disagreement between theoretical and MadGraph2.9 results for t-channel processes

Asked by Yong Du on 2021-02-10

Hi,

I notice that recently you have released MadGraph2.9, which can efficiently deal with the phase space integrals especially for t-channel processes. Congratulations!

I have then transferred from MadGraph2.6.7 to MadGraph2.9.1.2 for the neutrino trident production project. The process I am considering is a muon neutrino scatters off an oxygen target. However, MadGraph gives very different cross sections compared with the theoretical ones. For example, for the "vm nf- > vm mu+ mu- nf-" process (with nf- representing the oxygen target), when the incident neutrino energy is 100GeV, Madgraph gives "3.448e-06 +- 3.737e-09 pb" with 100k events and using the dipole form factor, while the theoretical prediction (using an equivalent photon approximation and a dipole form factor for the target) is 1.10917e-4. Alternatively, using CompHEP with also a dipole form factor, I got 1.1857e-4 (uncertainty is within 1%).

In addition, when the incident neutrino energy is around 500GeV, the resulting cross section is of O(10) when I turn off the form factor. In comparison, the theoretical prediction is of O(1e-3) with the form factor either on or off. This seems to me that a divergent result is returned from MadGraph or the sampling is taken only for large momentum transfer where the contributions are expected to be negligible. ---- To produce the above numbers by MadGraph, I have removed all cuts applied to the leptons in the run_card.

Do you have a clue about why the difference for the cross sections? My UFO file, run_card, proc_card will be attached below for debugging.

To provide more information: Since all the processes are t-channel ones, while using CompHEP, I specify the kinematics as well as the regularization to tell CompHEP how to deal with the situation where the virtual propagators become on-shell. Given the difference on the cross sections above, I am thinking that if MadGraph could also allow us to set the kinematics and/or the regularization similar to CompHEP so the dangerous regime of the phase space integral can be avoided. Thanks.

Best,
Yong

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Last query:
2021-02-18
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2021-02-18
Yong Du (fallive) said : #1

It looks like I can not upload my files here. So I shared my UFO file, the run_card and the proc_card from a link to my dropbox. Please let me know if you prefer another method to get the files. In the meantime, if you need other files/info, please let me know. Thanks.

https://www.dropbox.com/s/znck9zody3m7bct/NeutrinoTrident.zip?dl=0

Best,
Yong

Hi,

From my understanding you have a divergency of your matrix-element.
And therefore you obviously have issue if you do not specify a cut preventing the cross-section to be infinite.

How is this handle in comphep without a cuts? Do you have a reference for that. We certainly not have "regulator" in place but it would be intersting to learn what they did and then I can consider add that in a future versions

Cheers,

Olivier

PS: Dropbox is perfect (the other solution is to create a bug report where attachment are allowed)

> On 10 Feb 2021, at 09:31, Yong Du <email address hidden> wrote:
>
> Question #695456 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/695456
>
> Yong Du gave more information on the question:
> It looks like I can not upload my files here. So I shared my UFO file,
> the run_card and the proc_card from a link to my dropbox. Please let me
> know if you prefer another method to get the files. In the meantime, if
> you need other files/info, please let me know. Thanks.
>
> https://www.dropbox.com/s/znck9zody3m7bct/NeutrinoTrident.zip?dl=0
>
> Best,
> Yong
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Yong Du (fallive) said : #3

Hi Olivier,

<< From my understanding you have a divergency of your matrix-element.

I just updated the third paragraph. I shall agree with you on the divergence when the incident neutrino energy is large. However, in the 100GeV case described in the second paragraph, MadGraph gives a result that is about 100 times smaller than the theoretical one. Do you also think this is caused by a divergent S-matrix element?

<< And therefore you obviously have issue if you do not specify a cut preventing the cross-section to be infinite.
<< How is this handle in comphep without a cuts? Do you have a reference for that. We certainly not have "regulator" in place but it would be intersting to learn what they did and then I can consider add that in a future versions

I shall mention that MadGraph predicts larger results compared with the theoretical ones only when I turn off the form factor, while it always predicts 10-100 (sometimes 1000 if the incident neutrino energy is at the 1GeV scale or smaller) times smaller results when I turn on the form factor. It looks to me that after including the form factor, which gets convoluted with the S-matrix element when doing the phase space integral, it becomes unclear for MadGraph how to do the sampling safely without falling into the divergent region.

