# Factorization scale

Hi calcHEP authors,

I was told that by default MadGraph uses sqrt(M^2+pT^2) as the factorization scale where the mass and pt belong to a resonance in the s channel, I suppose. I am not sure how to include this number in the batch file, I tried

alpha Q : sqrt(M12^2+Pt12^2)

but it does not recognize Pt12^2. Is there a way to include this number? The final cross section seems to be very sensitive to this number and I cant get MadGraph to agree with calcHEP.

By the way, I was also told that this number should be the mass of the resonance M12, so I am planning to use that number for my final cross sections, and I dont understand why madgraph does the other thing.

Thanks.

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 Revision history for this message Neil Christensen (neil-christensen-qft) said on 2014-03-11: #1

I am confused because in CalcHEP we use 1 and 2 to refer to the two incoming particles which have no pT. So, do you mean the pT of particles 3 and 4?

I think we need to first determine how to set this scale in the gui. Once we figure that out, we can figure out if there are any subtleties in setting it in the batch.

Please take a look at Section 5.4 of the manual (QCD coupling). It describes the kinematic variables that can be used to set the scale. Are these sufficient for you? Or, do you need something else?

Best wishes,
Neil

 Revision history for this message Angel (campoverdeangelf) said on 2014-03-11: #2

Hi,

I have a process in which gluon(1) gluon(2) -> resonance(12) -> W(34) W(56)->q(3)q(4)q(5)q(6), so I am interested on the pt and the mass of the resonance, that I thought would be the pt and mass of the system 3456 (w,w), not 12, you were right.

I think I know how to specify the value of the factorization scale ( sqrt(M12^2+T3456^2) ). However we have decided to set the scales to a fixed number, the mass of the resonance, in both generators. But I still get different cross sections. I think the problem might be in madgraph. This is the batch file:

Model: SMRS
Model changed: False
Gauge: unitary

Process: g,g->jb,j,jb,j

Composite: j=u,d,c,s,b
Composite: jb=u~,d~,c~,s~,b~

Remove: a,W+,W-,H,d,s,b,u,c,t,g

pdf1: PDT:cteq6l1 (proton)
pdf2: PDT:cteq6l1 (proton)

p1: 4000
p2: 4000

Run parameter: Mhh
Run begin: 1600
Run step size: 400
Run n steps: 1

#alpha Q : sqrt(M12^2+T3456^2)
alpha Q : M12

Kinematics: 12 -> 34,56
Kinematics: 56 -> 5,6
Kinematics: 34 -> 3,4

Regularization momentum: 12
Regularization mass: Mhh
Regularization width: Whh
Regularization power: 2

Regularization momentum: 34
Regularization mass: MZ
Regularization width: WZ
Regularization power: 2

Regularization momentum: 56
Regularization mass: MZ
Regularization width: WZ
Regularization power: 2

Number of events (per run step): 1
Filename: pp_KKGraviton_ZZjjjj
NTuple: False
Cleanup: True

Parallelization method: local
Walltime: 0.15
Memory: 1
Max number of cpus: 5
sleep time: 10
nice level : 19

nSess_1: 5
nCalls_1: 50000
nSess_2: 5
nCalls_2: 50000

and the model file is http://cp3-origins.dk/content/uploads/2013/12/SMRS-CH.zip

 Revision history for this message Neil Christensen (neil-christensen-qft) said on 2014-03-12: #3

I am still a little confused because p_3+p_4+p_5+p_6 = p_1+p_2 so there is no pT in the final total momentum either.

M12 is not exactly the mass of the resonance. It is the collision energy sqrt((p_1+p_2)^2) which changes event to event. If this is what you want, that is fine. Of course, if your width is very small, then the resonance mass dominates. So, maybe it is ok. On the other hand, if you want the actual mass of the resonance to always be used, you should use the mass symbol for that particle.

I have compared CalcHEP and MadGraph many many times. In my experience, when there is a discrepancy, it usually comes down to something set differently between the two. If I work long enough, I can usually figure out how to set everything in the two to get agreement.

I see here that you have removed a bunch of diagrams in CalcHEP. Are you sure you do not break gauge invariance by removing these diagrams? Are you sure your result is not effected by breaking gauge invariance? How have you done this in MadGraph? Are the resonances always on shell in MadGraph? I don't see any cuts. Have you removed the cuts in MadGraph? You might want to try producing the resonances and then decaying them to compare first to remove the possibility of gauge invariance problems. The only difference would be in spin correlations, but you may not be strongly affected by that.

