1. 1 Correcting LO W  (Z  ) Cross Sections to NLO Al Goshaw Duke University December 1, 2010

2. 2 The goal is to make NLO (LO in QCD) corrections to the LO (EWK) W  (Z  ) cross sections. For us the LO cross sections are produced with Baur/Madgraph matrix elements+ PYTHIA. The general problem The procedure can be applied to either fiducial or inclusive cross sections where the k-factor could be different. The NLO correction depends explicitly on the pdf used for the Monte Carlo generation. For us this is CTEQ6L1. The logic for making the NLO k-factor corrections was developed at CDF after we consulted with Uli Baur.

3. 3 The general logic. Assume here we want inclusive k-factors. The procedure 1. Generate the LO parton-level events with the desired photon kinematic cuts: E T (  ) > 10 GeV and  R(l-  ) > 0.5. 2. Plot the M(e- ) at this parton level: “FSR” “ISR + WW  ” (just an example) 3. Cut at M(e- ) ~ 75 GeV (vary by a few GeV as a systematic). Then calculate cross sections  LO-FSR and  LO-ISR+WW 

4. 4 The procedure 5. Calculate LO -> NKO k-factor corrections:  Use the NLO/LO W inclusive cross sections for the the  LO-FSR k-factor scaling.  Use the NLO/LO Baur W  cross sections for the  LO-ISR+WW  k-factor scaling. Explicitly, the k-factors are: k =  NLO-with NLO pdf /  LO-with LO pdf where LO pdf = CTEQ6L1 =>k o FSR from the W inclusive NLO/LO cross scetions k ISR+WW  (E t  ) from the Baur W  cross sections Note: At the Tevatron we found that k o FSR ~ k ISR+WW  (at low E t  ) as it should.

5. 5 The procedure 6. Finally, the NLO k-factor corrected inclusive W  cross section for E T (  ) > 10 GeV and  R(l-  ) > 0.5 is:  Total (W  ) = k o FSR x  LO-FSR + k ISR+WW  (E t  ) [d  LO-ISR+WW  (E t  )/dE t  ] dE t  CDF photon E T distribution from Z  events compared to SM predictions using this procedure.

6. 6 Estimate of k o FSR I used the W inclusive cross section calculations from: ATL-COM_PHYS-2010-695 I scaled these to the k o FSR we need as defined above, that is relative to a LO cross section that uses CTEQ6L1. I will write up the details. This provides W inclusive NNLO and NLO k-factors using a NNLO pdf MRSTW2008 = lhapdf 21200. The result is: k o FSR scaled to NNLO = 1.41 +- 0.12 k o FSR scaled to NLO = 1.37 +- 0.12 where the uncertainty is due to NNLO pdf+  s (5%), scaling to CTEQ6L1 pdf (5%) and a guess (5%) for the assumption W inclusive =~ Wg from FSR.