if the higgs field is not a gauge field, then the Higgs field can not be gauge invariant...It's logical! — riemannium, Jul 20 '13 at 20:22
Alfred, a gauge field IS gauge invariant by definition, does it?Hence the name! If the Higgs field is not gauge field, how could it be gauge invariant? It is an issue of mathematical definition... — riemannium, Jul 20 '13 at 20:35
@riemannium, it's an issue of understanding fundamental concepts. A gauge field is a part of a covariant derivative with non-physical degrees of freedom that transform in such a way as to render a theory locally gauge invariant. — Alfred Centauri, Jul 20 '13 at 20:49

Trimok · Answer 1 · 2013-07-20T08:53:44.033

3

It is interesting to look at interaction part of Lagrangians:

Linearized Gravity (first order, scalar field): $\partial^\mu ~ \Phi ~\partial^\nu\Phi ~h_{\mu\nu} = T^{\mu\nu}~h_{\mu\nu}$

Electromagnetism : $\bar \psi \gamma^\mu \psi ~ A_\mu = j^\mu A_\mu$

Higgs for bosons: $B^\mu H B_\mu H $

Higgs for fermions: $e_R (E_L H) $

One sees that it is not possible to find a general "source" for the Higgs field which makes sense.

Maybe, in the fermion case, you could consider, that, in some sense, there would be a ($e_R E_l$) "source" for the Higgs, but it would be more an abuse of language.

edited Jul 20 '13 at 08:53

answered Jul 20 '13 at 08:48

Trimok

17,567

1

Typo in the first eq: change a $\partial^\mu$ to $\partial^\nu$. Otherwise good. – Michael Jul 20 '13 at 08:52

score 0 · Answer 2 · answered Jul 19 '13 at 18:32

Every fundamental interaction in Physics comes from "some field"

Every fundamental particle comes from "some field". So, what is the "source" of the electron and neutrino fields and of the quark fields?

In the context of the Standard Model, the fields are fundamental; the particles are quanta of the (modes of the) field.

The (ordinary) Higgs fields are two complex, self-interacting scalar fields with 4 associated quanta (particles and anti-particles).

The Higgs fields are electroweak charged and form a weak isospin doublet (like the electron-neutrino doublet and the up-down' quark doublet) and thus interact with the electroweak gauge fields.

The Higgs fields also interact with the fermion (matter) fields via Yukawa interactions.

So, to summarize, to ask for the source of the Higgs fields, it seems to me, is to ask for the source of quantum fields in general. But, as far as we know, quantum fields are fundamental.

I deleted some inappropriate comments. – David Z Jul 20 '13 at 07:28 — David Z, Jul 20 '13 at 07:28

Higgs boson sources

2 Answers2