# Discrepancy in ttbar inclusive cross-section using MadGraph with it's theoretical value

Asked by Prasham Jain on 2020-04-28

I am trying to understand the inclusive cross-section(xsec) for ttbar production. When I generate 1M events of SM ttbar exclusive, I get xsec=447.5 pb. For exclusive SM ttbar+1jet, xsec=307.7 pb and for exclusive SM ttbar+2jets, I get xsec=141.7 pb with cuts on jets (jet pT>20GeV and jet \eta<2.5). The sum of these is xsec(inclusive till 2 jets)=896.9 pb. However, we know that theoretical calculations give xsec(inclusive)=832 pb which agrees with experimental measurements quite well. I am assuming that inclusive xsec includes ttbar + all possible jets. Of course, the latest theoretical calculation also has the loop contributions and thus, I was expecting that the number 896.9 pb would be less than 832 pb. Is this apparent discrepancy due to the large scale dependence (I have used dynamical scale choice = 1) of the number 896.9 pb and maybe negative contribution from the loops? Or am I missing some more basic physics issues?

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2020-05-02
2020-05-04
 Olivier Mattelaer (olivier-mattelaer) said on 2020-04-28: #1

Hi,

I guess that your number are after Pythia (and after applied a jet veto), since we can not compute exclusive cross-section. Additionally if you want to have inclusive cross-section, you have to keep the highest multiplicity inclusive.

Which scheme did you use to combine those samples? MLM? CKKW-l? (another one?)

Concerning the rest of your question, those computation should have a large scale uncertaintly that can be estimated easily by our code (this is default if you have lhapdf installed with python support).
Additionally, you should estimate the merging uncertainty by varying your merging scale (i.e. when you vary your definition of "exclusive")

Cheers,

Olivier

PS: You can be interested in this thread:

> On 28 Apr 2020, at 15:18, Prasham Jain <email address hidden> wrote:
>
> New question #690286 on MadGraph5_aMC@NLO:
>
> I am trying to understand the inclusive cross-section(xsec) for ttbar production. When I generate 1M events of SM ttbar exclusive, I get xsec=447.5 pb. For exclusive SM ttbar+1jet, xsec=307.7 pb and for exclusive SM ttbar+2jets, I get xsec=141.7 pb with cuts on jets (jet pT>20GeV and jet \eta<2.5). The sum of these is xsec(inclusive till 2 jets)=896.9 pb. However, we know that theoretical calculations give xsec(inclusive)=832 pb which agrees with experimental measurements quite well. I am assuming that inclusive xsec includes ttbar + all possible jets. Of course, the latest theoretical calculation also has the loop contributions and thus, I was expecting that the number 896.9 pb would be less than 832 pb. Is this apparent discrepancy due to the large scale dependence (I have used dynamical scale choice = 1) of the number 896.9 pb and maybe negative contribution from the loops? Or am I missing some more basic physics issues?
>
> --

 Prasham Jain (jainprasham33) said on 2020-04-29: #2

Hi,

The numbers I have quoted are at parton level. I have not used pythia. These are for processes p p > t t~, p p > t t~ j and p p > t t~ j j.

Also, could you please elaborate on the phrase "..since we can not compute exclusive cross-section..". MG5 can calculate exclusive cross-section, right?

 Olivier Mattelaer (olivier-mattelaer) said on 2020-04-29: #3

Hi,

The implementation of CKKW matching/merging (ickkw=2) allowing to have exclusive cross-section directly from MadGraph was never complete (was only available for the final state radiation). It has been deprecated in years. Therefore since MG5aMC can not compute any Sudakov form-factor (either numerically or analytically) it is impossible that we return exclusive cross-section.

All the other method (CKKW-L, MLM,...) that I know for exclusive cross-section, relies on the parton-shower in order to multiply by the associated sudakov form factor.

Cheers,

Olivier

 Prasham Jain (jainprasham33) said on 2020-04-29: #4

We are calculating the exclusive cross-section at the parton level for t t~ j where the j is hard. We have a pT cut pT>20 GeV
on the jet. So I am still having some trouble understanding your comment. MG5 is indeed giving us a cross-section for the hard exclusive process.
Similar exclusive parton level cross-sections are also available from ALPGEN. Our question was why the
cross-section for t t~ + t t~ j (j is hard) + t t~ j j (both jets are hard) obtained by MG5 is bigger than the actual inclusive cross-section?
I hope my question is clear now.

 Olivier Mattelaer (olivier-mattelaer) said on 2020-04-29: #5

Hi,

I guess we do not have the same definition of the "inclusive/exclusive" cross-section.

