# definition of wgt for weight group "Central Scale variation"

I am having trouble understanding the "Central scale variations" in a ttbar+0,1,2p LHE file.

<weightgroup type="Central scale variation" combine="envelope">
<weight id="1"> mur=1 muf=1 </weight>
<weight id="2"> mur=1 muf=2 </weight>
<weight id="3"> mur=1 muf=0.5 </weight>
<weight id="4"> mur=2 muf=1 </weight>
<weight id="5"> mur=2 muf=2 </weight>
<weight id="6"> mur=2 muf=0.5 </weight>
<weight id="7"> mur=0.5 muf=1 </weight>
<weight id="8"> mur=0.5 muf=2 </weight>
<weight id="9"> mur=0.5 muf=0.5 </weight>
</weightgroup>
I am interested in 1, 4, and 7.

Take as an example an event with:

<event>
12 0 +8.0215042e-01 3.05007300e+02 7.54677100e-03 1.09105500e-01
....
<clustering>
<clus scale=" 305.007"> 2 3 1 -1</clus>
<clus scale=" 305.007"> 1 3 2 -1</clus>
</clustering>
<rwgt>
<wgt id="1">0.80215</wgt>
<wgt id="2">0.731702</wgt>
<wgt id="3">0.882719</wgt>
<wgt id="4">0.67234</wgt>
<wgt id="5">0.613292</wgt>
<wgt id="6">0.73987</wgt>
<wgt id="7">0.973543</wgt>
<wgt id="8">0.888042</wgt>

I interpret this to mean that weight 1 is the default and 4 and 7 refer to doubling and halving the scale
in alphaS in the ME calculation (since this tree level MG).

Thus, the weight for “4” = (.101/.1091)^2*0.80215 = 0.687
“7” = (.120/.1091)^2*0.80215 = 0.970
I base the new numbers on the Pythia8 calculation of alphaS with alphaS(mZ)=0.130.

The weights are off from the LHE file, even though alphaS( Qfac) matches the value in <event>.

The case is worse when there is an additional 1 or 2 partons. Then, I assume that the weights are:
0.82015 * alphaS( k*clus scale 1)*alphaS(k*clus scale 2)*alphaS(k*clus scale 3) / ( alphaS( clus scale 1) … alphaS( clus scale 2) )
(this is the 1 additional parton case)

where k=2 and 0.5 for weights 4 and 7.

In this case, I clearly do not reproduce the weights in the file, getting 0.602 vs 0.668
and 1.101 vs 0.980.

Where could I find the exact definition of these weights?

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Alexis Kalogeropoulos Edit question
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Stephen Mrenna
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 Revision history for this message Alexis Kalogeropoulos (alkaloge) said on 2016-05-12: #1

Hi Steve

> I base the new numbers on the Pythia8 calculation of alphaS with alphaS(mZ)=0.130.

is 0.130 also consistent with the PDF you initially used to generate events ?
In any case, for the matched-case, the W for FSR at each vertex is given by W *= alpha_s(k* cluster_scale)/alpha_s(cluster_scale). (The ^2 is accurate for the unmatched case of course)

For ISR is pretty close to your description, but also multiplied and divided by a factor standing for the reweighting of the PDFs for a given scale. Sorry, it is not possible to use proper formatting here to quote the formulation. (we are in the process of finalizing the paper though). In any case here

>0.82015 * alphaS( k*clus scale 1)*alphaS(k*clus scale 2)*alphaS(k*clus scale 3) / ( alphaS( clus scale

you have mistyped the weight (ie it is 0.802)

Hope this helps

 Revision history for this message Stephen Mrenna (stephen-mrenna) said on 2016-05-12: #2

I downloaded SysCalc and ran the executable sys_calc on a few events from the LHE file.
Here are my conclusions:

Since the LHE file specified <rscale> 2 ... </rscale>, it determines the number of powers of
QCD (n_qcd) to be = 2.

Thus, if one is only doing muR variations (so that the PDF factor is unchanged), the
weight value =

alphas(muR*central_scale_value)^2 / alphas(central_scale_value)^2

The picture here is that we are considering variations around the hard process, but leave the
other (matched) emissions untouched.

This is why my evaluation of the new weight based on the +0p process was "close" to the correct answer,
whereas it was increasingly off for the +1p and the +2p processes. Furthermore, the evaluation of
alphaS from the PDF (using LHAPDF) is slightly different than from both: 1) the Pythia8 code, and 2) the get_alphas code
provided by SysCalc.

 Revision history for this message Alexis Kalogeropoulos (alkaloge) said on 2016-05-12: #4

Hi Steve

Just for completeness

SysCalc should work for both unmatched & matched cases (validation plots show it is ok vs dedicated samples), but indeed formulation on those two cases is different as you point out.

>2) the get_alphas code provided by SysCalc

SysCalc calls the LHAPDF routine, so I guess the difference here is boils down to the that between Pythia vs LHAPDF - I haven't checked if the routine has changed from LHAPDF5 vs LHAPDF6 though.

Regards

Alexis