Estimating cross-section of QCD multijet and W/Z pair production

Asked by Pete

Hello,

I am hoping to generate the cross-sections of QCD multijet events and W/Z pair production. I was wondering if this would be possible with Madgraph5?

What I have in mind is to look at background events for an all hadronic ttbar so it would be something like

p p > j j > j j j j j j

for QCD and

p p > j j > w-w+ (z z or w z) > j j j j j j

for W/Z pair

I have ran the ttbar cross-section at NLO without any problems p p > t t~ > j j j j j j [QCD] but when trying the QCD multijet (as written above) it resulted in this error after running for a while:

Command "generate p p > j j > j j j j j j" interrupted with error:
NoDiagramException : No amplitudes generated from process Process: g/u/c/d/s/u~/c~/d~/s~ g/u/c/d/s/u~/c~/d~/s~ > g u c d s u~ c~ d~ s~> g/u/c/d/s/u~/c~/d~/s~ g/u/c/d/s/u~/c~/d~/s~ g/u/c/d/s/u~/c~/d~/s~ g/u/c/d/s/u~/c~/d~/s~ g/u/c/d/s/u~/c~/d~/s~ g/u/c/d/s/u~/c~/d~/s~ WEIGHTED=18 @1. Please enter a valid process

Thank you so much.

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Rui Zhang (ruirui) said :
#1

Firstly, for tree-level, "generate p p > x > j j j j j j" means "generate p p > j j j j j j" and you also want a s-channel particle x, so "generate p p > j j > j j j j j j" is the same as "generate p p > j > j j j j j j". And j equals to g u u~ d d~ c c~ s s~, so now it's "generate p p > g u u~ d d~ c c~ s s~ > j j j j j j". We know the 2-to-6 process can't have 9 s-channel particles, and that's why no amplitudes are generated.

If you just want to produce 6 jets with 2 s-channel quark or gluon, I recommend you to use "generate p p > j j j j j j" directly. You may want to use "generate p p > g | u | u~ | d | d~ | c | c~ | s | s~ > j j j j j j" to emphasize a s-channel particle. But it's not necessary, because there are at least 4 s-channel particles. And maybe this is not well defined at NLO.

By the way, I don't think the process "p p > j j > w- w+ > j j j j j j" can be generated. Because it's hard to let madgraph know if the particle j is before w+. So I think you should only use 2 ">" in a single process.

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Olivier Mattelaer (olivier-mattelaer) said :
#2

Hi,

Let me add some comment on rui zhang contribution:

If you are interested in the contribution where the Z/W are onshell, you can use the following syntax:
generate p p > w+ w- j j, w+ > j j , w- > j j
you can also do
generate p p > w+ w- j j
and then use madspin in order to ask to decay the w+/w- only into jets.

If you use five flavors (which does not seems to be the case), you can also veto the onshell-top contribution:
generate p p > w+ w- j j $ t t~, w+ > j j , w- > j j
or
generate p p > w+ w- j j $ t t~

Note that the syntax with the coma is not supported for NLO computation (and MadSpin method is the only way)
The difference of precision between the two method is only at the cross-section level where MadSpin use the NWA for the cross-section while the decay chain syntax (the one with comma) performs actual phase-space integration.
The normalised differential cross-section is otherwise identical (both method include off-shell effects up to a threshold and include full spin correlation).

The pure 6 jet QCD background is a quite challenging computation. You can in principle do it like suggested:
generate p p > j j j j j j
but this is valid only for 6 hard jet well separated.

In general, for such type of sample, you want to also correctly cover the case where some jet are not that hard or not that well separated. In that case you need matched and merged sample.

I would advise you to look at this tutorial:
https://indico.cern.ch/event/775229/contributions/3222198/attachments/1796209/2928229/19_02_14_tuto_VBS.pdf
where you have the description (and exercise) of many of the syntax.

Cheers,

Olivier

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