Vertex Corrections

1. Nov 24, 2007

Moth

I am currently studying particle collisions. Before I begin I need latest mass values of the leptons, bosons and quarks. However I have been told that I will need to slightly modify these due to vertex corrections. (Due to the incoming particles interacting before colliding, see attachment for an example) I am also aware that these corrections depend on the incoming particles' momenta. I have been searching for values of these vertex corrections, without success.

Can anyone point me to where I can find vertex corrections to the mass/charge, for any leptons, at any momentum?

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2. Nov 24, 2007

blechman

These are very nontrivial, and I don't know if you can just find them - they might be in old papers somewhere, but beyond one-loop, they're usually don't have a closed-form solution and you need numerics; and if it's not QED you're talking about, then it's even worse! It depends on what you want to do. Are you an experimentalist? The major MC routines have all this built in (such as PYTHIA).

The best place to start looking is the PDG (http://pdg.lbl.gov).

3. Nov 25, 2007

Moth

I am doing a final year MPhys project using some software called CalcHEP. It uses Monte Carlo integration to solve the necessary calculations for finding the cross section for particular particle collisions at particular momenta. However my supervisor and I are not sure whether the program has taken into account vertex corrections. The program has a number of parameters for particle masses, which I need to verify, and these values may need the vertex corrections applied to them before running the calculations. I am interested in finding the corrections so that I may test to see if it makes the program more accurate or less, against experimental data.

4. Nov 25, 2007

blechman

No, CalcHEP only has tree-level rules. This was done on purpose, since incorporating loop corrections opens a whole new can of worms. Usually, if you need the higher-order corrections, you need PYTHIA or ISAJET.

Particle masses are physical quantities: they are what they are (you can find them in the PDB). If you're worried about the RG running of the parameters, then you need PYTHIA.

I need to know more details of what you're trying to do if I'm to give you any useful help. Are you an experimentalist or a theorist? I was under the impression that CalcHEP was not very useful to experimentalists for exactly this reason. The idea was to let theorists calculate cross sections/widths quickly, and if they see something interesting, then they can write up a paper (since you generally don't care about loop corrections to a model you haven't even seen yet!). If you are a theorist, what are you considering? If it's just a SUSY-based model, PYTHIA and ISAJET have SUSY built in, so you should be able to modify it easily enough to include any loop corrections (if they're not already in there).

Remember that loop corrections come in all shapes and sizes, contributing to all different types of processes. Even the (relatively) simple QED diagram you included in your post actually contributes to *two* operators! And if you're doing EW, it's even worse! There's an entire subfield of theorists who's careers are based entirely on organizing these calculations ("Electroweak Precision").

Well, let me know more details if you want and I'll try to help you.

5. Nov 26, 2007

Moth

This is for my final year undergraduate project. My supervisor has supplied CalcHEP on a computer and told me to do a project on the Standard Model. My friend has chosen to study ways of finding the Higgs with CalcHEP, and I have chosen to study the broad subject of mass. My intentions were to use CalcHEP to reconstruct some typical experiments, such as the virtual Z resonance in electron positron annihilation. It has also been suggested that I look into the decay of leptons. And I was also hoping to run some experiments that depend on quark mass, so that I could see how sensitive the quark mass parameters are when I modify them within the model. However all of these depend on the abilities of CalcHEP. If CalcHEP is not suitable to these tasks I intend to simulate more appropriate experiments with CalcHEP. For my project the one thing that is a certainty is that CalcHEP will be used.

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 in to 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.

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?

6. Nov 26, 2007

blechman

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.

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! :yuck:), 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!

7. Oct 6, 2008

qwer12

hi,

i have found you through the net when searching about calchep, can you help about a few questions on calchep.

i am trying 2-> 3 processes in little higgs. At some processes i get negative points...in diffrential crossection vs. E diagrams. How can i handle them.

secondly how can i get S (cm momentum vs total crossection graphs),

i really read the manual but i still could not find the S dependence switch...

i have more but thanx for your help...