e1, A => e1, E2, e2

Dear Camilla,
thanks for your question. Probably we'll need a few iterations to clarify all the points. FIrst of all, I thought it a typo when you had just "e" in second process definition but Whizard accepts this. The compile_analysis does not do anything as you have not defined any analysis yet (this would anyways just be Whizard's internal analysis, which is not the most sophisticated one). By just writing a simulate statement into the Sindarin file, the integration is done automatically with the default settings. The integrations look reasonable, with the exception of the last one, but they are certainly not at their best. You can specify the integration after the beam definitions and before the simulation statement, e.g.
integrate (proc) { iterations = 7:100000:"gw", 3:150000 }
where you have 7 iterations of 100k calls with adaptation of MC grids and weights, and then 3 iterations of 150k for the final cross section definition. This gives a smaller final error and a higher efficiency in generating unweighted events (faster generation):
|=============================================================================|
| VAMP: parameter mismatch, discarding grid file 'proc.m1.vg'
   1 100000 5.2594787E+07 4.02E+06 7.65 24.18* 0.06
   2 99994 4.8872726E+07 1.47E+06 3.01 9.53* 0.17
   3 99988 5.2679498E+07 8.04E+05 1.53 4.83* 0.38
   4 99981 5.2132485E+07 4.50E+05 0.86 2.73* 0.79
   5 99977 5.1616033E+07 2.11E+05 0.41 1.29* 2.57
   6 99972 5.1937510E+07 1.49E+05 0.29 0.90* 3.32
   7 99966 5.1807596E+07 9.54E+04 0.18 0.58* 7.51
|-----------------------------------------------------------------------------|
   7 699878 5.1825130E+07 7.36E+04 0.14 1.19 7.51 1.21 7
|-----------------------------------------------------------------------------|
   8 149997 5.1885578E+07 8.13E+04 0.16 0.61 6.43
   9 149997 5.1873474E+07 8.23E+04 0.16 0.61 5.42
  10 149997 5.1869505E+07 8.00E+04 0.15 0.60* 4.91
|-----------------------------------------------------------------------------|
  10 449991 5.1876139E+07 4.69E+04 0.09 0.61 4.91 0.01 3
|=============================================================================|
| Time estimate for generating 10000 events: 0d:00h:00m:12s
With such a setting, also the third process yields a good adaptation:
|=============================================================================|
| It Calls Integral[fb] Error[fb] Err[%] Acc Eff[%] Chi2 N[It] |
|=============================================================================|
| VAMP: parameter mismatch, discarding grid file 'proc2.m1.vg'
   1 95256 1.6025809E+10 2.57E+09 16.04 49.49* 0.02
   2 81736 1.4856683E+10 6.01E+08 4.05 11.57* 0.09
   3 83968 1.5991087E+10 3.22E+08 2.02 5.84* 0.23
   4 81936 1.5661464E+10 5.96E+07 0.38 1.09* 1.62
   5 86832 1.5713709E+10 1.06E+07 0.07 0.20* 10.28
   6 86832 1.5723771E+10 4.74E+06 0.03 0.09* 29.31
   7 88592 1.5718344E+10 3.48E+06 0.02 0.07* 33.03
|-----------------------------------------------------------------------------|
   7 605152 1.5719695E+10 2.71E+06 0.02 0.13 33.03 0.83 7
|-----------------------------------------------------------------------------|
   8 149688 1.5718336E+10 2.24E+06 0.01 0.06* 32.99
   9 149688 1.5718542E+10 2.23E+06 0.01 0.05* 32.98
  10 149688 1.5716489E+10 2.23E+06 0.01 0.05 32.97
|-----------------------------------------------------------------------------|
  10 449064 1.5717788E+10 1.29E+06 0.01 0.05 32.97 0.26 3
|=============================================================================|

Note that this is only the case because this is a 2->2 process and you have energy-momentum conservation, so that the photon in the final state cannot become arbitrarily soft. For 2->3 processes, you usually need to specify a selection cut at generator level to get a finite cross section. The sizes of the cross sections seem reasonable to me. For the size of the cross section confer the comparison plot on slide 13, upper right, of the talk here: https://indico.cern.ch/event/838435/contributions/3635693/attachments/1968538/3273996/JRR_2020_FCC_WHIZARD.pdf
There you also find a reference for an analytic calculation of (double) Compton scattering: M. Ram(SUNY, Buffalo), P.Y. Wang(SUNY, Buffalo) (1971), Phys.Rev.Lett. 26 (1971) 476-479.
Now to your third question: first of all, there are options to scan over parameters, e.g.
scan beam_momentum = (199.991 GeV => 200 GeV /+/ 0.001 GeV) {
   integrate (proc) { ....}
   simulate (proc)
}
etc. There are also several options to take into account beam effects. The easiest is a Gaussian smearing of the beam profile, or a specific beam event file that can be read in. In case you have a Guinea Pig simulation of your beam profile that could also be translated into a CIRCE spectrum inside Whizard. Note that more or less all of these options have not yet been really tested with asymmetric beams though Whizard has been used for Belle II simulations.
I leave it with that for a first answer, let's iterate from here.
Best,
   JRR (Juergen Reuter)

Dear Juergen,
thank you so much for replying so fast!