Also, you might want to focus on individual subprocesses in your comparison to figure out where the problem is.

Best wishes,
Neil

 Revision history for this message Angel (campoverdeangelf) said on 2014-03-13: #4

I am still a little confused because p_3+p_4+p_5+p_6 = p_1+p_2 so there is no pT in the final total momentum either.
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Yes, you are right, madgraph actually uses a more complicated expression for this scale, I was wrong about that (page 8 of https://cp3.irmp.ucl.ac.be/projects/madgraph/attachment/wiki/ManualAndHelp/Manual-March-2007.pdf)
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M12 is not exactly the mass of the resonance. It is the collision energy sqrt((p_1+p_2)^2) which changes event to event. If this is what you want, that is fine. Of course, if your width is very small, then the resonance mass dominates. So, maybe it is ok. On the other hand, if you want the actual mass of the resonance to always be used, you should use the mass symbol for that particle.
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I think M12 is better than the actual mass of the resonance, this seems the simplest choice and I am not sure if there is a right way of choosing this number, different people seem to do different things here.
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I have compared CalcHEP and MadGraph many many times. In my experience, when there is a discrepancy, it usually comes down to something set differently between the two. If I work long enough, I can usually figure out how to set everything in the two to get agreement.

I see here that you have removed a bunch of diagrams in CalcHEP. Are you sure you do not break gauge invariance by removing these diagrams? Are you sure your result is not effected by breaking gauge invariance? How have you done this in MadGraph? Are the resonances always on shell in MadGraph? I don't see any cuts. Have you removed the cuts in MadGraph?
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I know that if one has the lagrangian and if one transforms it with an element of SU(2)XSU(3)XU(1) and if it does not change its functional form the lagrangian is gauge invariant, I dont know how that is related to what I wrote in the batch file, I removed those subprocesses because I need the cross section for only g g > resonance > w w > qqqq and both the resonance and the ws can be offshell. That is what one will measure in a detector and that keeps spin correlations, which one is also going to see in the detector, so this is the closest thing to what one sees.

In madgraph I did generate p p > hh,(hh > w+ w-, w->jub jd,w+>ju jdb) and also p p > jub,jd,jdb,ju/a,h,z,g,u,d,s,c,b . In the first way of doing this the resonances are on shell in the second way offshell contributions should be allowed. Yes, I made sure every cut was removed in MadGraph.
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You might want to try producing the resonances and then decaying them to compare first to remove the possibility of gauge invariance problems. The only difference would be in spin correlations, but you may not be strongly affected by that.
************************************************
You mean, if I produce the resonance and then decay them into ws and then the ws into quarks (everything onshell, no spin correlations) and If I get the same cross section in both generators and if then I do the thing directly from the gluons to the quarks (offshell allowe and spin correlations) and I get different results, I am violating gauge invariance? If that happens, the events in both madgraph and calchep are wrong? The events themselves are wrong or just the cross sections? What would happen with the kinematic distributions, Can they still be used? If they can, should the right cross section be the one where everything was onshell?
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Also, you might want to focus on individual subprocesses in your comparison to figure out where the problem is.
************************************************
Ok, I will try to focus on that, but by what I saw all the subprocesses have cross sections that differ.

 Revision history for this message Alexander Pukhov (pukhov) said on 2014-03-31: #6

M12 is good for Drell-Yan processes only. In other cases it leads to too large scale. Expearience of calculation of loop corrections tells us that more appropriate scale is mass of produced heavy particle. It could be a mass of resonance in case of multi-particle reactions and M21 in case of Drell-Yan.

 Revision history for this message Angel (campoverdeangelf) said on 2014-03-31: #7

Hi,

You mean if the mass point is MG= 1 TeV I should write 1000 instead of M12, right? This is a kind of gluon fusion.

 Revision history for this message Alexander Pukhov (pukhov) said on 2014-04-01: #8

You can write MG directly. About the best scale. In any case it is only a recomendation.
If in your process 2 guons annitilate into s-channel resonance, than I expect that M12 will work better. Otherwize I guess MG is better.

 Revision history for this message Alexander Belyaev (alexander.belyaev) said on 2018-11-28: #9