Negative distributions with MC@NLO

Asked by Rob Verheyen on 2020-06-22

Dear Madgraph authors,

I'm running into issues trying to do something unusual with the MC@NLO machinery. I want to use the real correction events at fixed order NLO without a shower. I obviously cannot use the H events directly because the same phase space receives contributions from the S events with a single shower emission. I thus have to add a single shower emission to the S events. My process is the following:

- I generate p p > t t~ [QCD]
- Do launch -p and select PYTHIA8 as the shower option
- Write a Pythia program that uses a user hook to only add a single shower emission to the S events. I load in the cmdn card I find in the PYTHIA81 directory in MG5 to ensure I'm using the correct settings.

When I then plot some distributions of the resulting events I find that some go negative. In particular, infrared-sensitive quantities (like the top+gluon invariant mass) go negative at small values. It seems that this would originate mostly from S events with negative weight that do a small-scale shower branching, because the H events have no enhancement in the IR region.

I'm wondering if my problem is technical or conceptual. My understanding is that the events I obtain after this procedure should be physically sensible, but maybe I'm missing something.


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MadGraph5_aMC@NLO Edit question
Rikkert Frederix Edit question
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Rikkert Frederix
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Rikkert Frederix (frederix) said : #1

Hello Rob,

The single emission on the S-events restores the NLO accuracy of the results (which is not there when not showering at all). However, I don't think it's guaranteed that this makes the predictions physical, in the sense that all IR-safe observables are positive definite. In effect, I'm not surprised that observables that are sensitive to the IR structure of the events go negative. These observables are very sensitive to multiple shower emission (or, if you want, come with a large IR logarithm), and therefore multiple emissions might change them considerably.


Rob Verheyen (robverheyen) said : #2

Hi Rikkert,

Thanks for the answer!

If I'm correct, I think what that would mean is that I should get a proper distribution if I were to only keep events that really have a single emission after running a full shower right? Then the IR logs are included in the no-emission Sudakov and I should really be looking at a physical distribution.


Best Rikkert Frederix (frederix) said : #3

Hi Rob,

I'm not sure that's what you want, in the sense that 'having exactly one emission after a full shower' is not a physical observable. It's not an IR-safe observable and therefore most-likely not NLO correct.

What is it that you are trying to achieve?


Rob Verheyen (robverheyen) said : #4

Hi Rikkert,

Yes, I should probably have explained. I'm doing this for the following reason: I'm working on a generative machine learning model that is able to be trained on weighted events, and in particular on events with negative weights. So the purpose of all of this is just to find an example of some real physics application that produces negative weights, and to show that we can train the model on that and produce similar results. But maybe I should be looking elsewhere to accomplish that.

Thank you for your help so far!


Rob Verheyen (robverheyen) said : #5

Thanks Rikkert Frederix, that solved my question.