WHIZARD

Size of cross section with restrictions vs. factorized

Asked by Yehia Abdelaziz

I tried to generate a process of the form ee > VLL VLL~ , and the decay VLL > mu- X , VLL~> mu+, X.

I tried with two methods that give me two different answers.

The first is to use the factorized method: In this method, the cross section was the same for all X masses. Which is what I expected since the VLL has a branching ratio of 1 to X and muon.

When I used the restrictions method, things changed. Now the cross section, changes with the mass of X.

Which one is the correct one?

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WHIZARD Edit question
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Juergen Reuter Edit question
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Juergen Reuter
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Juergen Reuter (j.r.reuter) said : 		#1

Hi Yehia,
indeed, using a factorized approach gives always the production cross section, while a single decay channel for the unstable command always result in a branching ratio of 1. This should be approximately reproduced by the process with restrictions, however, the total width in the input needs to be adjusted to match the changes in the parameters of the decay. If you increase the mass of the particle X, due to the shrinking phase space the partial width gets smaller and smaller, and hence also the total width. If the total width is kept constant, the decay part of the matrix element becomes smaller, but the production part stays constant if the total width is not adjusted. Is that what happened?
Cheers,
    JRR (Juergen)

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Yehia Abdelaziz (yehia95) said : 		#2

Thank you Juergen,

I think this is this what happened. I thought the decay width would be relevant only for calculating the branching ratio.
Do you mean that I should calculate the width using the automatic method and then put the calculated value of width before the integrate command?

Best regards
Yehia

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Best Juergen Reuter (j.r.reuter) said : 		#3

Yes, indeed. If you have the exact analytic expression for the width, you can also implement it in the Sindarin file. Another alternative (besides the one you mentioned) is to generate a series of SLHA-like input files where the width varies with the mass of the X particle, and then scan through the files.

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Yehia Abdelaziz (yehia95) said : 		#4

Ok thank you. Another question which I don't know if it is related or not. But when calculating the production cross section only without the decay, the cross section decreased with increased mass. But when it is allowed to decay, the opposite happened.

Why do you think the reason for this?

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Yehia Abdelaziz (yehia95) said : 		#5

Thanks Juergen Reuter, that solved my question.

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Juergen Reuter (j.r.reuter) said : 		#6

Your question is a bit too vague to answer (and probably also not a MC question). If you mean by 'mass' the mass of the X particle, then the production cross section e+e- -> VLL VLL cannot depend on it, unless there is a t-channel X exchange. If that t-channel dominates it becomes more pronounced with smaller and smaller X mass, and the cross section rises.