For me "inclusive" cross-section means that the computation is done in a renormalisable way at a given scale for the renormalization of the strong coupling and for the PDF. Consequently, the computation is inclusive since radiation below such scale are included in the running of the strong coupling and/or in the DGLAP evolution of the PDF.

The parton-shower is the tool to pass from an inclusive computation to a set of exclusive one. (This is why the parton-shower does not change the cross-section).
If you want to have exactly 0j, you have to multiply the matrix-element by the Sudakov form-factor estimated between the renormalization/refactorization scale and the hadronization scale. This is something that we are not able internally without the help of a parton-shower program.

Since you claim that MG5 returns "hard exclusive process.". we clearly not have the same definition of "exclusive". So could you ellaborate?

Note that as far as i know (but I'm not an author of ALPGEN) ALPGEN is not able to compute the sudakov form factor and therefore can only produce inclusive sample and not exclusive one.

To come back to your final question, you can not sum those two cross-section like that since you will face huge double counting. (due to the fact that the sample are inclusive).

Cheers,

Olivier

 Prasham Jain (jainprasham33) said on 2020-04-30: #6

We are referring to the numbers in table 20 of the ALPGEN manual https://arxiv.org/pdf/hep-ph/0206293.pdf
They also say that "In the case of 0 and 1 jet, we find agreement with the results obtained using the O(αs^3 ) code of ref. [48]."
Ref [48] is M. L. Mangano, P. Nason and G. Ridolfi, Nucl. Phys. B 373 (1992) 295.
So when we are referring to 0 or 1 jet, we are using the same meaning as them.

 Olivier Mattelaer (olivier-mattelaer) said on 2020-04-30: #7

Hi,

- Did you check their statement at the end of page 2 and beginning of page 3?
- Where do you see in that paper that such number are exclusive? ( I actually do not see any definition of exclusive in the paper)
- Where do you see in that paper that you can simply sum such number?

My understanding is that such number are ALL inclusive (and comparable to those provided by MG5aMC). It means
that you can NOT sum those numbers without applying the method mention in the paper at page 2 (and this is what I commented above).

Cheers,

Olivier

 Prasham Jain (jainprasham33) said on 2020-05-02: #8

Hi,

I think I am mistaken in my nomenclature of "inclusive/exclusive" as you pointed out. However, I still need some clarification on the matter. In the table 20 first row of https://arxiv.org/pdf/hep-ph/0206293.pdf , could you please explain the cross-section numbers? For instance, if cross-section for N=0 is 530pb then shouldn't inclusive cross-section for N=1 (462pb) be more than that? Is this where I am wrong?
Alternatively, could you please explain the meaning of the cross-section value when I generate p p > t t~ j? For us, jet is an additional parton(default MG5 definition).

Prasham

 Olivier Mattelaer (olivier-mattelaer) said on 2020-05-04: #9

Hi,

You should look at slide 58 of this presentation

This is generated (the 4 curve) with the equivalent of N=0 sample in the paper that you mention.
and then using Pythia to have the jet distribution in exclusive sample.
The 4 curve are distribution of the second hardest jet.
The difference between the four curve are parameter of pythia (shower evolution and starting scale for the shower).

This shows that using only N=0 sample is not trustable if you have multiple hard jet.
This is why it is mandatory to use N=1 or N=2,... sample.
The issue is that you have overlap between those samples (see slides 61) and that you typically need to combine more than one of those. Special method (MLM, CKKW-L,...) have been developed for that.

> For instance, if cross-section for N=0 is 530pb then shouldn't inclusive cross-section for N=1 (462pb) be more than that?

In N=1 you asked for at least one hard jet, so this is include in N=0 (which does not request any).
So it makes sense that the higher you go in the number of requested jet your cross-section decrease.
Now this depend of the technical cut that you use at parton-level that you use to avoid all the singularity.
In MLM (and similar) computation this is a pure technical cut which should not change your final cross-section and distribution since only the merging scale should matter (otherwise you screw up the procedure)

Cheers,

Olivier

> On 2 May 2020, at 10:47, Prasham Jain <email address hidden> wrote:
>
> Question #690286 on MadGraph5_aMC@NLO changed:
>
>
> Prasham Jain is still having a problem:
> Hi,
>
> I think I am mistaken in my nomenclature of "inclusive/exclusive" as you pointed out. However, I still need some clarification on the matter. In the table 20 first row of https://arxiv.org/pdf/hep-ph/0206293.pdf , could you please explain the cross-section numbers? For instance, if cross-section for N=0 is 530pb then shouldn't inclusive cross-section for N=1 (462pb) be more than that? Is this where I am wrong?
> Alternatively, could you please explain the meaning of the cross-section value when I generate p p > t t~ j? For us, jet is an additional parton(default MG5 definition).
>
>
> Prasham
>
> --