# Setting QED and QCD coupling orders in mg5

Hello,

I would like to ask a clarification on how someone can specify the QED/QCD order in the production.

My understanding is that if nothing is specified, the lowest QED order is considered.
Now I am trying to isolate some high order QED diagrams like the famous
W+W+ EWK production therefore I though about writing something like:

generate p p > e+ mu+ vl vl j j QED=6

(I know that this process alone is not gauge invariant but I assume that this will not be a big problem with the generator).
When looking at the list of diagrams I (surprisingly) see some diagrams with order:
QCD=2, QED=4 ....

Is this expected?
Obviously those diagrams go away if I also requires QCD=0.
The problem with that is that obviously I cannot then use the NLO calculation ([QCD])
since I get the message:

WARNING: Some loop diagrams contributing to this process are discarded because they are not pure (QCD)-perturbation.
Make sure you did not want to include them.

... and obviously the real emission diagrams are not there.

thanks a lot,

Valerio

## Question information

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marco zaro Edit question
Last query:
 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2015-01-04: #1

Hi Valerio,

Nothing surprising, since when you specify one, all the other coupling not specify are allowed to be set at infinity.
Also the use of the "=" sign is unfortunate and in the latest version of the code, the sign "<=" is preferred even if they have the same meaning.

Cheers,

Olivier

 Revision history for this message Valerio Dao (valerio-dao) said on 2015-01-04: #2

Hi Olivier,

thanks for the prompt answer .... but I am quite puzzled now.

For instance:
"since when you specify one, all the other coupling not specify are allowed to be set at infinity."
.... but then how is it possible that, when I set QED=6 I find diagrams that are QCD=2,QED=4?

I performed few tests on the "in"famous process p p > l+ l+ lv lv j j and
I have to say I don't fully understand.

without specifying any order:
generate p p > e+ mu+ vl vl j j
--->Total: 12 processes with 144 diagrams
... those corresponds ONLY to the order QCD=2,QED=4 (which is the lowest QED one).
Interestingly, doing the generate I see the log: WEIGHTED=10 (which is what I expect for QCD=2,QED=4)

generate p p > e+ mu+ vl vl j j QCD=2
--->Total: 12 processes with 1818 diagrams
here, if you trust me, you see both QCD=2(QED=4) and QCD=0(QED=6) diagrams, the latter are the majority

generate p p > e+ mu+ vl vl j j QCD=0
--->Total: 12 processes with 1674 diagrams
here the diagrams QCD=2(QED=4) have been removed

generate p p > e+ mu+ vl vl j j QED=6
--->Total: 12 processes with 1818 diagrams
why this isn't giving me the same result than the line above?

generate p p > e+ mu+ vl vl j j QED=4
--->Total: 12 processes with 144 diagrams
this seems to work as expected since it retains only the lowest order QED diagrams

P.S. : I am already using v2.2.2, would
generate p p > e+ mu+ vl vl j j QCD<=1
allow me to run the NLO correction as well?

thanks,

Valerio

 Revision history for this message Valerio Dao (valerio-dao) said on 2015-01-04: #3

generate p p > e+ mu+ vl vl j j QCD<=1 [QCD]
INFO: Restrict model loop_sm with file models/loop_sm/restrict_default.dat .
INFO: Change particles name to pass to MG5 convention
Kept definitions of multiparticles l- / j / vl / l+ / p / vl~ unchanged
Defined multiparticle all = g gh gh~ d u s c d~ u~ s~ c~ a ve vm vt e- mu- ve~ vm~ vt~ e+ mu+ b t b~ t~ z w+ h w- ta- ta+
INFO: Generating FKS-subtracted matrix elements for born process: u u > e+ mu+ ve vm d d QCD=1 [ QCD ] (1 / 20)
Command "generate p p > e+ mu+ vl vl j j QCD<=1 [QCD]" interrupted with error:
FKSProcessError : Cannot map born/real configurations between u u > e+ mu+ ve vm d d QCD=1 [ QCD ] and u u > e+ mu+ ve vm d d g WEIGHTED=2 QCD=2 [ QCD ]: not same number of configurations: 184 0

... this is basically the reason why I wanted to drive everything from the point of view of the QED order (without specifying the QCD one) since the QCD one "cannot be fixed" when going to NLO.