On the other hand, while using CompHEP, I did not specify any cuts on the initial or the final state particles except explicitly setting the "kinematics" and the "regularization". The "kinematics" tells CompHEP how to repeatly split the multi-body phase space integral into two-body phase integral, while the "regularization" setup tells CompHEP how to deal with on-shell internal particles -- with the setup, it will smooth the sharp peak. Probably you can look at their manual, which I find very helpful, at

https://theory.sinp.msu.ru/lib/exe/fetch.php/comphep/manual-3.3.pdf

Best,
Yong

Hi,

How do you activate/deactivate the form-factor?

I have try to run your process for the default benchmark of the model (since you did not specify your benchmark)
and I do reproduce a cross-section 3.44e-6 but this computation actually includes some cuts.
Did you keep those on purpose?

In your computation, I'm also surprise by the fact that your mass for your oxigen target is so light with only 1GeV for the target mass but highly boosted since it has 15GeV energy.
So for me this looks like more like a low energy accelerator of proton than oxygen.
Could you explain the logic here?

Cheers,

Olivier

Yong Du (fallive) said : #5

Hi Olivier,

Sorry for my late reply due to the holiday here, and Happy Chinese New Year!

<< How do you activate/deactivate the form-factor?

To activate the form-factor, I include the form-factor in the vertices.py and the lorentz.py files accordingly as you can see therein. To deactivate the form-factor, I use a bash script to replace the form_factors.py file with one that returns only the "Z" factor instead.

<< I have try to run your process for the default benchmark of the model (since you did not specify your benchmark) and I do reproduce a cross-section 3.44e-6 but this computation actually includes some cuts. Did you keep those on purpose?

I suppose you were using the run_card I sent to you in the zipped file? If yes, the only cut applied in my run_card shall be the drll cut. In my bash script, I did set this cut to -1.0 (The one I sent to you contains this cut since I generate the files manually instead of using my bash script), but I still got disagreement and that was why I thought the drll cut shall not be the reason for the disagreement. To be more specific, when I remove the drll cut in the run_card I sent to you and keep everything the same, I got "3.526e-06 +- 3.834e-09 pb", which is slightly larger than the previous result as expected. But it is still two orders of magnitude smaller than the theoretical value 1.10917e-4pb. Am I missing something?

<< In your computation, I'm also surprise by the fact that your mass for your oxigen target is so light with only 1GeV for the target mass but highly boosted since it has 15GeV energy. So for me this looks like more like a low energy accelerator of proton than oxygen. Could you explain the logic here?

Let me explain. I use MadGraph in the bash mode, and in my bash script, I use the command "set MNF 15" to modify the mass of the oxygen. The 1GeV you were talking about should be the value in the parameters.py, right? Since my original code is written for the hydrogen target, that is why it has a default value of 1GeV.

However, based on my experience, the "set MNF 15" command shall ensure a correct setup before MadGraph doing the simulation, do you mean it is not? Thank you.

Best,
Yong

Yong Du (fallive) said : #6

<< However, based on my experience, the "set MNF 15" command shall ensure a correct setup before MadGraph doing the simulation, do you mean it is not? Thank you.

Just to add one comment: The mass of the oxygen is indeed 15 GeV as can be seen in the run_card. From your last comment, I just realize that since I generated the events manually on my laptop, MNF was not updated to 15GeV in the param_card. After correcting MNF to 15GeV in the param_card and using the run_card I sent to you with drll set to -1.0, surprisingly, I got "1.642e-17 +- 1.534e-20 pb" that is way smaller than the theoretical prediction of 1.10917e-4pb. I am confused at this point, could you double-check on this? I will do more tests as well. Thank you.

So does it work for Hydrogen?

The most likely place of issue is within your model.
Do you use the same model in comphep ?

Can you check the matrix-element for a single phase-space point?
This would allow to check if the issue is within the phase-space integration (I strongly doubt on that) or in the evaluation of the matrix-element (my best bet).

Cheers,

Olivier

Yong Du (fallive) said : #8

Hi Olivier,

<< So does it work for Hydrogen?

No, I got a similar problem with the Hydrogen target. A detailed discussion for the hydrogen target, or a comparison between the hydrogen and the oxygen based on my previous investigation would be too much to show here. I will follow your suggestion below to investigate more.

<< Do you use the same model in comphep ?

Yes but except the "kinematics" and "regularization" setup I mentioned earlier, and that is the reason why I asked earlier if MadGraph could also allow a similar setup as in CompHEP to customize the phase space integration order and to deal with the case where intermediate particles become on-shell for these t-channel processes.

<< Can you check the matrix-element for a single phase-space point?
This would allow to check if the issue is within the phase-space integration (I strongly doubt on that) or in the evaluation of the matrix-element (my best bet).

Thank you for your patient help and suggestion along the way. I can look into this again more carefully.

Best,
Yong

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