MadGraph5_aMC@NLO

Clarification on Reported Errors in Cross Section at NLO

Asked by Ketan Jadav

Hi,

I am trying to better understand the errors reported along with the cross section values at NLO. I generated 10,000; 100,000; and 1,000,000 events for the processes under consideration. However, I noticed that the errors do not decrease as expected with 1/Sqrt(N).

For instance, for the process p + p -> t + c~ + b~ at NLO, I obtained the following results:

Events | Cross Section [t] | Error
10,000 | 10.627 | 0.208
100,000 | 11.353 | 0.144
1,000,000 | 11.198 | 0.116

As shown, when increasing the number of events from 10,000 to 100,000, the error does not reduce by a factor of 1/Sqrt(10). The same holds when increasing from 100,000 to 1,000,000 events.

Could you please clarify whether these errors are purely statistical, or if they also include systematic components, or possibly something else?

I would greatly appreciate your explanation on the meaning of these errors.

Thank you,
Ketan

Question information

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English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
Rikkert Frederix Edit question
Solved by:
Rikkert Frederix
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Best Rikkert Frederix (frederix) said : 		#1

Dear Ketan,

The uncertainty is the statistical uncertainty from the Monte-Carlo integration of the cross section. In principle this is independent from the number of unweighted events you generate -- although, in practice you want the relative uncertainty be smaller than 1/sqrt(N) with N the number of events to generate. (It's a bit more tricky, because there are both positive and negatively weighted events: the 1/sqrt(N) uncertainty should be the relative uncertainty when integrating the absolute value of the integrand, but those are details). Anyway, by default, the code tries to satisfy this, but might not completely get there when asking more than 1M events.

You can force the code to compute the total rate with higher accuracy through lowering the relevant parameter ("req_acc") in the run_card.dat.

best,
Rikkert

Revision history for this message
Ketan Jadav (ketan02) said : 		#2

Thanks Rikkert Frederix, that solved my question.