# Cross-section of W production

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?

## Question information

- Language:
- English Edit question

- Status:
- Solved

- Assignee:
- No assignee Edit question

- Solved by:
- Olivier Mattelaer

- Solved:
- 2018-09-20

- Last query:
- 2018-09-20

- Last reply:
- 2018-09-20

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:

> https:/

>

> 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?

>

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

Maksym Ovchynnikov (name-xxx) said : | #2 |

Thanks Olivier Mattelaer, that solved my question.