MadGraph5_aMC@NLO

Missing diagrams and most relevant ones

Asked by Caue Evangelista

Hello dear community,

I'm generating the process p p > t t~ z in MadGraph, where I'm defining the initial-state particle p as a multiparticle label including:
p = g, u, c, d, s, b, u~, c~, d~, s~, b~.

After running the generate command, I get the following output listing all subprocesses:

INFO: Trying process: g g > t t~ z WEIGHTED<=4 @1
INFO: Process has 8 diagrams
INFO: Trying process: u u~ > t t~ z WEIGHTED<=4 @1
INFO: Process has 4 diagrams
INFO: Trying process: c c~ > t t~ z WEIGHTED<=4 @1
INFO: Process has 4 diagrams
INFO: Trying process: d d~ > t t~ z WEIGHTED<=4 @1
INFO: Process has 4 diagrams
INFO: Trying process: s s~ > t t~ z WEIGHTED<=4 @1
INFO: Process has 4 diagrams
INFO: Trying process: b b~ > t t~ z WEIGHTED<=4 @1
INFO: Process has 4 diagrams
6 processes with 28 diagrams generated in 0.158 s
Total: 6 processes with 28 diagrams

My first question is: when I look at the postscript diagrams, I cannot find the c c~ > t t~ z and s s~ > t t~ z subprocesses. I know the html version does not contain all the diagrams, but since I'm looking at the .ps files I should be able to find the c and s diagrams, right?

My other question is: I'm wondering if MadGraph shows the diagrams by relevance order. In my case all of them are "QCD=2, QED=1", so could I say that they are equily relevant to the overall p p > t t~ z cross section??

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

Hi,

>My first question is: when I look at the postscript diagrams, I cannot find the c c~ > t t~ z and s s~ > t t~ z subprocesses. I know the html version does not contain all the diagrams, but since I'm looking at the .ps files I should be able to find the c and s diagrams, right?

The eps file will be dependent on the stage at which the code is asked to generate them.
So if you do
generate p p > t t~ z
display diagrams

Then at that stage you will have one eps file for each flavor

if you do
generate p p > t t~ z
output PATH

then within the output stage
1) The processes are grouped by flavor having identical Feynman diagram
2) Only one of those identical processes will be requested to created one eps file.

If you look at the info.html page, you will have the information about which flavor are grouped with which flavor.

>My other question is: I'm wondering if MadGraph shows the diagrams by relevance order. In my case all of them are "QCD=2, QED=1", so could I say that they are equily relevant to the overall p p > t t~ z cross section??

They are two things to distinguish here:
1) By default we only keep the diagram that have the higher order of alpha_s,
This is why you do not have the QED=3 amplitudes. If you want those you need to change your syntax to
generate p p > t t~ z QED<=3
The reason for such default is indeed that in general adding pure EW diagram is negligeable.

2) For the diagram in "QCD=2, QED=1", we do not know a priori which diagram (or any set of gauge invariant diagram) are
more relevant than others. Now they do not all have the same contribution (and such relative contribution also depend of your cuts/beam energy/...)

Cheers,

Olivier

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Caue Evangelista (evangcaue) said : 		#2

Hi Olivier,

Thank you for your reply!

Regarding the first question: I understand it now — I was able to locate the grouped flavors and all the corresponding diagrams.

As for the second question: Just to make sure I’ve understood correctly (please excuse the naive question) — we cannot determine in advance which specific diagram with "QCD = 2, QED = 1" is more relevant, but we can say that, in general, all diagrams with "QCD = 2, QED = 1" are more relevant than those with "QCD = 2, QED = 3", right?

Cheers,
Caue

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

 "QCD = 2, QED = 1" means that the amplitude will be proportional to g_s^2 g_w
while
 "QCD = 2, QED = 3" means that the amplitude will be proportional to g_s^2 g_w^3

So in perturbative term the second diagram should be within the NNLO (Electroweak) correction.
Since the full framework that we use rely on perturbative expansion, yes we do (have to) assume that those amplitude are suppressed compared to the first one.
But this is not that hard to assume for each amplitudes since g_s^2 g_w^3 = g_s^2 g_w times g_w^2.
(Now the number of amplitude can sometimes be an issue like in the Higgsplosion case)

Now the question is more complex when you compare
 "QCD = 2, QED = 1"
and
 "QCD = 1, QED = 2"
since you compare g_s^2 * g_w and g_s* g_w^2
since g_w << g_S this will also be the case but with cut you can tune the importance of each amplitude such that this does not hold any more (think VBF cut or onshell Z-cut for dijet,...).

Cheers,

Olivier

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Caue Evangelista (evangcaue) said (last edit ): 		#4

Thanks Olivier! That helped me to settle things!