Moth said:
The first thing I noticed when exploring CalcHEP is that the parameters set certain masses such as the electron mass to zero. I can see that this is not an issue for high energy collisions, but if I wished to study lower energies and decays, this might have an effect. My supervisor also thought the missing parameters should be filled into make the list more complete. However he warned me that I would have to supply vertex corrections, adding the fact that vertex corrections are momentum specific and there is no simple formula to work them out.
Thus at the start of my project I have set out to find values of mass (easy), and some vertex corrections, which I though I might be able to find for electrons at 45GeV at least, because that is the Z boson resonance.
Ah, I see. You can program vertices and masses directly into CalcHEP, and it can do the rest, but CalcHEP cannot compute these things. But your advisor is right: if you really want to include the full radiative corrections, you need to go to PYTHIA or ISAJET; there are no closed-form formulas that I know of for such beasts, especially in the full EW theory.
I still have a fair amount of research to do to understand the topic. Currently I simply wish CalcHEP to produce graphs of cross section vs. momentum, producing the easily recognisable resonance peak. This is a task that I have the ability to do via a batch script. I was hoping to produce these graphs to simulate the data that experimentalists would have seen when doing the experiment. Would a lack of vertex corrections produce a significant difference between my results and experimental results?
Yes! At tree level, the SM is ruled out to something like 120*sigma! You will definitely need loop corrections to get it all right. However, if this is an undergrad project, I imagine that you are not expected to get into all that. How much field theory do you know? Have you studied radiative corrections before - they're quite a difficult subject to get a grasp of!
This is not really how CalcHEP is used in practice. As I said before, we model-builders use CalcHEP when working with models of physics beyond the SM ("BSM"), where loop corrections are irrelevant (one or two sig figs is enough). If you're trying to do a detailed analysis, CalcHEP is the wrong tool.
I'm also a little confused what you mean by the sentence "I have chosen to study the broad subject of mass." What does any of this have to do with mass? The Higgs-boson proposal was closer!
If I were you, here's what I would propose: since you're dead-set on using CalcHEP (and as someone who also advises students, I would suggest you be dead-set against doing radiative corrections! ), you should take a different tactic. One thing you can do is compute the Z-width or production cross section in electron-positron collisions, and compare it to the known values, giving you an idea of how large radiative corrections can be. You can try to get a solid understanding of why tau-physics is so much richer subject than muon-physics! You can also perhaps ask what happens when you add new physics: for example, people are very interested in decays like \mu\rightarrow 3e - this cannot happen in the SM, but it is quite common in SUSY or extra dimension models, and it happens at tree-level. You can study this decay and use it to put bounds on models of SUSY or extra dimensions. Things like that have been done in the literature (with programs like CalcHEP, no less), so you'll have something to compare it to.
Good luck, and Have fun!
