WHIZARD

isr_q_max

Asked by Zhang, YJ

If we calculate a process including ISR like e+ e- --> HZ, what does isr_q_max correspond to?
a. isr_q_max is the maximum mass of the final state particles without photon?
b. isr_q_max is the maximum energy of an isr photon, only one isr photon is allowed?
c. isr_q_max is the maximum energy of isr photons，>=0 isr photons are allowed?
d. else?

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WHIZARD Edit question
Assignee:
Juergen Reuter Edit question
Solved by:
Krzysztof Mekala
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Juergen Reuter (j.r.reuter) said : 		#1

This is explained in Sec. 5.5.6 of the manual, https://whizard.hepforge.org/manual.pdf,
and including formulae in the documented source code, https://whizard.hepforge.org/whizard.pdf,
sections 16.6 and 10.1.1.
So isr_q_max is the upper limit of the kinematic integration when extracting an electron PDF (a.k.a. ISR
structure function) in collinear factorization, and it is the hardness scale of the PDF,or in other
words the factorization scale. The default is sqrt(s).

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Zhang, YJ (yjazhang) said : 		#2

Dear Juergen,

Thank you very much!

But I still have a question. If I increase the isr_q_max from 0.1 sqrt(s) to 1.0 sqrt(s) by the step of 0.1 sqrt(s), the cross section will decrease. If isr_q_max is the upper limit of kinematic integration, the cross sections are increased. What is wrong?

Kind regards,

YJ

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

Dear YJ,
that depends very much on the process and on the collider energy. If I take e+e- -> mu+mu- and 500 GeV, the cross section rises when changing from the scale (isr_q_max) from 10 GeV to 500 GeV = sqrts.
Cheers,
       JRR

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Zhang, YJ (yjazhang) said : 		#4

Dear Juergen,

Thank you very much!

If isr_q_max is the upper limit of kinematic integration, and the lower limit of kinematic integration is independent of isr_q_max, then the cross sections are increased?

So, the lower limit of kinematic integration here depends on isr_q_max here?

Kind regards,

YJ

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Juergen Reuter (j.r.reuter) said : 		#5

See equations (10.2) and (10.3) of the documented source code: the two limit are related, but in the ultra-relativistic limit assumed here, they become independent.

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Zhang, YJ (yjazhang) said : 		#6

Thanks.

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Zhang, YJ (yjazhang) said : 		#7

Thanks Juergen Reuter, that solved my question.

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Zhang, YJ (yjazhang) said : 		#8

Dear Jürgen,

Thank you so much!

Sorry to bother you with this again.

If I increase the isr_q_max from 0.1 sqrt(s) to 0.2 sqrt(s), the cross section will decrease. This means that the cross section of the isr photon from 0.1 sqrt(s) to 0.2 sqrt(s) is negative, an unphysical result.

If I want to calculate e+ e- ---> HZ, and require the energy of the ISR photon to be less than 0.1 sqrt(s), would I set isr_q_max = 0.1 sqrt(s)?

Kind regards,

YJ

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Best Krzysztof Mekala (krzysztofmekala) said : 		#9

Dear YJ,
I'm afraid I have to disagree with your findings. I've tried to integrate this process at different collision energies, and the cross section always increases with the larger phase space. Please, provide us with your Sindarin file.

As highlighted by Juergen, isr_q_max is a factorization scale which is not the same as the photon energy. To generate events with ISR photons below some energy scale, you can use the "select" statement. A matching procedure and an example Sindarin file are given in [2004.14486].

Regards,
Krzysztof

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Zhang, YJ (yjazhang) said : 		#10

Thanks Krzysztof Mekala, that solved my question.