# Cross-section of W production

Asked by Maksym Ovchynnikov on 2018-09-20

I generated a cross-section of leptons production in W decays at sqrt[s] = 13 TeV:

p p > w+, w+ > e+ ve

The total cross-section is approximately 9 nb.

Next, I tried to generate cross-sections for the processes

p p > w+ j, w+ > e+ ve,

p p > w+ j j, w+ > e+ ve,

and it turned out that the total cross-section for these two processes is something like 3.4 nb which is significantly lower than the cross-section for p p > w+, w+ > ve e+.

What I'm interested in is in the relashionships between these processes in MadGraph. Am I right that the cross-section of the process p p > w+, w+ > ve e+ is the total w+ production cross-section computed before parton showering and in principle can be obtained by summing the cross-sections for the processes p p > w+ nj, w+ > ve e+, where we sum over integer n?

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Olivier Mattelaer
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2018-09-20
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2018-09-20
2018-09-20
 Olivier Mattelaer (olivier-mattelaer) said on 2018-09-20: #1

Hi,

> and it turned out that the total cross-section for these two processes is something like 3.4 nb which is significantly lower than the cross-section for p p > w+, w+ > ve e+.

Which is expected since your cross-section is multiplied by a_S.
In top of that you have some cut on the minimal pt of the jet to avoid the singularity
(otherwise your cross-section will be infinite)

> Am I right that the cross-section of the process p p > w+, w+ > ve e+ is the total w+ production cross-section computed before parton showering

That's correct. Remember that the parton-shower does not change the cross-section so this is also the cross-section after parton-showering.

> in principle can be obtained by summing the cross-sections for the processes p p > w+ nj, w+ > ve e+, where we sum over integer n?

not that's not correct.
In order to have the relation between the cross-section of those processes, you need to forbid the double counting. (the one jet process include the cross-section of the two jet process, ...).
In consequence, you have to include the Sudakov form-factor inside your computation.
In literature they are three (main) way to include such Sudakov
1) MLM (include in a approximate way via a veto after the parton-shower stage)
2) CKKW (the Sudakov is include analytically when integrating the matix-element)
3) CKKW-L (the Sudakov is include exactly by applying the sukakov veto DURING the parton-shower)

Cheers,

Olivier

> On 20 Sep 2018, at 10:52, Maksym Ovchynnikov <email address hidden> wrote:
>
> New question #674232 on MadGraph5_aMC@NLO:
>
> I generated a cross-section of leptons production in W decays at sqrt[s] = 13 TeV:
>
>
> p p > w+, w+ > e+ ve
>
>
> The total cross-section is approximately 9 nb.
>
>
> Next, I tried to generate cross-sections for the processes
>
> p p > w+ j, w+ > e+ ve,
>
>
> p p > w+ j j, w+ > e+ ve,
>
> and it turned out that the total cross-section for these two processes is something like 3.4 nb which is significantly lower than the cross-section for p p > w+, w+ > ve e+.
>
> What I'm interested in is in the relashionships between these processes in MadGraph. Am I right that the cross-section of the process p p > w+, w+ > ve e+ is the total w+ production cross-section computed before parton showering and in principle can be obtained by summing the cross-sections for the processes p p > w+ nj, w+ > ve e+, where we sum over integer n?
>
>
> --