# Homework Help: Finding the Higgs

1. Dec 9, 2005

### jonas_nilsson

Hi,
I've been looking at ways to create Higgs bosons in lepton colliders, mostly muon colliders. I have a question on how one would be certain that it is actually the Higgs that has been found.
The main channel that is going to be used seems to be the so-called s-channel, where
$$\mu^+ + \mu^- \rightarrow H \rightarrow b + anti~b$$

Is the following reasoning correct?
The H will essentially be at rest at the collision point. When it decays, the b-quarks will create two jets. Some tracks in the tracking chamber will have kinks, indicating the decay of a b-hadron, which would "mark" the event as interresting.

But what about other processes giving similair events? Could someone give a few examples?

The quantities of information gathered in particle physics give so many degrees of freedom that I can't really get rid of the feeling that just about any theory could be confirmed, based on the data. Now I don't believe that's the case, I believe I need to fill in the gaps in my understanding. Some help from you people would be very nice!

2. Dec 9, 2005

### CarlB

Well one background would be, I suppose, the muons creating a virtual photon that then decays into a quark / antiquark pair. The reason this is different from the Higgs is that the photon is spin-1. To distinguish it, you need to have some sort of information about the spin of either the muons or quarks (probably the muons). So are they using polarized muons?

By the way, I recently went through Phys Review and downloaded all the articles by Schwinger from the 1950s that I could find. One that speaks to the question of whether or not the Higgs is necessary caught my eye:
http://prola.aps.org/abstract/PR/v125/i3/p1043_1

From the way I understand the above article, Schwinger says it isn't, so don't say he didn't warn you if the experimenters are caught empty handed. Schwinger's articles are some of the most elegant I've read.

Carl

3. Dec 11, 2005

### jonas_nilsson

Yes, of course the experimentalists can stand there empty handed. But I think that for example the LHC will be historical anyway, either since it discovered the Higgs or because it proved the theory wrong. And just the effort of building the LHC+experiments will be worth a note in the history books.

Back to the muons: I've not thought specifically of polarized/unpolarized beams. I suppose polarization of particle beams refers to the projection of the spin (?). In what way would polarized beams change the situation?

Have I understood you right if I say the photon is virtual since it for a while violates conservation of momentum/energy? I mean, conservation of momentum requires momentum zero, but a photon always carries a momentum and won't just sit still at the interaction point, right?

4. Dec 11, 2005

### CarlB

Oh, by standing there empty handed I don't mean to say the LHC would be a failure. In fact, the experimentalists would be standing there empty handed with crap-eating grins on their faces, quite proud of their success.

The reason there is a polarization (spin) effect is because the photon is a spin-1 particle while the Higgs is a spin-0 particle.

Yes, the photon (or Higgs) is a virtual particle. QM is kind of strange. Let me try and explain why the concept of a description of the activities of a virtual photon (especially in this case) sort of bothers my intuition.

The Feynman diagrams that contribute to the interaction all have to be added up before one computes a probability. After you run the experiment you will get some result and upon repeating the experiment, you hopefully find that the probabilities match your predictions.

That said, for any one of those experiments you really can't say which Feynman diagrams were involved. So there really isn't any way to pin a particular activity onto a particular virtual particle.

In addition, Feynman diagrams are mostly calculated in momentum space instead of position space. In momentum space, particles don't have specified positions.

Schwinger, as it turns out, developed a method of working with particles that are defined partially in momentum space and partially in position space. That would be a more realistic description of a particle. It's called "Source Theory". Here's a link:
http://www.osti.gov/accomplishments/schwinger.html

Carl

5. Dec 13, 2005

### CarlB

Here's a link that might be of interest that just came out on Arxiv today:

"stinguishing New Physics Scenarios at a Linear Collider with Polarized Beams"
http://www.arxiv.org/abs/hep-ph/0512131

Carl