Phase space integral of process H-> e+ e- mu+ mu- gamma.

So in top of the multi-channel, we split each channel of integration in two mode, one for the e+ e- onshell and one for the mu+ mu- onshell (plus likely a lot of other combination due to the presence of the photon.

For the rest, this should simply follow this paper:
    hep-ph/0208156 [hep-ph]

Dear Olivier,

Many thanks for your kind reply. I am looking after the paper. Hopefully, I will find the answer.

Thanking you.

Regards,
Biswajit

Dear Olivier,

I am getting a bit higher decay width than MadGraph with a wide variety of cuts. It seems that MadGraph is doing some approximation in multichannel integration where certain interference terms are neglected(may be due to their small values). Is it so? or are there other optimization/approximations?

Thanks.

Regards,
Biswajit

We do use the optimization introduced in the following paper:
2102.00773
But I have reverse to the previous mode of optimization for the helicity and the result are stable.
The same if I remove any filtering over helicity.
I have look at log and they are not warning/suspecious behavior here.

We do not use any hidden approximation here.
Now note that you are handling a one body decay but apply cut that does not really makes sense for such process (what is PT?)

Cheers,

Olivier

Dear Olivier,

Thanks for the references. The pT is the transverse momentum of the photon. I have a few questions to raise about this process.

First, form equation no. (27) and (28) of paper 2102.00773, it seems that the interference terms are neglected in Madgraph for this process in the 'classical limit'. Is it so? Or all interference terms are included properly in Madgraph?

Second, in this process, the photon can be soft and collinear. The results should be unstable in these regions; also, there are experimental cuts that avoid these regions. Surprisingly, Madgraph computes stable results for this process without any cuts, whereas our code fails to calculate this process without any cuts. Are there any intrinsic cuts in MadGraph to get stable results for this process?

Third, as our code fails to give stable results(which is obviously due to soft and collinear photons), I use certain cuts on the transverse momentum(pT) of photons and minimum distance between photons and leptons(deltaR). With these cuts, I get stable results that are a bit higher than Madgraph(with the same cuts and 'cut_decays = True'). There is no decay of intermediate Z-bosons; all are off-shell in our computation. I suppose this is due to the first point mentioned above. I want a few comments in this regard.

Thanks a lot.

Regards,
Biswajit

Hi,

> First, form equation no. (27) and (28) of paper 2102.00773, it seems
> that the interference terms are neglected in Madgraph for this process
> in the 'classical limit'.

The approximation noted in Eq. (27) is not used in the code and therefore only the first term of Eq. (28) is used within the code.

If Equation (27) is valid then the phase-space integrator will have higher efficiency and if not then the efficiency will be bad (a bit or a lot depending of the case). But this impact only the efficiency of the code, not the final result.

> Or all interference terms are included properly in Madgraph?

Yes all interference terms are included.

> Second, in this process, the photon can be soft and collinear. The
> results should be unstable in these regions; also, there are
> experimental cuts that avoid these regions. Surprisingly, Madgraph
> computes stable results for this process without any cuts, whereas our
> code fails to calculate this process without any cuts. Are there any
> intrinsic cuts in MadGraph to get stable results for this process?

1) We do have an internal cut that remove all matrix-element which are insanely large.
2) Our LO phase-space integrator is not designed for integrating over soft/collinear singularities.

This being said, we do have issue without any cut:
1) the code is slow
2) it goes to a second refine stage (i.e. the cross-section is not stable between the survey and the first refine and the code fails to reach the number of events at the first refine
3) the code generates a very small amount of events (only ~150 when asking 10k)
4) If I run twice the code, the cross-section differs by an error much larger than the quoted statistical error.

So I would not say that madgraph is trustable without cuts and we certainly have an issue with the unregulated soft/collinear (as we should).

> Third, as our code fails to give stable results(which is obviously due
> to soft and collinear photons), I use certain cuts on the transverse
> momentum(pT) of photons and minimum distance between photons and
> leptons(deltaR). With these cuts, I get stable results that are a bit
> higher than Madgraph(with the same cuts and 'cut_decays = True').

Since you ask for a generation of events for a particle at rest.
The notion of PT is not well defined since they are not beam direction.
So I wonder if you are indeed generating h > e+ e- mu+ mu- a
or if you use a collider syntax like
 p p > h > e+ e- mu+ mu- a
 p p > h, h > e+ e- mu+ mu- a
(or any other variation).
In which case, you might have onshell cut and/or some off-shell effects.

> There
> is no decay of intermediate Z-bosons; all are off-shell in our
> computation. I suppose this is due to the first point mentioned above.
> I want a few comments in this regard.

I do not understand your comment here.

Cheers,

Olivier

> On 28 Nov 2022, at 13:40, Biswajit Das <email address hidden> wrote:
>
> 2102.00773