Cheers,

Valerio

 Revision history for this message Olivier Mattelaer (olivier-mattelaer) said on 2015-01-04: #4

Hi Valerio,

I think that you will understand more easily all your example, if you replace the QCD=X by QCD<=X both syntax are actually equivallent,
but it's then clear why you can have QED=4 QCD=2 diagram when you type
generate p p > e+ mu+ vl vl j j QED=6
since this is the same as
generate p p > e+ mu+ vl vl j j QED<=6

For the NLO, you have to specify the order of the born that you want, and the [QCD] will specify that you want it at NLO in QCD, and we handle the real as needed.

Clearly a problem occur in your process, I have assign Marco to this bug such that he can take a look since this is is part.

Cheers,

Olivier

 Revision history for this message Valerio Dao (valerio-dao) said on 2015-01-04: #5

Hi Olivier,

thanks for the clarification.
I had clearly misunderstood the usage of the ordering setting.

so in principle:
generate p p > e+ mu+ vl vl j j QED<=4 (only QED=4,QCD=2)
and
generate p p > e+ mu+ vl vl j j QCD<=0 (only QED=6,QCD=0)

will give me what I want and should work also in [QCD], but for some reason the latter
does not seem to work for this process,
is this correct?

thanks,

Valerio

 Revision history for this message marco zaro (marco-zaro) said on 2015-01-04: #6

Ciao Valerio,
what happens if you type
generate p p > e+ mu+ vl vl j j QED=6 QCD=0 [QCD]
this should normally work ok, for what concerns the code generation, apart the warning on the discarded loop diagrams.

About this warning, this is due to the fact that you have loop diagrams, which are QCD corrections, but with electroweak bosons in the loop which are discarded in the current version of MG5_aMC.
In simpler processes which are purely EW at the LO, such as VBF, single-top, ... these diagrams are however 0 or heavily suppressed, so it is not a big problem to throw them away.

Your process is clearly a different case.
Note however that your process is extremely challenging by the integration point of view, as you cannot veto diagrams with s-channel vector bosons as in VBF, otherwise you break gauge invariance. In this case you can have situations where you have QCD radiation from the decay of a vector boson, which is currently not handled in an efficient way.

In short, even if the generation would be working ok with
generate p p > e+ mu+ vl vl j j QED=6 QCD=0 [QCD]
it is extremely hard that you can get events in a reasonable amount of time.

All these issues will be fixed once we will automate the mixed EW-QCD corrections, but for the time being, i fear this process is not feasible.

Let us know if you need more...
Cheers,

Marco

 Revision history for this message Valerio Dao (valerio-dao) said on 2015-01-04: #7

Thanks Marco for the detailed explanation (although the outlook is quite negative)

I tried both
A) generate p p > e+ mu+ vl vl j j QED=6 QCD=0 [QCD]
and
B) generate p p > e+ mu+ vl vl j j QED=4 QCD=2 [QCD]

and in the former (but not in the latter) case I see the warnings you are mentioning.
There is indeed a large difference in the number of diagrams in both cases:
A) INFO: Generated 20 subprocesses with 30736 real emission diagrams, 2604 born diagrams and 12040 virtual diagrams
B) INFO: Generated 20 subprocesses with 3808 real emission diagrams, 224 born diagrams and 5264 virtual diagrams

At the same time when I try to generate events, both setup crashes with incredibly long logs about not being able to compile the processes .... so I would agree with you that the process is not feasible.

Saying that there are few things in your explanation I don't fully get given my limited knowledge:
" as you cannot veto diagrams with s-channel vector bosons as in VBF, otherwise you break gauge invariance. In this case you can have situations where you have QCD radiation from the decay of a vector boson,"
naively I would have thought that:
- choosing same sign will implicitly veto any s-channel vector boson, no?
- since I am explicitly requiring the boson to decay leptonically, how can I have radiation from a decay of a vector boson?

thanks a lot,

Valerio

 Revision history for this message marco zaro (marco-zaro) said on 2015-01-08: #8

Ciao Valerio,
so, i think what you get when try (QCD,QED) = (0,6) and (2,4) makes sense:
The latter case correspond e.g. to QCD production of a w boson pair plus 2 jets, and should be equivalent to what you would get without specifying any order. In this case, if you do QCD corrections, you never have loops in which a vector boson enters, so you don't have the warning.

For the s-channel thing, I was referring to the QED=6 QCD=0 case, in which you can have diagrams where the two jets you ask for come from a (resonant) vector boson, different from the two from which the leptons come.

Is it more clear?

Let me know if you need more.

Cheers,

Marco