Nikhef Higgs InformalDiscussion

Question: [MM]

How can we possibly experimentally verify that the Higgs particle is a quantum of a field that has a non-zero vacuum expectation value (apart from the theory) ?

If I look in analogy to the pion as a scaler boson: this was the particle describing the strong interaction potential (the Yukawa potential) with a coupling to fermions that is analogous to the Higgs Yukawa couplings (hence the name): psi-bar * psi * phi (psi=fermion field, phi=scalar field). But we never consider assigning a non-zero v.e.v. to the "pion field". So my naieve question is how we ever can experimentally conclude that the Higgs field has a vacuum expectation value?

My dream fantasy would be if there could be some experiment analogous to e.g. the Aharanov-Bohm experiment that shows that in electromagnetism the A-vector-field is physical, even where the B-field is zero. Even a gedanken-experiment would be nice.

discussion: [RK]

a good question indeed! In fact there are arguments *against* a nonzero v.e.v. for a field with a `mexican hat' potential. This is based on the fact that the *effective* potential (that is, including all loop corrections) must always be concave, i.e. bowl-shaped with no bump. If that potential has the same symmetry as the original one, I think the minimum must necessarily lie at phi=0 i.e. no SSB. Of course there are questions about this picture: does it hold for gauges interactions? If there is no SSB then how do we get the particle masses? The concavity argument follows if you believe in path integrals, but not necessarily if you use canonical quantisation - so does that mean that those two approaches are, after all, *not* equivalent? Unfortunately teaching keeps me from attending on 4/9 but I think that these points are still very unsettled, and your suggestion of an A-B type Gedanken experiment is very interesting - ideas, anyone?

Question: [EK]

The Higgs field permeates all space: is this true for the entire universe? I know one experimental argument that is based on the observation of distant stars: they emit radiation compatible with spectral lines from a hydrogen atom. This would indicate that at least mass is the same. Is this from theory point of view conclusive evidence? Can we say 'the Higgs field density is uniform' ?

discussion: [RK]

On els' question: it is possible that SBB occurs in different `directions' and that would leaed to domain walls where the two incompatible regions meet. That would be observable I guess since I think that SBB happens after inflation. On the *absolute value* of the v.e.v.: in the SM that must always be the same since otherwise the Higgs potential would not be symmetric in teh first place. So here is the result of the Nijmegen jury: apart from domain walls, the vev must have the same value everywhere and therefore the electron mass ought to be the same everywhere etcetera (unless you would like to argue that the Yukawa couplings are not the same everywhere, thereby breaking translation invariance and momentum conservation...)

discussion: [BS] But that is precisely the point: the higgs vev depends on lambda and mu^2 , and those parameters might very well depend on space and time. That is what these experiments Marcel mentioned try to find out. If you allow different domains for the direction of the vev, that already breaks translation invariance anyway.

One experiment has reported a 4 sigma deviation in alpha. That has nothing to do with the Higgs vev directly, but if correct the translation invariance argument is clearly invalid, and then there is no reason why the Higgs vev (and the Yuakawas) might not vary as well.

discussion: [RK] I fully agree. My remarks were just intended to point out the consequences of non-uniformity of the vev. So again, I agree with you!