MadGraph5_aMC@NLO

Statistical uncertainty of reweighted events

Asked by akash

Dear experts,

The following model and process details are just for illustrative purposes for this question...

I have a model with the muon g-2 implemented via the modified photon-muon coupling. The process is e+e- -> mu+mu- explicitly via gamma only. I produce 20 runs of 50K events each, totalling 1M events. Each run has an associated cross section and uncertainty, which as I understand it, is the statistical uncertainty of the integration method that Madgraph uses.

Now suppose I reweight the events produced for g-2=0 for some other g-2 != 0. I get samples with cross sections very close to the cross section for dedicated samples produced for g-2 !=0. The stat uncertainty for the reweighted samples is larger than the dedicated samples, which is expected.

My question is: how does Madgraph compute the stat uncertainty of the reweighted events? Is the original uncertainty multiplied by the same factor by which the event weights are modified? Is there any literature/documentation/slides for understanding the error handling in reweighted events?

Thank you

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Olivier Mattelaer
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Olivier Mattelaer (olivier-mattelaer) said : 		#1

Hi,

It is just a normal error propagation
the new cross-section is given by cross_new = <R> cross_old
so the error on cross_new is given by error_new = error_R cross_old + <R> error_old

To estimate error_R, we assume gaussian distribution of the weight and take the 1-sigma error.

Cheers,

Olivier

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akash (ranade1) said : 		#2

Dear Olivier,

Thanks very much for the quick reply.

Just for clarification, <R> is the event-by-event distribution of weight modifications? I.e. M^2(new)/M^2(old) ?

Thanks

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Best Olivier Mattelaer (olivier-mattelaer) said : 		#3

<R> is the average reweighting factor.
Independently of the definition of such factor (which is different between LO and NLO, and actually not unique even at LO)

Cheers,

Olivier

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akash (ranade1) said : 		#4

Thanks Olivier Mattelaer, that solved my question.