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!

Question: [PdJ]

Well, how should I imagine EWSB had we been around in the early universe to observe it? I imagine the Higgs potential changing shape from a parabola into a Mexican hat; is that a correct picture? Would it be fast, or slow? Would it start out somewhere in the universe and spread to other places? If it happens at multiple places, there would be no need for the chosen 'direction' to be the same everywhere, would it? How would such domain walls be observable? Could there be slight variations in v after all from place to place due to some quantum effects?

[Reply: Schellekens] About the SM domain walls:

After a brief discussion (with Marieke Postma and Chris Korthals-Altes) we concluded that in the SM there are no such domain walls, This Higgs could point in any direction, but by means of gauge transformations you could rotate it in the same direction everywhere. So there are not really any different domains, and hence no domain walls. Domain walls can occur (and can be problematic) if there are discrete symmetries, for example in the MSSM.

Question: [MV]

I don't know the answer, but the related question (to that of Els Koffeman) whether the electron to proton mass is constant over time gets a lot of attention astronomy. Both pro- and contra- evidence has been reported, but all not really conclusive. Interesting to notice is that the VU group of Ubachs and our own Lex Kaper is involved in this topic.

Question: [MV] By the way, I have another question, more basic one. Would the "speed of light in what we call vacuum" be different with and without a Higgs field? If so, can one calculate easily by how much?

[Answer: Kleiss] First the easy bit: if the speed of photons were changed by the presence of a Higgs field, they would become massive. Unless you mean to say that there would be 2 constants of nature, one `c without Higgs' and one `c with Higgs'. To my mind that is extremely unattractive.

Question: [NN]

Een elektron heeft bijv. een elektrische lading, spin en massa. Die elektrische lading is een quantum getal van het elektron, en die lading gaat interacties aan via fotonen doen als er een ander geladen deeltje in de buurt is. Zouden deeltjes ook een massa hebben als er geen Higgs veld was, maar zou die massa dan niet tot "expressie" komen?

Question: [SC]

Related to the hierachy problem. Considering the SM contributions to the Higgs mass, the higgs mass gets contributions from top loops which are quadratically divergent in the cut of scale. Such things are usually dealed with by renormalization. I think this should make the higgs mass a 'running mass'. Since the divergency is quadratic it might have a huge effect (just learnt from Ronald/Wim that it is likely just a log effect).

My questions: Would it make sense to construct such a renormalized higgs mass and to measure the higgs mass H as a function of the scale q2 in e.g. via ZH production and measure the higgs mass at two different q (e.g. 200 and 2000 GeV).

- How large would be the expected effects ? Is this measurable at a linear collider?

- Would that give a handle to high q2 physics (since the quadratic higgs divergency has the largest contributions at largest scale), i.e. to physics beyond the cms energy.

A related question: - Can we somehow experimentally test if there is a 'hierachy problem' or if this is just an artefact from not knowing high scale (quantum gravity) physics ? - Is the fine tuning a real problem from the theoretical point of view? As there is no real way to rule out SUSY for a long time and it will need additional large funding. At this point, the question about the fine tuning becomes crucial and I would like to have a detailed discussion on the topic.

Question: [PF]

Also I am wondering how appealing the simplest extensions of the standard model (without supersymmetry), the so called 2HDMs can be from the thoeretical point of view.

Question: [NT+PK]

CP eigenvalue: - How to determine if Higgs is CP odd or even?

  Or is that obvious from the final state?
  ( CP(H) = CP(gamma)xCP(gamma) , assuming spin = 0 ?)

- Could e.g. the 125 GeV scalar particle be CP odd?

  What would that mean for the couplings?

- There are models that have CP violating couplings.

  How does this work precisely? Could we construct and measure
  CP violating observables (e.g using ZZ and WW final states)
  to test this hypothesis? 

Question: [FL+NT]

Vacuum energy: Why is vacuum energy 10^120 off?

Question: [NT]

Graviton: If the graviton determines the gravitational coupling, then the graviton and Higgs couple equally to matter (up to a constant); is that obvious?

Question: [NT]

Higgs field vs Higgs particle. How does the higgs field couple to particles at 'our' energies? Isn't the Higgs particle too off-shell for that? How should I see the link between the Higgs field, and the Higgs particle?

Question: [NT]

Higgs field 'wind'? Does the Higgs density vary if you move at different velocities? Can their be a preferred frame with lowest vacuum exp. value, just as there is a preferred cosmic frame where the CMB has equal temperature in all directions?

Question: [PK]

Supppose that the particle at 125 GeV is not the expected
 Higgs scalar but a spin 1 or a spin 2 particle.
 - What kind of measurements could one perform to distinguish the Higgs scale for the new particle X.
    Can one say anything on production cross sections and branching ratios?
    Is it possible to write down a consistent renormalizable theory with such a particle?

Question: [PK]

Suppose that the particle is a scalar but there are more Higgses around.

 - How could we figure this out by measuring properties of the 125 GeV scalar particle? Can we say anything about the other Higgses?