Initial state: mass and collinear divergences

Asked by Gennaro Corcella on 2019-04-30

Hello,

I have been simulating e+e- -> gamma gamma processes in QED, possibly adding BSM contributions due to
axion-like particles. so called ALPs.
It is well known that the electron mass regulates the initial-state collinear singularities, while the total cross section is divergent if one neglects the electron mass.
May I ask you how MadGraph handles the initial-state electron masses and related collinear divergence?

In fact, I noticed that, if I run ee->gamma gamma with no cuts, the inclusive cross section is very unstable and unreliable, while
setting cuts, e.g., on photon rapidities leads to sensible results. Therefore, I suspect that mass effects may not be fully
included and one needs to set cuts to avoid the collinear divergence and get reasonable cross sections.

Thanks in advance,

Gennaro

Question information

Language:
English Edit question
Status:
Solved
For:
MadGraph5_aMC@NLO Edit question
Assignee:
No assignee Edit question
Solved by:
Olivier Mattelaer
Solved:
2019-05-06
Last query:
2019-05-06
Last reply:
2019-05-03

Hi,

Is your electron massless or massive in your model?

Cheers,

Olivier

> On 30 Apr 2019, at 12:43, Gennaro Corcella <email address hidden> wrote:
>
> New question #680558 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/680558
>
> Hello,
>
> I have been simulating e+e- -> gamma gamma processes in QED, possibly adding BSM contributions due to
> axion-like particles. so called ALPs.
> It is well known that the electron mass regulates the initial-state collinear singularities, while the total cross section is divergent if one neglects the electron mass.
> May I ask you how MadGraph handles the initial-state electron masses and related collinear divergence?
>
> In fact, I noticed that, if I run ee->gamma gamma with no cuts, the inclusive cross section is very unstable and unreliable, while
> setting cuts, e.g., on photon rapidities leads to sensible results. Therefore, I suspect that mass effects may not be fully
> included and one needs to set cuts to avoid the collinear divergence and get reasonable cross sections.
>
> Thanks in advance,
>
> Gennaro
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Gennaro Corcella (gcorcella) said : #2

Hello,

Yes, we have massive electrons, coupled to photons and ALPs
and we are running ee-> gamma gamma, as well as ee->gamma+alp,
for a positron of 550 MeV hitting a fixed electron target.

Thanks, Gennaro

Then you should have it, (you can check within the standalone mode if the matrix-element diverges or not.
Now this is 6 order lower than the energy of one beam so one can expect some issue with the divergence near the threshold, (very large weight close to the threshold), putting cut can certainly help in that case.

Cheers,

Olivier

Gennaro Corcella (gcorcella) said : #4

Hello,

Just to sum up everything, if I calculate analitycally the total LO inclusive (I mean, no cuts) cross section of
ee->gamma+gamma or ee-> gamma+alp, I get a finite result with a (large) log(m_e^2/s), which is
however weighted by small coupling constants (with respect to, say, alpha_s).

If I implement a model with electron masses in MadGraph, shall I then expect the same total
cross section, with the same large mass logarithms? Or shall I rather expect some instability
whenever the photon is roughly parallel to the incoming positron?

Cheers,

Gennaro

Hi,

I actually do not reproduce any instability in that case.
I have done the following:

import model sm-full
generate mu+ mu- > a a
output
launch
set no_parton_cut
set mm 0.5
set ebeam1 550
set ebeam2 0.5

(I use the muon since the electron is massless even in the sm-full model)

and i get (very quickly):
     Cross-section : 1700 +- 1.496 pb
     Nb of events : 10000

For the rest, If your log comes from the phase-space integration of the LO matrix-element then yes it will be present. Now such large log can sometimes lead to instability but this does not seems to be the case here.

Cheers,

Olivier

Gennaro Corcella (gcorcella) said : #6

Hello,

Thank you. I understand that our problems are then due to the inclusion of the
axion-like-particle, whose mass is about 10 MeV. I will work it out.

Gennaro

Gennaro Corcella (gcorcella) said : #7

Thanks Olivier Mattelaer, that solved my question.