MadGraph5_aMC@NLO

Default Factorization and Renormalization Scales

Asked by Marc Thomas

Hi MadGraph Team,

Sorry to ask a basic question, but I'm trying to understand the default factorization and renormalization scale in MG.
I see the description in,
https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/FAQ-General-13
and also some previous questions about it, but these still don't make it entirely clear to me?

As an example, I'm generating p p > j ve ve~ at LO in MGv2.3.3, and trying to understand the scale used.
From https://cp3.irmp.ucl.ac.be/projects/madgraph/wiki/FAQ-General-13, it says that the scales are:
"set to the central mT^2 scale after kT-clustering of the event".

My question regarding this:
If I only have 1 jet (pp > j ve ve~), is my 2->3 event being clustered back to a 2->2 event (are the 2 neutrinos being "clustered" back to the Z they come from)? Or does this clustering only apply to multi-jet or merged samples, so in this case we take the central mT^2 scale for all 3 final state particles? Or as the neutrinos come from a Z, is the scale just mT^2 of the Z (which is not the central mT^2 of the event)?

Is there any reference to an explicit algorithm or equation?

Thanks in advance,
Marc

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Olivier Mattelaer
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Marc Thomas (mct1g11) said : 		#1

Hi, is there any progress on answering this question or do you need me to clarify anything?
Thanks,
Marc

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Best Olivier Mattelaer (olivier-mattelaer) said : 		#2

Hi,

Sorry to take time but if you want more details on the algorithm in this precise case, I was force to run it with debug statement on True and look at the log to see the details, I put that (obviously) in low priority.

So, here is my findings: For such simple case, the clustering seems unique for each diagram (which is expected).
Here is the details, (therefore diagram by diagram):

For the S-channel diagram: u g > u > Z u > ve ve u
the clustering applied is
1) ve + ve > Z
2) Z + u > Z(2)
3) g Z(2) > u (the initial vertex)

For the T-channel diagram: u g > Z u > ve ve u
the clustering applied is
1) g u > u (the t-channel)
2) ve ve > Z
3) Z u > u

For the gluon ISR radiation u u~ > Z g
the clustering applied is
1) g u > u
2) v2 v2 >Z
3) u Z > u~
(so the same as fo the T-channel)

The scale corresponds to the transverse mass of the particle get by the last clustering in each case.

> Is there any reference to an explicit algorithm or equation?

You can look at the exact algorithm in
cluster.f and reweight.f

In order to decide if we use S or T channel, this is based on the single diagram enhancement technique described (and introduced) in
hep-ph/0208156
I’m not sure if they are a proper reference of those code in any paper. (they are short description in many but not one paper describing all the details/special case/…

Cheers,

Olivier

> On Apr 19, 2016, at 17:52, Marc Thomas <email address hidden> wrote:
>
> Question #290925 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/290925
>
> Marc Thomas posted a new comment:
> Hi, is there any progress on answering this question or do you need me to clarify anything?
> Thanks,
> Marc
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Marc Thomas (mct1g11) said : 		#3

Thanks Olivier Mattelaer, that solved my question.

Revision history for this message
Marc Thomas (mct1g11) said : 		#4

Thanks Olivier for the clarification.

I'd already looked at cluster.f and reweight.f, and didn't find it easy to tell exactly what was going on!
I'll take a look at hep-ph/0208156

I think I'll change it to a simpler scale definition whenever I need to be certain what the factorization scale is, such as comparing to other Generators.

Cheers,
Marc

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

Hi Marc,

> I’d already looked at cluster.f and reweight.f, and didn't find it easy to tell exactly what was going on!

I agree on that.

> I think I'll change it to a simpler scale definition whenever I need to
> be certain what the factorization scale is, such as comparing to other
> Generators.

Sure this dynamical scale is too complicated for cross-validation with other generator. (since you do not have a unique analytical formula and since the exact same event can be assigned to different scale). It is however the most natural one for matching/merging.

Note that since 2.3.0, you have the parameter “dynamical_scale_choice” in the run_card which allow you to switch to some more simple dynamical scale.
(like sqrt(\hat S), HT, HT/2, …), you can see the description here: https://answers.launchpad.net/mg5amcnlo/+faq/2014

Cheers,

Olivier

> On Apr 21, 2016, at 18:27, Marc Thomas <email address hidden> wrote:
>
> Question #290925 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/290925
>
> Marc Thomas posted a new comment:
> Thanks Olivier for the clarification.
>
> I'd already looked at cluster.f and reweight.f, and didn't find it easy to tell exactly what was going on!
> I'll take a look at hep-ph/0208156
>
> I think I'll change it to a simpler scale definition whenever I need to
> be certain what the factorization scale is, such as comparing to other
> Generators.
>
> Cheers,
> Marc
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Revision history for this message
Marc Thomas (mct1g11) said : 		#6

Hi Olivier,

Yes thanks, I've just been looking at this "dynamical_scale_choice" parameter. This make changing the scale definition particularly easy.

I see now that this default scale is chosen with to make matching/merging easier.
I had thought it was just unnecessarily complicated!

Cheers,
Marc