Strange Cross Section Behavior at High Energies

Asked by chris on 2018-02-19

Hi,

I'm studying reaction cross sections at high energies using madgraph and am getting some strange behavior in regards to the W and Z bosons. Interactions involving the W boson have their cross section explode to high values very quickly. For example, if install a fresh copy of madgraph from the v2.6.1 archive and without changing anything run

define W = w+ w-
generate W W > W W
output WW_WW
launch
set ebeam1=1e13
set ebeam2=1e13

I get a cross section of around 2.7e49 pb. Running with w+ and w- boson separated has the same problem, as does running w z > w z, or w+ w- > z z. Furthermore, the z z > z z cross section goes as 1 over s at first, but for some reason at beam energies of around 1e10 GeV, it starts increasing instead. Again if I extract a fresh version of madgraph from the archive I can replicate the problem. If I run z z > z z with both ebeams at 1e9 GeV I get a cross section of 1.628e-13 pb, at 1e10 GeV I get 3.126e-15 pb, but at 1e11 GeV it goes back up to 3.186e-13. Is the program behaving as expected here? or is something going wrong?

Question information

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MadGraph5_aMC@NLO Edit question
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Last query:
2018-02-21
Last reply:
2018-02-22

Hi,

I guess that what you observe here should be related to numerical precision.
Especially since onshell relation goes like the square so you are definitively in suspicious territory for numerical precision.

Cheers,

Olivier

PS: This actually reminds me my first contact with Madgraph version4, when I did the exact same process (without Higgs) to compare with analytical computation. The fun part of the story was that the code was (still in beta) so unstable that time, that it entered a infinite loop that kills the computer of Fabio.

> On 19 Feb 2018, at 22:37, chris <email address hidden> wrote:
>
> New question #664631 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/664631
>
> Hi,
>
> I'm studying reaction cross sections at high energies using madgraph and am getting some strange behavior in regards to the W and Z bosons. Interactions involving the W boson have their cross section explode to high values very quickly. For example, if install a fresh copy of madgraph from the v2.6.1 archive and without changing anything run
>
> define W = w+ w-
> generate W W > W W
> output WW_WW
> launch
> set ebeam1=1e13
> set ebeam2=1e13
>
> I get a cross section of around 2.7e49 pb. Running with w+ and w- boson separated has the same problem, as does running w z > w z, or w+ w- > z z. Furthermore, the z z > z z cross section goes as 1 over s at first, but for some reason at beam energies of around 1e10 GeV, it starts increasing instead. Again if I extract a fresh version of madgraph from the archive I can replicate the problem. If I run z z > z z with both ebeams at 1e9 GeV I get a cross section of 1.628e-13 pb, at 1e10 GeV I get 3.126e-15 pb, but at 1e11 GeV it goes back up to 3.186e-13. Is the program behaving as expected here? or is something going wrong?
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

chris (cmwedin) said : #2

Hi,

Thanks for your response! Checking the cross sections using calchep's MC simulation, I was able to get a cross section for z z > z z that agreed with madgraph, up until 1e10 GeV mark, where calchep's cross section continued going as 1/s and madgraph's cross section starts going as s. I'm just curious as to whats causing the discrepancy between these two programs.

Thanks again,

Chris

David d'Enterria (CERN) (dde) said : #3

Hi Oliver,

why is this exponentially increase of the sigma(WW->WW) scattering x-section vs. sqrt(s) a "numerical precision" problem ?
How does one cure this numerical precision problem ?

Thanks,

David

Hi David,

calchep is performing the computation analytically when ours is numerical. So it is possible that they are more numerically stable than us.

The fact that we agree with CH is a sign that everything should be under control and that we do not have real bug in our code.
Finding the source of this pure numerical issue is something that I do not plan to do. But if you find it, please tell me this can come usefull.

Cheers,

Olivier

PS: If I would have to investigate it, I would start by setting all the masses to zero to see if this helps.

Can you help with this problem?

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