# addition of four particle vertex does not give cross-section value comparable to the theory

Hello,

I want to simulate a model of spin 0 magnetic monopoles where the diagrams are :

https:/

The process has one 4 particles vertex (photon-

To achieve that, I have written a MadGraph UFO model which is kept here:

https:/

The coupling of the 4 particle vertex is defined here:

https:/

The Lorentz structure is defined here:

https:/

There is no compilation issue and MadGraph is giving me a total cross-section based on this model. But unfortunately, when I compare the cross-section value with the theoretical prediction, I see that the two values differ significantly.

Interestingly, when I multiply the Lorentz factor of the 4 particle vertex by 10:

https:/

the cross-section values of MadGraph and the theory matches. The cross-section plot is shown here:

https:/

This was a scalar-

When I use spin 1/2 magnetic monopole (with a similar UFO model, but monopole spin is now 1/2), the process does not have any 4 particle vertex. The diagrams are here:

https:/

. There the theory and MadGraph cross-section match fantastically:

https:/

Does this mean the 4 particle vertex calculation is unstable for MadGraph5? Is there any way MadGraph model can reproduce the theoretical prediction when there is a 4 particle vertex?

Any help is appreciated.

Thank you,

Arka

## Question information

- Language:
- English Edit question

- Status:
- Answered

- Assignee:
- No assignee Edit question

- Last query:
- 2017-11-30

- Last reply:
- 2017-11-30

Hi,

4 point particle are used without any problem in many model (including the sm model with the 4 gluon and 4 weak boson vertex).

I also know model with 6 and 8 point interaction which were working without any problem.

So I’m quite confident that 4 point interaction are stable and working as expected.

Cheers,

Olivier

> On Nov 29, 2017, at 16:32, Arka Santra <email address hidden> wrote:

>

> Question #661243 on MadGraph5_aMC@NLO changed:

> https:/

>

> Summary changed to:

> addition of four particle vertex does not give cross-section value comparable to the theory

>

> Description changed to:

> Hello,

> I want to simulate a model of spin 0 magnetic monopoles where the diagrams are :

> https:/

>

> The process has one 4 particles vertex (photon-

> monopole) out of three vertices.

>

> To achieve that, I have written a MadGraph UFO model which is kept here:

> https:/

>

> The coupling of the 4 particle vertex is defined here:

> https:/

>

> The Lorentz structure is defined here:

> https:/

>

>

> There is no compilation issue and MadGraph is giving me a total cross-section based on this model. But unfortunately, when I compare the cross-section value with the theoretical prediction, I see that the two values differ significantly.

>

>

> Interestingly, when I multiply the Lorentz factor of the 4 particle vertex by 10:

> https:/

>

> the cross-section values of MadGraph and the theory matches. The cross-section plot is shown here:

> https:/

>

>

> This was a scalar-

>

> When I use spin 1/2 magnetic monopole (with a similar UFO model, but monopole spin is now 1/2), the process does not have any 4 particle vertex. The diagrams are here:

> https:/

>

> . There the theory and MadGraph cross-section match fantastically:

> https:/

>

>

> Does this mean the 4 particle vertex calculation is unstable for MadGraph5? Is there any way MadGraph model can reproduce the theoretical prediction when there is a 4 particle vertex?

>

> Any help is appreciated.

>

> Thank you,

> Arka

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

Arka Santra (santra-arka) said : | #2 |

Hi Olivier,

Thank you for confirming that MadGraph implementation of 4 point vertex was extensively studied before. This means I am implementing the vertex in a wrong way.

I worked only with the 4 point vertex to see if there is any problem with it (diagram shown here: https:/

Here I noticed that the cross-section depends on g^2 when g is the (EWK) coupling strength of the 4 point vertex. I am confused because if the diagram shows QED=2, does not it mean that the matrix element is proportional to g^2? In that case, won't the cross-section depend on g^4?

I changed the QED order of the 4 point vertex diagram to be 16, yet I see that the cross-section depends on g^2. This seems strange to me. What is the right way to fix the coupling order of a vertex?

This is how I did that in my model:

1. This is the place where I define the coupling order:

https:/

2. This is the 4 point vertex definition:

https:/

Is there any mistake in implementing the coupling order?

Thank you,

Arka

Hi,

> I worked only with the 4 point vertex to see if there is any problem

> with it (diagram shown here:

> https:/

> —> Diagram 1, QCD = 0, QED=2).

This is expected to be the order for amplitude not the matrix-element squared.

Now this information is only used for diagram filtering not in the actual computation of the amplitude.

(But if that part was generated automatically, you might want to check that the coupling of that vertex have the correct dependencies)

Cheers,

Olivier

> On Nov 30, 2017, at 01:52, Arka Santra <email address hidden> wrote:

>

> Question #661243 on MadGraph5_aMC@NLO changed:

> https:/

>

> Status: Answered => Open

>

> Arka Santra is still having a problem:

> Hi Olivier,

> Thank you for confirming that MadGraph implementation of 4 point vertex was extensively studied before. This means I am implementing the vertex in a wrong way.

>

> I worked only with the 4 point vertex to see if there is any problem

> with it (diagram shown here:

> https:/

> ---> Diagram 1, QCD = 0, QED=2).

>

> Here I noticed that the cross-section depends on g^2 when g is the (EWK)

> coupling strength of the 4 point vertex. I am confused because if the

> diagram shows QED=2, does not it mean that the matrix element is

> proportional to g^2? In that case, won't the cross-section depend on

> g^4?

>

> I changed the QED order of the 4 point vertex diagram to be 16, yet I

> see that the cross-section depends on g^2. This seems strange to me.

> What is the right way to fix the coupling order of a vertex?

>

> This is how I did that in my model:

> 1. This is the place where I define the coupling order:

> https:/

>

> 2. This is the 4 point vertex definition:

> https:/

>

>

> Is there any mistake in implementing the coupling order?

>

>

> Thank you,

> Arka

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

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