MadGraph5_aMC@NLO

How does MadGraph calculate Drell-Yan process

Asked by zwx

Just curious about it: For DY process qqbar->Z/gamma->l+l-, does MadGraph calculate and sample the distribution of Z firstly, then decay Z into l+l-; or, does it directly calculate the dilepton final state, then mark the reconstructed boson as Z? These should be a little bit different.

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

So here we have two channel of integration one for the photon and one for the Z.
Using the SDE strategy, they both cover the full phase-space with damping probability M^2_g/(M^2_g+M^2_Z) for one and the opposite for the second.

Then all event generated from the Z channel which are onshell (i.e. respect onshell condition) will be included in the lhef file to indicate to the parton-shower to not shuffle such mass.

How the Z channel itself is probed is not relevant, but yes we first sample the Z invariant mass and sample the decay.

Cheers,

Olivier

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zwx (uoxmh) said : 		#2

Hi Olivier,

thanks very much for the reply. Still I have several points to ask. To make sure I’m not misunderstanding anything, since some other event generators directly do calculation directly on final state, which can’t provide information of intermediate bosons, does it implies that MadGraph is different from those generators, in this aspect?

Also, if Z boson is firstly sampled, can I switch off the boson decay?

Another thing that confused me is that I once set mll_sf=106 for the process p p > Z > l+ l-. I found that there are lots of events with no Z boson recorded. If mll_sf is set to be higher (170 for example), non of the events have Z. But if Madgraph does probe Z channel separately, why does it happens in my case?

Thanks a lot!

All the best

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Olivier Mattelaer (olivier-mattelaer) said : 		#3

>thanks very much for the reply. Still I have several points to ask. To make sure I’m not misunderstanding anything, since some other event generators directly do calculation directly on final state, which can’t provide information of intermediate bosons, does it implies that MadGraph is different from those generators, in this aspect?

No, any generator can had such information. For any event you can throw a random number according to M^2_g/(M^2_g+M^2_Z) to decide the write the Z or not, of course such method assumes small interference and does not work far off-shell , this is why we do have an onshell condition in top of that.

>Also, if Z boson is firstly sampled, can I switch off the boson decay?
no we can not evaluate off-shell amplitude

> Another thing that confused me is that I once set mll_sf=106 for the process p p > Z > l+ l-. I found that there are lots of events with no Z boson recorded. If mll_sf is set to be higher (170 for example), non of the events have Z. But if Madgraph does probe Z channel separately, why does it happens in my case?

As said they are two conditions
1) we need to be in the Z channel, putting strong cut, will kill the Z-channel and the photon channel will be more and more important reducing the number of Z
2) You need to not be too far from the Z peak since otherwise we will not write the Z information since such information does not make sense due to strong interference between the Z and the photon.

Cheers,

Olivier

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zwx (uoxmh) said : 		#4

Thanks! So is this strategy (decide z or photon exchange first then calculate boson decay, rather than directly calculate and sample over the final state leptons) same for invariant mass far from Z pole? Say, m < 50 GeV or m > 150?

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Best Olivier Mattelaer (olivier-mattelaer) said : 		#5

So we have two channel
1) The photon-channel which does those steps:
 - generate s hat according to a 1/q^2 law (this law will be updated iteration after iteration by machine learning)
   Note that shat can go from 0 to S.
 - generate the (two) angle for the decay (in a flat way, again this will be improve iteration after iteration)
 - build the full momenta
 - check the cuts
 - evaluate the PDF
 - select which flavor for the quark to use according to the PDF
 - evaluate the matrix-element and the multi-channel factor (M^2_g/(M^2_g+M^2_Z))
 - determine which helicity can be associated to the events
 - update the estimator of the cross-section
 - determine if the events needs to written on disk or not (unweighting stage is based on the maximum of the integrand --including the multi-channel factor)
 - determine the color to write for the events --only one for your DY --
- determine which propagator needs to be include --here this is a photon so never written--

2) For the Z this is quite similar:
 - generate a random number according to flat law but do a change of variable that remap such variable on a breit-wigner shape.
  (this law will be updated iteration after iteration by machine learning)
   Note that shat can go from 0 to S.
 - generate the (two) angle for the decay (in a flat way, again this will be improve iteration after iteration)
 - build the full momenta
 - check the cuts
 - evaluate the PDF
 - select which flavor for the quark to use according to the PDF
 - evaluate the matrix-element and the multi-channel factor (M^2_Z/(M^2_g+M^2_Z))
 - determine which helicity can be associated to the events
 - update the estimator of the cross-section
 - determine if the events needs to written on disk or not (unweighting stage is based on the maximum of the integrand --including the multi-channel factor)
 - determine the color to write for the events --only one for your DY --
- determine which propagator needs to be include --here this is a Z so only written if the invariant mass of the Z is consider in the onshell window--

Then we do combine the two samples into a single one according to their relative importance via another unweighting procedure.

Note that both integral go from 0 to S (so nothing change below or above a given mass for the phase-space point of view, only the decision of writting or not a propagator does depend of threshold).
And that the decision of how much important are the contribution of "photon" or "Z" channel is technically done last because this is done via the last unweighting procedure. However, the decision on how much "Z" are written within the "Z" channel are done within the Z channel itself.

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zwx (uoxmh) said : 		#6

Thanks a lot. It really helps!