e+ e- > e+ X diverges for large etal

Hi,

> 1. how does MadGraph compute the processes e+ e- > e+ X, when the final e+ becomes collinear?

We just evaluate the matrix-element for that kinematic, if you matrix element is divergent then you will hit the singularity and even if the singularity is technically integrable (is it in your case) the result will be some insanely high number.

> 2. also, how is the pdf of a photon from electron implemented in MadGraph?
> We found something explicit mentioned for the pdf of a photon from a proton here (on the Manual-March-2007), but nothing regarding photon from electron.

That's the same implementation as for the photon from proton, you just have to set lpp1 and/or lpp2 to 3 in that case.
In that case, your process should be define as the photon in the initial state, i.e.
generate a e- > vl w-

Cheers,

Olivier

> On 6 Jul 2017, at 18:53, Filippo Sala <email address hidden> wrote:
>
> New question #646548 on MadGraph5_aMC@NLO:
> https://answers.launchpad.net/mg5amcnlo/+question/646548
>
> Hi,
>
> 1. how does MadGraph compute the processes e+ e- > e+ X, when the final e+ becomes collinear?
>
> 2. also, how is the pdf of a photon from electron implemented in MadGraph?
> We found something explicit mentioned for the pdf of a photon from a proton here (on the Manual-March-2007), but nothing regarding photon from electron.
>
> The reasons of the above questions is the following problem.
>
> We are interested in a process like
>
> e+ e- > e+ vl w-
>
> with e+ undetected.
>
> Therefore we’d like to integrate the above cross section for all the final e+ that do not enter the detector, so say with \theta < mrad (eta >~ 5).
>
> The cross section computed with the photon pdf should in principle provide an upper bound to the result, cause it is obtained by summing on the available final e+ phase space. Correct?
> MadGraph indeed gives a finite result for this calculation, as expected.
>
> We find that the cross section for e+ e- > vl e+ w- diverges as we increase etal at the generator level, while it should converge to the value obtained using the photon pdf.
> Is there anything we don’t understand in the way this is implemented in MadGraph?
>
> We find these results using v2_5_5 and v2_4_3.
>
> Thank you in advance
>
> Dario, Filippo and Andrea
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Hi Olivier,

Thank you for the prompt reply!
There has been some misunderstanding, let us clarify.

Yes, we know how to select the photon from electron in MadGraph.
Our question is about which formula of the pdf is actually implemented, and if there is some implicit setting of the parameters that one can change.

We investigated more and found a previous similar question, that however does not fully address our need (https://answers.launchpad.net/mg5amcnlo/+question/224904).
There we learn that you used eq. (20) hep-ph/9310350, but that at the time it was not possible to play with theta_c.
Now, our physics problem (described below the questions in our first message) requires to specify a theta_c, because we want to integrate from theta = 0 to theta_c ~ mrad.
Is it possible, in the latest Madgraph versions, to choose a theta_c in the equivalent of eq. (26) of hep-ph/931035?
If it is possible, that would solve our problem.

Otherwise we would have to compute
e+ e- > e+ v w-
and somehow match it with
a e- > v w-
to avoid double counting the collinear region.

If we compute e+ e- > e+ v w-, then we find a result that diverges for increasing etal at generator level, which is not physical.
Indeed we are setting the electron mass to a finte value, and we have a mass gap between the initial and final state that prevents y to go to zero. This cuts off the collinear divergence because the photon virtuality cannot go to zero.
Does MadGraph compute the matrix element alone, and only later weight it with the phase space, so that close to divergences of the matrix elements it may experience difficulties?

Hope this clarifies our question.

Dario, Filippo and Andrea

Hi,

Nothing change in that part of the code since the previous thread. So the conclusion of the previous thread are still valid.
Maybe another solution in your case is to implement your upper bound on theta_c via a new cut in cuts.f

> Does MadGraph compute the matrix element alone, and only later weight it with the phase space, so that close to divergences of the matrix elements it may experience difficulties?

The mass of the electron is also quite small so depending of the energy of your system you can hit numerical inaccuracy even if the cross-section is technically finite.

Cheers,

Olivier

> On 7 Jul 2017, at 18:17, Filippo Sala <email address hidden> wrote:
>
> Question #646548 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/646548
>
> Status: Answered => Open
>
> Filippo Sala is still having a problem:
> Hi Olivier,
>
> Thank you for the prompt reply!
> There has been some misunderstanding, let us clarify.
>
> Yes, we know how to select the photon from electron in MadGraph.
> Our question is about which formula of the pdf is actually implemented, and if there is some implicit setting of the parameters that one can change.
>
> We investigated more and found a previous similar question, that however does not fully address our need (https://answers.launchpad.net/mg5amcnlo/+question/224904).
> There we learn that you used eq. (20) hep-ph/9310350, but that at the time it was not possible to play with theta_c.
> Now, our physics problem (described below the questions in our first message) requires to specify a theta_c, because we want to integrate from theta = 0 to theta_c ~ mrad.
> Is it possible, in the latest Madgraph versions, to choose a theta_c in the equivalent of eq. (26) of hep-ph/931035?
> If it is possible, that would solve our problem.
>
> Otherwise we would have to compute
> e+ e- > e+ v w-
> and somehow match it with
> a e- > v w-
> to avoid double counting the collinear region.
>
> If we compute e+ e- > e+ v w-, then we find a result that diverges for increasing etal at generator level, which is not physical.
> Indeed we are setting the electron mass to a finte value, and we have a mass gap between the initial and final state that prevents y to go to zero. This cuts off the collinear divergence because the photon virtuality cannot go to zero.
> Does MadGraph compute the matrix element alone, and only later weight it with the phase space, so that close to divergences of the matrix elements it may experience difficulties?
>
> Hope this clarifies our question.
>
> Dario, Filippo and Andrea
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.