# One Gluon splitting

Hello,
I was interested in a process in which two gluons are produced and then only one of them splits to two b quarks. So, if g1 and g2 are two gluons (I am just labelling them for convenience), I want

p p > g1 g2, g1 > b b~

or

p p > g1 g2, g2 > b b~

Unfortunately, when I use

p p > g g, g > b b~, both gluons split to the di-bottom state.

I have tried p p > g g, g > b b~ QCD<=3. (max. order of QCD coupling in the amplitude is 3), but to no avail.

The process p p > g b b~ obviously also includes the process where the gluon is radiated off a bottom quark line, so this doesn't work either.

Kindly help.

Thanks,
Debjyoti

## Question information

Language:
English Edit question
Status:
Solved
For:
Assignee:
No assignee Edit question
Solved by:
Olivier Mattelaer
Solved:
Last query:
 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2021-08-24: #1

Hi,

Is this even make sense?

You are certainly here in a regime, where it would make more sense to edit the output file by hand such that you control exactly what is written and in particular how the symmetry factor is computed.
To have the set of feynman diagram the following syntax should work
generate p p > g g, g > b b~, g > g

But as said above please check gauge/lorentz invariance of such computation (likely they are not)
and check how the symmetry factor is assigned ( I guess one is set but this need to be checked).

Cheers,

Olivier

> On 24 Aug 2021, at 06:15, Debjyoti Bardhan <email address hidden> wrote:
>
> p p > g1 g2, g1 > b b~

 Revision history for this message Debjyoti Bardhan (debjyotiarr) said on 2021-08-24: #2

Hello,

I think you're right about the gauge invariance. I wanted to simulate this to obtain the fraction of di-bottom pairs that come from gluon splitting as a function of pT. Your suggestion worked and at least from the Feynman diagrams, I think I have the events I wanted.

I am a little curious as to why p p > g g, g > b b~ QCD<=3 doesn't work though. The generated Feynman diagrams seem to ignore the QCD order constraint completely.

Thanks for the solution,
Debjyoti

 Revision history for this message Debjyoti Bardhan (debjyotiarr) said on 2021-08-24: #3

Thanks Olivier Mattelaer, that solved my question.

 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2021-08-24: #4

Hi,

It is because madgraph generates independently

p p > g g
and then
g > b b~ QCD<=3
So your QCD <=3 only applies to g > b b~
The various diagram are in a second stage merged together into unique Feynman Diagram

A syntax applies to applies restriction after the merging
p p > g g, g > b b~ @0 QCD<=3
Here "@0" is a separator without any physical meaning but all coupling restriction applied after are on the full process and not on a single piece.

You will see with that syntax that the "generate" command will work (no merge at that stage)
But the output will crash during the merge with the following message:

Command "output " interrupted in sub-command:
"output" with error:
InvalidCmd : No matrix elements generated, check overall coupling orders

Since the code decays the two gluon and than check if the resulting diagram match the constraint or not (and therefore here no diagram matches such constraint)

Cheers,

Olivier

 Revision history for this message Debjyoti Bardhan (debjyotiarr) said on 2021-08-24: #5

Hi Olivier,
Thank you for the detailed reply. It helps a lot.

Thanks,
Debjyoti