# Finding cross section of a given process in 2HDM

Asked by Shreya Saha on 2020-08-16

Hello,
I have generated some Monte Carlo samples using MadGraph_aNLO, Version 2.3.3 for ttX (tt -> semileptonic + dileptonic decays, X->uu) for studying the 2HDM+Scalar model, and I am trying to check if the phenomenology papers regarding this model, is in line with what was generated, by comparing the predicted production cross-section of the ttX process. Below is a short snippet of my JobOptions file, here h3 refers to X -
---------------------------------------------------
import model 2HDM
define p = g u c d s u~ c~ d~ s~
define j = g u c d s u~ c~ d~ s~
define l+ = e+ mu+
define l- = e- mu-
define vl = ve vm
define vl~ = ve~ vm~
generate g g > t t~ h3, (h3 > mu+ mu-),(t > W+ b, W+ > l+ vl),(t~ > W- b~, W- > j j)
add process g g > t t~ h3, (h3 > mu+ mu-),(t > W+ b, W+ > j j),(t~ > W- b~, W- > l- vl~)
add process g g > t t~ h3, (h3 > mu+ mu-),(t > W+ b, W+ > l+ vl),(t~ > W- b~, W- > l- vl~)
--------------------------------------------------

I can find the respective cross-sections for the three processes defined above in the log.generate file, as shown below, and I am trying to back-calculate the production cross-section of the ttX process for a given luminosity, for my analysis. I am getting stuck at the branching ratio of X->uu taken into account when calculating the values below. I have looked it up in the param card, but I am not sure I understand it completely. The idea would be to place limits on the BR (X->uu), and consider it as 1 and let it float, hence I would like to figure of the production CS of ttX and scale it to the current luminosity value, to place meaningful upper limits on BR (X->uu).
-----------------------------------------------------------------------
number xsec (pb) xerr (pb) xmax (pb)
1 1.1937e-05 2.4015e-08 1.3443e-09
2 1.1917e-05 2.3975e-08 1.3443e-09
3 4.0091e-06 8.0657e-09 1.3443e-09
-----------------------------------------------------------------------

Also, I would like to know the value of k-factor used in the above NLO calculations, and where I can find some more information within the various EVNT and log files, about the same.
Please let me know if you would need more details.

Thank you very much.
Best,
Shreya Saha

## Question information

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Solved by:
Olivier Mattelaer
Solved:
2020-08-21
Last query:
2020-08-21
2020-08-19
 Olivier Mattelaer (olivier-mattelaer) said on 2020-08-16: #1

Hi,

> I can find the respective cross-sections for the three processes defined above in the log.generate file,

I do not know that file but fine.

> I am trying to back-calculate the production cross-section of the ttX process for a given luminosity,

cross-section does not depend of luminosity.

> I am getting stuck at the branching ratio of X->uu taken into account when calculating the values below. I have looked it up in the param card, but I am not sure I understand it completely.

In general, the value of the Branching ratio is not there since MG5aMC does not use the narrow-width approximation to make this computation. If you want to compute the branching ratio, you can ask madgraph to generate
h3 > mu+ mu-
and then take the ratio with the total width present in your param_card.
(so one way to set this BR to one, is to set the total width to the partial-width --assuming NWA hold)

> Also, I would like to know the value of k-factor used in the above NLO calculations,

The computation above is LO accurate and not NLO accurate.
The model that you use is also only LO capable so I do not think that you would be able to compute k-factor with model.

Cheers,

Olivier

> On 16 Aug 2020, at 19:40, Shreya Saha <email address hidden> wrote:
>
> New question #692396 on MadGraph5_aMC@NLO:
>
> Hello,
> I have generated some Monte Carlo samples using MadGraph_aNLO, Version 2.3.3 for ttX (tt -> semileptonic + dileptonic decays, X->uu) for studying the 2HDM+Scalar model, and I am trying to check if the phenomenology papers regarding this model, is in line with what was generated, by comparing the predicted production cross-section of the ttX process. Below is a short snippet of my JobOptions file, here h3 refers to X -
> ---------------------------------------------------
> import model 2HDM
> define p = g u c d s u~ c~ d~ s~
> define j = g u c d s u~ c~ d~ s~
> define l+ = e+ mu+
> define l- = e- mu-
> define vl = ve vm
> define vl~ = ve~ vm~
> generate g g > t t~ h3, (h3 > mu+ mu-),(t > W+ b, W+ > l+ vl),(t~ > W- b~, W- > j j)
> add process g g > t t~ h3, (h3 > mu+ mu-),(t > W+ b, W+ > j j),(t~ > W- b~, W- > l- vl~)
> add process g g > t t~ h3, (h3 > mu+ mu-),(t > W+ b, W+ > l+ vl),(t~ > W- b~, W- > l- vl~)
> --------------------------------------------------
>
> I can find the respective cross-sections for the three processes defined above in the log.generate file, as shown below, and I am trying to back-calculate the production cross-section of the ttX process for a given luminosity, for my analysis. I am getting stuck at the branching ratio of X->uu taken into account when calculating the values below. I have looked it up in the param card, but I am not sure I understand it completely. The idea would be to place limits on the BR (X->uu), and consider it as 1 and let it float, hence I would like to figure of the production CS of ttX and scale it to the current luminosity value, to place meaningful upper limits on BR (X->uu).
> -----------------------------------------------------------------------
> number xsec (pb) xerr (pb) xmax (pb)
> 1 1.1937e-05 2.4015e-08 1.3443e-09
> 2 1.1917e-05 2.3975e-08 1.3443e-09
> 3 4.0091e-06 8.0657e-09 1.3443e-09
> -----------------------------------------------------------------------
>
> Also, I would like to know the value of k-factor used in the above NLO calculations, and where I can find some more information within the various EVNT and log files, about the same.
> Please let me know if you would need more details.
>
> Thank you very much.
> Best,
> Shreya Saha
>
>
>
> --

 Shreya Saha (ssaha93) said on 2020-08-16: #2

Hello Olivier,
Thank you for the detailed clarification, sorry for the choice of wording for the cross-section and luminosity, I was a bit confused there.

I am presently setting the decay width of h3 to 1.8e-4 in the joboptions file and the param card, and I am assuming that this the narrow width approximation we will be using.
Does this mean that the cross-section values I see in the log file, do not take into this above decay width value ?

I will generate only h3>mu+ mu- and check the CS value I get and then set that as the decay width, if I understand it correctly ?

Thank you.
Best,
Shreya

 Olivier Mattelaer (olivier-mattelaer) said on 2020-08-19: #3

> I am assuming that this the narrow width approximation we will be using.

We only use narrow-width approximation (NWA) if the width is so small that we will get numerical stability issue during the phase-space integration. Using NWA is good for the total cross-section but quite bad for distributions but for the peak but also for spin-correlation. So even if you put the width below the numerical stability threshold, we are not fully using NWA see : https://answers.launchpad.net/mg5amcnlo/+faq/3053

> Does this mean that the cross-section values I see in the log file, do not take into this above decay width value ?

No that's the opposite, if you were using NWA, you will only care about the branching ratio and of the total width.
For the phase-space integration, we do not use any partial width/ Branching ratio computation, we simply integrates over the propagator which obviously depend of the total width value.
Consequently, if/when NWA is valid our cross-section will automatically behaves like one over the total width.
But our computation is more precise since it is also valid when NWA is not valid and even if the NWA is valid our computation contains correction terms of the order of (width/mass) which are neglected in the NWA case.

Cheers,

Olivier

 Shreya Saha (ssaha93) said on 2020-08-21: #4

Thanks Olivier Mattelaer, that solved my question.