MadGraph5_aMC@NLO

Error computation for FO NLO EW

Asked by Alberto Navarro

Dear MG5 experts,

I'm considering the process of an (SM) Higgs decay to 4 charged leptons at NLO EW. I generated h > l+ l- l+ l- aS=0 aEW=3 [QED] within the complex mass scheme with the loop_qcd_qed_sm_Gmu UFO model. For the fixed-order computation with 0.01 accuracy, the results for the partial width and its error (with default params) quoted by MG5 are 5.059e-07 +- 1.5e-09 GeV.

I am trying to reproduce these results using the weights from the LHE file produced by MG5. The result I obtain for the partial width using \sum_i w_i = 5.05884e-07 GeV agrees with that from MG5, but the error obtained with \sqrt(\sum_i w_i^2) is 1.52708e-07 GeV, which is clearly worse than what MG5 gives. Is this expected, or am I doing something wrong? In principle, I could increase the accuracy of the FO computation, but I will still get \sqrt(\sum_i w_i^2) much larger than what MG5 gives, so how is the error that MG5 gives computed? Is it not computed using the weights?

Thanks a lot for your help.

Best,
Alberto

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

Hi,

How do you compute the error at FO? Events are correlated, so one need to take that into account within the error computation.

Second, indeed the error is not computed on the lhe file (in general we do not have produce lhe file for FO).
Since
1) the lhef file has some unweighting performed to reduce the size of the file.
2) the normal error is computed on multiple iterations while the lhef is only done for the last iteration.

Cheers,

Olivier

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Alberto Navarro (an1798) said : 		#2

Hi Olivier,

Thanks for your reply.

I guess I'm considering uncorrelated events as I'm computing the error by adding up the squares of the weights. Could you elaborate more on why/how the events are correlated? Is it because the events with an extra emission are computed by attaching the photon to any external leg of the born events? Also, I see that the lhe file contains event groups, so should I correlate only the events within the same group or with all the events in the lhe file?

Regarding 2). If I have N lhe files produced with different seeds, I can compute the partial width for each file using the sum of weights. This will give a distribution for the values of the partial width, and the stv of the distribution should be comparable to the error quoted by MG5, is this correct?

Thanks again for your help.

Best,
Alberto

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

Hi Alberto,

Yes all entry in an "event group" are correlated since this correspond to the event use to substract the singular behaviour (i.e. the counter-event). So for error computation (and it should be the case too for the average) you should sum all their weights first before computing the average/error. For the average, it only matters if the number of counter-events is not always the same which is technically possible but likely not the case for your process.

> Regarding 2). If I have N lhe files produced with different seeds, I can compute the partial width for each file using the sum of weights. This will give a distribution for the values of the partial width, and the stv of the distribution should be comparable to the error quoted by MG5, is this correct?

I guess not exactly but this should be similar indeed.

Cheers,

Olivier

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Alberto Navarro (an1798) said : 		#4

Thanks Olivier Mattelaer, that solved my question.