VBF diagram syntax in Madgraph

Hi Will,

Let first discuss physics.
All this diagrams contributes and interfere with each other.
In particular if you remove one of those diagram the result will be not be gauge invariant.
I know that some people (wrongly) claims that we don't care about gauge invariance but we do.
In any case MG result are (most of the time) not Lorentz invariant if the result are not gauge invariant.
So you need those diagrams in your analysis.

You have one exception, if the Z is on shell, in that case, the interference drops. and you can remove the contribution.
This is exactly the meaning of the the following two expressions:
p p > z u u, z > mu+ mu- (only keep the on shell contribution of diagram 3,4,7,8,9,10.11 and 12)
p p > mu+ mu- u u $ z (keep everything but the previous contribution)

This: "p p > mu+ mu- u u $z " is the expression that you should use!

The following MG tutorial includes a full section on the various syntax, their meaning and why using the
"/" syntax and other way to brute force the diagram selection are NOT physical.
https://indico.cern.ch/getFile.py/access?contribId=4&resId=2&materialId=slides&confId=234296
(I just update the slide to make the points clearer without me presenting those)
You need to focus to slide 10 to 27.

This tutorial also indicates the syntax to one way to only keep the VBF diagrams (slide 26), but please use it only
if you have a good reason for it.

Cheers,

Olivier

On Apr 9, 2013, at 8:26 PM, Will Flanagan <email address hidden> wrote:

> New question #226332 on MadGraph5:
> https://answers.launchpad.net/madgraph5/+question/226332
>
> Hi Madgraph Experts,
>
> I generate the following 12 diagrams with Madgraph:
> http://hepr8.physics.tamu.edu/will/uu_uumumu_noa_QCD0_QED4.pdf
> using the command:
> "generate p p > u u mu+ mu- / a QCD=0 QED=4 ; display diagrams"
>
> You'll see that four of these diagrams are VBF production of muon pairs (diagrams 1, 2, 5, and 6). But this command also allows 8 non-VBF diagrams (3, 4, 7, 8, 9, 10, 11, and 12).
>
> Question 1: How can I distinguish between these two diagrams with Madgraph syntax?
>
> Alternatively, the 8 diagrams that I don't want can be made with the command:
> "generate p p > z z > u u mu+ mu- / a QCD=0 QED=4 ; display diagrams"
> http://hepr8.physics.tamu.edu/will/uu_zz_uumumu_noa_QCD0_QED4.pdf
>
> Question 2: Is there a way to subtract these diagrams from the previous command's diagrams? This would be an alternate solution to my problem.
>
> Finally, all of the diagrams that I don't want have an s-channel Z going to two muons (3, 4, 7, 8, 9, 10, 11, and 12 from my first pdf or all 8 diagrams in the second pdf).
>
> Question 3: If I add "$ z" to my command to exclude any s-channel Z bosons, none of the diagrams with Z->mumu go away.
> "generate p p > u u mu+ mu- / a $ z QCD=0 QED=4 ; display diagrams"
> Is there syntax which can exclude these diagrams?
>
> Even better, if you can point me to any further documentation, that would also be great. I've read their minimal user manual (arXiv:1106.0522), but thats it.
>
> Many thanks in advance!
> Will Flanagan
>
> --
> You received this question notification because you are a member of
> MadTeam, which is an answer contact for MadGraph5.

Hi Olivier,

Thanks very much for taking the time to help me.

You make a very good point with regards to interference. That is very important to keep in mind. In fact, this is something that has been getting lots of attention within our group. I am not yet trying to make a rigorous study, I just want to study the kinematics of weak boson fusion. To this end, I do want to just produce diagrams 1, 2, 5, and 6 for now.

With that in mind, can you think of a command to make only these diagrams? I am still just learning your nice tool, so I'm still quite weak on syntax.

Many thanks,
Will

Hi Will,

In fact you have all syntax explained on the tutorial that I put in link.
In you case, you need to use the $$ syntax

p p > mu+ mu- u u $$ z /a

MG5>generate p p > mu+ mu- u u $$ z /a
INFO: Checking for minimal orders which gives processes.
INFO: Please specify coupling orders to bypass this step.
INFO: Trying coupling order WEIGHTED=6
INFO: Trying coupling order WEIGHTED=7
INFO: Trying process: u u > mu+ mu- u u WEIGHTED=8 $$ z / a
INFO: Process has 4 diagrams
INFO: Trying process: u c > mu+ mu- u u WEIGHTED=8 $$ z / a
INFO: Trying process: c c > mu+ mu- u u WEIGHTED=8 $$ z / a
1 processes with 4 diagrams generated in 0.344 s
Total: 1 processes with 4 diagrams

I've also check the gauge/lorentz invariance and looks like that this is lorentz invariant
MG5>check p p > mu+ mu- u u $$ z /a
...
Lorentz invariance results:
Process Min element Max element Relative diff. Result
u u > mu+ mu- u u6.2628753519e-13 6.2628753519e-13 1.9347189307e-14 Passed
Summary: 1/1 passed, 0/1 failed
Gauge results (switching between Unitary/Feynman):
Process Unitary Feynman Relative diff. Result
u u > mu+ mu- u u 8.7514835656e-15 8.7514835656e-15 3.6056099486e-16 Passed
Summary: 1/1 passed, 0/1 failed
Process permutation results:
Process Min element Max element Relative diff. Result
u u > mu+ mu- u u 1.8518045901e-15 1.8518045901e-15 1.0649894020e-15 Passed
Summary: 1/1 passed, 0/1 failed

Cheers,

Olivier

Hi Olivier,

Ok I see it now. As a I browsed the tutorial, I didn't realize that there was a difference between "$" and "$$". I see that you mention "$$" on page 26. This is exactly what I was looking for.

I didn't see any mention of $$ in arXiv:1106.0522v1, so I wasn't aware of it. In fact, I am wondering if one of your examples in the appendix is a little misleading. In Table 7, you have "p p > b w+ t~ $ t" and it is described as "Exclude any diagrams with an s-channel t propagator". Would a better description perhaps be "Exclude any diagrams with an *on-shell* s-channel t propagator"?

It seems like "p p > b w+ t~ $$ t" is actually excluding *any* diagram with an s-channel t propagator. A "single $" diagram only excludes on-shell, right?

In fact "p p > b w+ t~" and "p p > b w+ t~ $ t" have the exact same diagrams, just different cross sections. So no diagrams are actually being excluded by "$ t".

Sorry, I don't mean to get too invested in semantics; I am just really trying to make sure I understand whats going on. I must emphasize that Madgraph 5 seems like an awesome tool and I am enjoying learning it.

Thanks again,
Will

Hi Will,

You are right, the paper is not correct anymore on that point.
The meaning of the $ command change at a point, to this current definition which is more safer/correct.
After some complains, we add the $$ syntax.

Cheers,

Olivier