# Matrix element of mirror process

Asked by Laura Moreno on 2018-10-07

Hi,

I am trying to compute the total cross section for the process pp > htj, but I am having some troubles, so I decided to study the different subprocesses in a more detailed way.

My doubt comes when studying the processes u b > h t d and b u > htd, i.e. just the mirror process so to say. When I use the standalone output to get the matrix elements and compute both processes, I obtain different results. As information, I write here the code I use.

>> import model loop_sm-no_b_mass
>> generate u b > h t d
>> output standalone ub_htd_st
>> launch

and the same for the other process.

For u b > h t d, I get:
Matrix element = 6.3550723077195101E-008 GeV^ -2

whereas for the b u > h t d:
Matrix element = 2.9000254780896340E-008 GeV^ -2

when, given that it is exactly the same process, it should yield exactly the same result. I already checked that the set of momenta used in both of them is the same, so the problem is not here. So I am not so sure where the problem can be. Am I computing something wrong? Or missing something that I did not take into account?

Also, when then - instead of using the standalone output, but the normal one - I get different values for the cross section, slightly different, but enough to be not in agreement between them.

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2018-11-17
 Olivier Mattelaer (olivier-mattelaer) said on 2018-10-08: #1

Hi,

In order to have the same matrix-element, you should not use the same phase-space point for the comparison but the mirror one.

Cheers,

Olivier

> On 7 Oct 2018, at 16:32, Laurent Vashmo <email address hidden> wrote:
>
> New question #674807 on MadGraph5_aMC@NLO:
>
> Hi,
>
> I am trying to compute the total cross section for the process pp > htj, but I am having some troubles, so I decided to study the different subprocesses in a more detailed way.
>
> My doubt comes when studying the processes u b > h t d and b u > htd, i.e. just the mirror process so to say. When I use the standalone output to get the matrix elements and compute both processes, I obtain different results. As information, I write here the code I use.
>
>>> import model loop_sm-no_b_mass
>>> generate u b > h t d
>>> output standalone ub_htd_st
>>> launch
>
> and the same for the other process.
>
> For u b > h t d, I get:
> Matrix element = 6.3550723077195101E-008 GeV^ -2
>
> whereas for the b u > h t d:
> Matrix element = 2.9000254780896340E-008 GeV^ -2
>
> when, given that it is exactly the same process, it should yield exactly the same result. I already checked that the set of momenta used in both of them is the same, so the problem is not here. So I am not so sure where the problem can be. Am I computing something wrong? Or missing something that I did not take into account?
>
> Also, when then - instead of using the standalone output, but the normal one - I get different values for the cross section, slightly different, but enough to be not in agreement between them.
>
>
>
> --

 Laura Moreno (laumova) said on 2018-10-08: #2

Hi Olivier,

thanks, that solved my problem.

But still there is something that I don't understand. Now I get the same matrix elements, but when I integrate over the whole phase space in order to get the total cross section (using in this case the normal output, modifying the run_card.dat, and generating the events) I get different values of the cross section for both values.

With nevents = 10^6 and a scale of (m_higgs + m_top)/4, using LHAPDF set 21000 and fixed scaled, I get:

cross-section u b > h t d = 16.670 +- 0.005 fb
cross-section b u > h t d = 16.256 +- 0.005 fb

which is not in agreement. But I am applying no cuts, so they should give the same... I also get the same problem when changing the scale, for example, I tried also with scale = (m_higgs + m_top)/2 and the results are (also with nevents = 10^6):

cross-section u b > h t d = 17.566 +- 0.006 fb
cross-section b u > h t d = 17.116 +- 0.006 fb

I also created a code that integrates over the phase space and over the pdfs using VEGAS, and for both processes I get the same result using the matrix elements from Madgraph, so the problem must be somewhere in my run from Madgraph, but I have no idea where, and I checked the run card and in both processes I have the same.

Do you have an idea of where the problem could be? Thank you so much!

Best,
L.

 Launchpad Janitor (janitor) said on 2018-10-24: #3

This question was expired because it remained in the 'Open' state without activity for the last 15 days.

 Laura Moreno (laumova) said on 2018-11-01: #4

Hi,

I have been working on each case separately, and I would like to add some information I found, maybe it could be helpful:

- the difference between cross-sections for mirror processes comes into play only for t-channel diagrams (for this process I mentioned before), so for the s-channel diagrams works well and yields the same result for the sub-process and the mirror one.

- if I compute both processes at the same time, e.g.
>> generate u b > h t d
>> add process b u > h t d
and I run the process, then I obtain twice the result for the u b > h t d, which is in fact the correct result

So the problem comes only for the mirror processes. But I still don't know why there is this difference between results.

Thanks again!
L.

 Launchpad Janitor (janitor) said on 2018-11-17: #5

This question was expired because it remained in the 'Open' state without activity for the last 15 days.