comparing EPA with full matrix element calculation

Asked by nblinov

Hello,

I'm simulating a photon-fusion process in an electron nucleus collision (e N > e N ax, ax is an axion, N is modelled as a charged fermion with a form factor) and decided to compare
the results from the electron equivalent-photon approximation (EPA) implementation (a N > ax N with lpp1 = 3 in the run_card) and direct calculation using the full 2->3 matrix element (e N > e N ax).

My expectation is that the EPA should be relatively close to the full calculation when one removes cuts (here the final state electron pT which regulates the collinear divergence), similar to the general results in https://arxiv.org/abs/2111.02442. Moreover, the EPA cross-section should be larger than the full ME since it captures the most singular region of phase space. However, I'm finding that the EPA cross-section is smaller by a factor of 20-40 over the mass and beam energy range I am considering, compared to the full matrix element calculation with a small pT cut. I also implemented the EPA by hand, and seem to find much larger total cross-sections as well.

My question is -- are there any hidden cuts in the EPA calculation that are not apparent in the run_card or banner.py that might lead to this discrepancy?

Thank you!

Question information

Language:
English Edit question
Status:
Answered
For:
MadGraph5_aMC@NLO Edit question
Assignee:
No assignee Edit question
Last query:
Last reply:
Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said :
#1

Is that not an issue of the form-factor?

Did you compare the different implementation of EPA available in the code?
How did you set your scales here?

One typically hidden cut is associated to the dynamical scale which cut any event with too low scale (since this is designed for collision with proton to keep the perturbative regime).

Cheers,

Olivier

Revision history for this message
nblinov (nblinov) said :
#2

Re: form factor -- yes I did check this as well by simulating e t > e t + ax (top quark mass happens to be similar to my nucleus, so the kinematics is similar) and the equivalent EPA process. Again the cross-section for the full ME calculation is much larger than the EPA one.

Re: different implementations. I've tried the standard one from MG 3.1.1 where the photon distribution comes from PhotonFlux.f; I also tried the iww = pdlabel1, and eva = pdlabel1 options MG 3.4.0, both giving similar cross-sectons (both ievo_eva options also give the same result).

For all the EPA calculations I've used
.true. = fixed_fac_scale1
and varied dsqrt_q2fact1 from 1 to 3 GeV (the cross-section is very weakly dependent on this, as expected)

By the way, my beam energy is low, 4 GeV and the target nucleus is at rest. Could the dynamical scale cut be the culprit here? if so, how can I change it? Thanks!

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said :
#3

I would suggest to use fixed scale for all parameter (both beam and factorization scale)

Cheers,

Olivier

> On 12 May 2022, at 06:15, nblinov <email address hidden> wrote:
>
> Question #701752 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/701752
>
> Status: Answered => Open
>
> nblinov is still having a problem:
> Re: form factor -- yes I did check this as well by simulating e t > e t
> + ax (top quark mass happens to be similar to my nucleus, so the
> kinematics is similar) and the equivalent EPA process. Again the cross-
> section for the full ME calculation is much larger than the EPA one.
>
> Re: different implementations. I've tried the standard one from MG 3.1.1
> where the photon distribution comes from PhotonFlux.f; I also tried the
> iww = pdlabel1, and eva = pdlabel1 options MG 3.4.0, both giving similar
> cross-sectons (both ievo_eva options also give the same result).
>
> For all the EPA calculations I've used
> .true. = fixed_fac_scale1
> and varied dsqrt_q2fact1 from 1 to 3 GeV (the cross-section is very weakly dependent on this, as expected)
>
> By the way, my beam energy is low, 4 GeV and the target nucleus is at
> rest. Could the dynamical scale cut be the culprit here? if so, how can
> I change it? Thanks!
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
nblinov (nblinov) said :
#4

I just tried this as well, but no luck unfortunately.
The "eva" EPA implementation does yield a higher cross-section compared to "iww", but both are still much smaller than the direct calculation ( factors of ~ 24 and 36, respectively).

Here are the run card snippets for these runs:

EPA (a t > ax t):
mixed = pdlabel
eva = pdlabel1 ! PDF type for beam #1
none = pdlabel2 ! PDF type for beam #2
 False = fixed_ren_scale ! if .true. use fixed ren scale
 True = fixed_fac_scale1 ! if .true. use fixed fac scale for beam 1
 True = fixed_fac_scale2 ! if .true. use fixed fac scale for beam 2
 3. = scale ! fixed ren scale
 3. = dsqrt_q2fact1 ! fixed fact scale for pdf1
 3. = dsqrt_q2fact2 ! fixed fact scale for pdf2

(this requires we generate the process with "set group_subprocesses False" as noted in 2111.02442; eva -> iww for the other implementation does not require this)

Direct (e- t > e- t ax):
all cuts are default except
 0.01 = ptl ! minimum pt for the charged leptons
-1. = etal ! max rap for the charged leptons

These settings lead to cross-sections with reasonably small uncertainties (for certain processes involving my nucleus I needed to play with -- t_strategy output option to get stable results as discussed in the appendix of https://arxiv.org/abs/2102.00773; however the defaults work fine for this top quark toy example).

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said :
#5

You still have
 False = fixed_ren_scale ! if .true. use fixed ren scale

Can you put that one to fixed too?

Revision history for this message
nblinov (nblinov) said :
#6

I have tried this as well, for both iww and eva implementations, along with variations of the scale parameter.
These changes didn't have an impact on the cross-section unfortunately.

Revision history for this message
Olivier Mattelaer (olivier-mattelaer) said :
#7

Good, this means that you do not face an hidden cut (which was my worry).

Now I do not agree that the two computation should match since this is a LO computation.
If you do not put any cut on the electron, that cross-section should actually be infinite (and technically cancel by NkLO contribution).
While the EPA actually do a resummation as needed (i.e. they do not have the same accuracy).

Cheers,

Olivier

Can you help with this problem?

Provide an answer of your own, or ask nblinov for more information if necessary.

To post a message you must log in.