# How to implement matrix element in MG5

Hi,

I am trying to generate a loop process and a tree level process and their interference. However it seems MG5 do not support generate both LO/NLO process at the same time.

So I am thinking if it's possible to calculate the matrix element by hand, say M_{loop}, M_{tree} and implement them in MG5? If it's not possible, is there any way for MG5 to calculate the interference term for LO/NLO processes?

I am also thinking about two loop processes, which seems MG5 can't do. In this case, I also wonder if I can implement calculated matrix element by hand in MG5.

## Question information

- Language:
- English Edit question

- Status:
- Answered

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- Last query:
- 2019-10-29

- Last reply:
- 2019-10-30

Dear Li,

> I am trying to generate a loop process and a tree level process and their interference. However it seems MG5 do not support generate both LO/NLO process at the same time.

We have a tutorial for such type of feature. This will allow to implement the interference that you are looking for

https:/

This being said the issue here is NOT the evaluation of the matrix-element but how you handle the associated phase-space integration. We do not have a good way to perform such computation (and we know example where the convergence was biased).

> I am also thinking about two loop processes, which seems MG5 can't do. In this case, I also wonder if I can implement calculated matrix element by hand in MG5.

Here it really depends what you want to do. If this is for NNLO, then implementing the two loop matrix-element is not enough (and therefore useless). For process which are Loop-Induced at LO, then we have everything in place obviously and this is possible. However note that you would also need to implement the color-link loop-induced born (and other matrix-element related to the substraction of the singularities).

Cheers,

Olivier

> On 29 Oct 2019, at 23:22, Li <email address hidden> wrote:

>

> New question #685499 on MadGraph5_aMC@NLO:

> https:/

>

> Hi,

> I am trying to generate a loop process and a tree level process and their interference. However it seems MG5 do not support generate both LO/NLO process at the same time.

> So I am thinking if it's possible to calculate the matrix element by hand, say M_{loop}, M_{tree} and implement them in MG5? If it's not possible, is there any way for MG5 to calculate the interference term for LO/NLO processes?

> I am also thinking about two loop processes, which seems MG5 can't do. In this case, I also wonder if I can implement calculated matrix element by hand in MG5.

>

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

Li (huangli-itp) said : | #2 |

Hi Olivier,

Thank you!

>https:/

Is this only validate for loop induced process?

>This being said the issue here is NOT the evaluation of the matrix-element but how you handle the associated phase-space integration. We do not have a good way to perform such computation (and we know example where the convergence was biased).

I see. So the major problem is how to treat the phase space integration ...

>For process which are Loop-Induced at LO

What do you mean by loop-induced at LO here? Do you mean that the two loops are both loop induced?

Last, may I ask what's the difference between using NLO process and the effective operators for the interference?

Best,

Li

Hi,

I guess that we do not agree about the meaning of LO and of NLO.

LO is the lowest order in perturbation theory to which you have Feynman diagram for the process under consideration. In general such process is at tree-level but in some rare case it is a loop-induced process.

NLO (in QCD) is the computation precise up to the next order in perturbation theory

It contains three contributions:

1. The Born (the LO contribution)

2. The Virtual (the interference between the Born and the +1 loop)

3. The Real (one more jet in the final state)

If your process is loop-induced then your virtual is the interference between a two loop-computation and the one loop (the born) and the real is a loop as well.

>> https:/

>

> Is this only validate for loop induced process?

This is the only non trivial case, the rest of interference is the type of loop computation that

we do for the NLO computation all the time. Obviously such matrix-element is not finite.

So if you are interested in the general case, then your statement is just wrong. We can generate such type of matrix-element.

Cheers,

Olivier

> On 30 Oct 2019, at 17:43, Li <email address hidden> wrote:

>

> Question #685499 on MadGraph5_aMC@NLO changed:

> https:/

>

> Li posted a new comment:

> Hi Olivier,

> Thank you!

>

>> https:/

>

> Is this only validate for loop induced process?

>

>> This being said the issue here is NOT the evaluation of the matrix-

> element but how you handle the associated phase-space integration. We do

> not have a good way to perform such computation (and we know example

> where the convergence was biased).

>

> I see. So the major problem is how to treat the phase space integration

> ...

>

>> For process which are Loop-Induced at LO

>

> What do you mean by loop-induced at LO here? Do you mean that the two

> loops are both loop induced?

>

> Last, may I ask what's the difference between using NLO process and the

> effective operators for the interference?

>

> Best,

> Li

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

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