I'm working on this recent idea https://arxiv.org/abs/2106.03255 and I used Whizard for the simulations therein (I perform the analysis separately after reading the output files).
Since I'm trying to further develop and cross check those preliminary results I decided to write here.

I'll for sure implement your suggestion on the integration (integrate (proc) { iterations = 7:100000:"gw", 3:150000 }).

I considered only the 3 processes e1, A => e1, E2, e2 e1, A => e1, E1, e1 e1, A => e1, A but (as shown in slide 13) I should also include e1, A => e1, A,A and possibly take into account also radiative components of the other two reactions... is it feasible using Whizard?

Concerning the values for the total cross sections: I obtain a perfect agreement between the Compton as in eq. 5 and Whizard but I see a difference for the other two as reported in eq.4 and summarized in table II. In particular the reaction e1, A => e1, E2, e2 cross section worries me... I know is a quite unsual setup with very asymmetric collision and close to the reaction threshold. For the cross section calculation I used the approach by Motz but I also found a paper by Athar giving the same value of Whizard, I'm still investigating. It would be important for me to know the Whizard cross section reference.

I don't have a beam profile, I would need a way to insert a Gaussian smearing in position and angle of the incoming beams (basically the emittance), is there an example I can look up?

Thank you very much for your help!
Camilla

Just some quick comments, we will discuss this in our collaboration meeting tomorrow. The process you were asking about, e1, A => e1, A, A should also work with WHIZARD, but of course you need a photon energy cut at generator level as this cross section would otherwise be divergent. I think, separation cuts from the beam axis and from the outgoing electron or dressed electrons (roughly, the theory equivalent of the Moliere radius in the ECAL) are not needed as the electrons are all massive. But one has to check the quality of the MC integration. With the equations you are referring to the arXiv reference above, right? Eq. (5) is then the one for inverse Compton scattering (ICS), glad that this one agrees. With the other two (disagreeing ones) you mean the TPP and MPP, so triple pair production and muon pair production, correct?
A first glance at the paper by Motz et al. and at the formula Eq. (4) in your paper shows that this is the Bethe-Heitler cross-section formula with some sort of corrections. This is the pair-production in the field of a nucleus which more or less does not recoil against the photon. This is definitely nothing that is implemented in Whizard, and I think this is also not the right approach here, as you really study e-gamma collisions. I didn't find the reference by Athar that you mentioned, so I would be grateful if you could point us to it.
Regarding the beam structure, there is a Gaussian beam profile implemented in Whizard, but that is only Gaussian in the beam energy spread, not in the angular variables. We have to discuss how easy it would be for us to provide this much more general setup.

Dear Juergen,
yes, for the equations I was referring to the arXiv and yes, our doubts are about MPP and TPP.
In the following a small summary of our studies up to now:

MPP cross section:
-we used from [1] formula at pg. 631-2 for triplet and applied it to muons as suggested at pg.602. For E_{cm}=346 MeV we obtain \sigma^{MPP}_{tot}= 216 nb
-Whizard gives \sigma^{MPP}_{tot} =52 nb
-a similar result to Whizard is reported in [2]
-in [4] I can't find the value of total cross section

TPP cross section:
-we used from [1] formula at pg. 631-2 for triplet. For E_{cm}=346 MeV we obtain \sigma^{MPP}_{tot}= 19 mb
-Whizard gives \sigma^{MPP}_{tot} =2.5 mb
-in [3] (if I interpret correclty figure 4) the value of total cross section is around 20 mb

[1] J. W. Motz, H. A. Olsen and H. W. Koch, Pair Production by Photons Rev. Mod. Phys. 41 (1969)
[2] H. Athar, Guey-Lin Lin and Jie-Jun Tseng, Muon pair production by electron-photon scatterings, PHYSICAL REVIEW D, VOLUME 64, 071302(R) (2001)
[3] D. Bernard, A 5D, polarised, Bethe-Heitler event generator for $\gamma \rightarrow e+e$ conversion (2018)
[4] D. Bernard, A 5D, polarised, Bethe-Heitler event generator for $\gamma \rightarrow \mu+\mu$ conversion (2019)

We are still investigating, any help from your side is super welcome, expecially in understaning what is implemented in Whizard.

Thank you very much for all the infos you can provide about e1, A => e1, A, A and the possible emittance implementation!
Grazie
Camilla

This question was expired because it remained in the 'Open' state without activity for the last 15 days.

Apparently, we weren't fast enough in providing an answer. Mainly, the question is also more about the physics to be studied in the first place, and only afterwards a question of the specific implementation. So, in summary, the specific processes like Bethe-Heitler etc. are not implemented in Whizard (and at the moment there is no person-power to do that), while the "elementary" processes, the double-Compton and trident processes are implemented and have been validated for asymmetric beams by the Belle collaboration.

Still to be discussed.

Thanks Juergen Reuter, that solved my question.