# incorrect forward Moller scattering

Hi, I am studying Moller scattering in QED with madgraph 2.9.2,

import model sm

generate e- e- > e- e- / Z

In madevent I set the beam energies at 100 GeV each. The only

cut I set is ptl. What I find is that for ptl between 10^(-1) and

10^(-3) the cross section grows as ptl^(-2) as it should.

But for ptl smaller than 10^(-3), say 10^(-4) and smaller, the cross

section stops growing which is obviously incorrect. I guess there is

some implicit cut or parameter I'm not aware of?

Thanks!

## Question information

- Language:
- English Edit question

- Status:
- Solved

- Assignee:
- No assignee Edit question

- Solved by:
- Olivier Mattelaer

- Solved:
- 2021-03-10

- Last query:
- 2021-03-10

- Last reply:
- 2021-03-10

## This question was reopened

- 2021-03-09 by Toshiro Shisude

When looking at the log of the channnel of integration that blows up,

you will see a lot of error message inside

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

Error in matrix element

This is a singularity detection mechanism and indeed the associated phase-space point are automatically cut.

If you really want to go to such extreme regime (where you might even have numerical stability issue, you can check where in the code that error is raised and changed the associated threshold.

Pointless to say that for such small pt cut, you have to introduce the mass of the lepton into the game (without having to speak of the importance of NLO correction into such regime...

Cheers,

Olivier

Thanks for your answer. I don't think 0.1 MeV is actually so extreme, though you are definitely right

that one should be careful with the stability. Can you give me a pointer to the threshold parameters in

the code?

Thanks for your answer. I don't think 0.1 MeV is actually so extreme, though you are definitely right

that one should be careful with the stability. Can you give me a pointer to the threshold parameters in

the code?

Hi,

> I don't think 0.1 MeV is actually so extreme,

For sure this is a pure subjective point of view and that statement also depend on your interest actually.

Experimentally such cut is likely impossible to handle for a lot of reason.

On a pheno point of view it is also difficult to justify since you neglect the mass of the electron.

On a mathematical point of view, I guess that indeed it makes a lot of sense to study such small cuts.

On a numerical point of view, if you are interested to the point where double/quadruple precision is necessary then obviously this makes sense as well

Can you give me a pointer to the threshold parameters.

grep "Error in matrix element" . -rin

I guess that this is part of auto_dsig.f but that file has some many name depending of the various options (like super_auto_dsig /...)

that the safest is to do the grep and then you will have it for your exact syntax that you are using.

Cheers,

Olivier

Just one comment on the physical relevance: first, Moller with massless electrons is just a toy example

to show the problem. More generally, in colliders there may be very forward taggers that handle very small

momentum transfers and scattering angles down to mrads. There were several such taggers at HERA, and

there are precision calorimeters at the LHC (at CMS, for example) to tag very forward protons. Of course,

in most cases those taggers do not measure scattering angle but just energy.

You are right that grepping is the best choice.

Thanks so much for your help!

Thanks Olivier Mattelaer, that solved my question.

Sorry to bother again with this. Just one comment: I changed the model

to sm-full to give mass to the electron, and I changed the line

IF (DSIGUU.LT.1D199) THEN

to read

IF (DSIGUU.LT.1D299) THEN

in auto_dsig1.f That's a full 100 orders of magnitude increase in the

threshold.

With these changes I find the same numerical values for the cross section

as before. This was to be expected in the case of the electron mass, since

the Coulomb divergence is not regularized by the mass. I seems then that

neither the mass nor the threshold are the problem here.

If you have other suggestions I would be very grateful.

The matrix-element returned is actually NaN, so changing the limit does not change that much.

So this sounds a numerical issue. In theory you should be able to convert the code from double precision to quadruple precision if you really want to.

By googling, this might be of some interest:

https:/

Cheers,

Olivier

HI Olivier,

thanks for taking the time to reply again. I appreciate that.

In this case I disagree with your assessment. Precision cannot be the problem here,

at least not as a matter of principle, because previous madgraph versions worked very

well in this regime, reproducing

the tree level analytical result for Moller scattering perfectly well all the way down to ptl

10^(-5) and beyond.

Cheers,

Toshiro

Hi,

comparing with previous version of MG5aMC makes a lot of sense since a lot have changed in the latest version

(2102.00773 <https:/

So in this case the NaN seems to be generated by the new phase-space integrator since the multi-channel weight leads to this NaN for those phase-space points.

As stated in the paper, you can go back to the previous phase-space integrator by setting

SDE_strategy to 1 in the run_card

> In this case I disagree with your assessment.

Well I stand by my assessment that this is a numerical issue linked to the precision of the computation.

Now this is really interesting to learn such numerical issue and the fact that the new phase-space sample is numerically unstable close to singular pole (which makes actually sense by construction)

Cheers,

Olivier

> On 10 Mar 2021, at 00:11, Toshiro Shisude <email address hidden> wrote:

>

> Question #695947 on MadGraph5_aMC@NLO changed:

> https:/

>

> Toshiro Shisude posted a new comment:

> HI Olivier,

>

> thanks for taking the time to reply again. I appreciate that.

>

> In this case I disagree with your assessment. Precision cannot be the problem here,

> at least not as a matter of principle, because previous madgraph versions worked very

> well in this regime, reproducing

> the tree level analytical result for Moller scattering perfectly well all the way down to ptl

> 10^(-5) and beyond.

>

> Cheers,

> Toshiro

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

>Well I stand by my assessment

OK, I obviously ignore everything about this so I won't even try

to argue with you.

The point is that setting SDE_strategy to 1 does the trick, now

the numerical results behave as they should. This solves the

problem for me. Thanks again for your help.

Thanks Olivier Mattelaer, that solved my question.