This twiki is intended to provide some information on the Drell-Yan spectrum which is the main background for a couple of analysis. Mostly the background prediction is taken from a LO or NLO Monte-Carlo Simulation, however, this requires to take into account correction factors from higher orders as well as a systematic uncertainty due to the choice of the PDF set.

Electroweak Corrections to the Drell-Yan Dimuon Spectrum

Since Monte Carlo samples including NLO QCD are available, the next important correction are higher electroweak corrections.

Here the results of a study using the event generator HORACE are presented, the k-factors obtained are always with respect to the NLO QCD cross section of Powheg.

The EW NLO contributions can be split into two contributions:

• NLO order diagrams
• In higher order processes it is also possible to have a photon in the initial state, these contributions are therefore called photon-induced in the following.

In order to evaluate the NLO EW contribution dimuon mass binned samples are produced with HORACE for LO and NLO in EW with the CT10 PDF set. To calculate the photon-induced contribution the MRST2004QED PDF is used which includes photon PDFs, this is the reason, why the EW NLO contribution is split into two parts. The obtained cross section as a function of the dimuon mass can be see in the following plot.

With these results it is easy to calculate k-factors to scale the cross section of the simulated sample to include the higher order EW contributions. The pure NLO EW contribution can be obtained by comparing the two HORACE samples of LO and NLO. As can be seen in the plot before, the NLO contributions are negative, resulting in a smaller cross section than the LO one. The effect is growing with increasing dimuon mass resulting in abouot 20 % correction at 1.8 TeV dimuon mass. On the other hand, the photon induced processes are possible at higher orders and add to the total cross section, this effect is also dimuon mass dependent, but not as strong as the one mentioned before. We define here three different k-factors, all of them with respect to the QCD NLO cross section of the Powheg Drell-Yan sample:

• Taking into account the EW higher order processes without the photon induced processes: k1 = 1 + (NLO EW - LO)/(NLO QCD)
• Only the contribution of the photon induced (PI) processes: k2 = 1 + PI / (NLO QCD)
• Combining the two contributions: k3 = 1+ (NLO EW + PI - LO) / (NLO QCD)

The result for the three k-factors as a function of the dimuon mass can be seen in the following plot. The combination of the two contributions still leads to a k-factor smaller than 1 with a small dependence on the dimuon mass.

The values for the k-factors can be found in the following table:

Mass Range [GeV]	k1	k2	k3
200 - 400	0.888	1.039	0.927
400 - 600	0.880	1.036	0.915
600 - 800	0.872	1.054	0.926
800 - 1000	0.841	1.058	0.899
1000 - 1200	0.829	1.080	0.908
1200 - 1400	0.805	1.082	0.887
1400 - 1600	0.819	1.090	0.910
1600 - 1800	0.780	1.090	0.870

PDF Uncertainties

Another downside of using simulation based background expectation is that it heavily relies on the PDF set used in the generation. However, there are recommondation how to evaluate the possible uncertainty due to the choice of the PDF set. Here we calculate the PDF uncertainty for the Powheg DY sample using the PDF4LHC recipe http://www.hep.ucl.ac.uk/pdf4lhc/. In order to evaluate the uncertainty three different PDF sets (CT10, MSTW2008, NNPDF 2.1) are chosen and the generated events are reweighted to the respective best fit of the PDF set as well as for all error PDFs. Following the recipe the 68 % CL intervals can be computed. The results normalized to the CT10 best fit for the three PDF sets can be seen in the following plot.

The recommendation for the PDF uncertainty is to use the envelope of the three sets, the result for various mass bins can be found in this table

Mass-Range [GeV]	Uncertainty [%]
200-300	3.9
300-400	3.8
400-500	4.2
500-600	5.8
600-700	6.1
700-800	6.4
800-900	7.7
900-1000	8.3
1000-1100	9.0
1100-1200	9.4
1200-1300	9.4
1300-1400	9.5
1400-1500	10.2
1500-1600	10.9
1600-1700	12.1
1700-1800	12.6
1800-1900	12.7
1900-2000	13.0