1. Some theoretical issues regarding Method 2 J. Huston Michigan State University

2. History • Based on a series of talks that I gave at Lepton + Jets meetings • May 21, 2004 • Nov. 7, 2003 • Oct. 10, 2003 • April 25, 2003 • Plus a paper that I wrote with John Campbell • “Heavy Flavor in W + Jets Production at the Fermilab Tevatron” • hep-ph/0405276 • Phys. Rev. D70:094021,2004 2

3. In Method 2, the calculated ratio for WbBj(j) to Wjjj(j) is used, along with the measured Wjjj(j) cross sections to estimate the heavy flavor background to top production The ratio is calculated at LO and then multiplied by a phenomenological factor of 1.5 for use in background subtractions It would be nicer to put this aspect of the analysis on a firmer basis NLO is firmer than LO The state of the art for NLO calculations is WbB and Wjj although recent advances make the 1 loop calculation of WbBj and Wjjj realistic…but don’t hold your breath WbB and Wjj are available now in MCFM; may give guidance Method 2 3

4. Scale dependence • As expected, scale dependence lessened at NLO • More so for exclusive final states than inclusive 4

5. K-factors • K-factors depend both on scale choice and pT cuts on jets • Ratio of K-factors (WbB/Wjj) is reasonably stable for scales of MW/2 and above 5

6. Wbb/Wjj ratio • Very dependent on kinematics (jet pT) at LO • More stable at NLO • Ratio is higher for inclusive final states than for exclusive final states • NLO prediction for exclusive ratio is in agreement with ratio assumed in Method 2 analyses (with factor of 1.5 applied) • but note that LO and NLO predictions in MCFM are reasonably close for a jet cut of 15 GeV/c 6

7. HT • Look at cross sections for WbB(j) and Wjj(j) as a function of the HT variable • Distributions look similar at LO but not at NLO 7

8. Ratios • So it appears that cross sections using very exclusive variables like HT may not have the same shape at LO and NLO • so this assumption should not be made in analyses • But inclusive variables like the lead jet pT are safer 8

9. PDF uncertainties • PDF uncertainties easily calculated using weight technique • Note talk given by Craig Group at TeV4LHC meeting in Oct on LHAPDF • Easier to use the weight technique to calculate pdf uncertainties in version 5 9

10. Calculation of pdf uncertainties • Note that CDF webpage seems to be recommending option 3 • Option 4 is preferred 10

11. LO vs NLO pdf’s for parton shower MC’s • For NLO calculations, use NLO pdf’s (duh) • What about for parton shower Monte Carlos? • somewhat arbitrary assumptions (for example fixing Drell-Yan normalization) have to be made in LO pdf fits • DIS data in global fits affect LO pdf’s in ways that may not directly transfer to LO hadron collider predictions • LO pdf’s for the most part are outside the NLO pdf error band • LO matrix elements for many of the processes that we want to calculate are not so different from NLO matrix elements • by adding parton showers, we are partway towards NLO anyway • any error is formally of NLO • (my recommendation) use NLO pdf’s • pdf’s must be + definite in regions of application (CTEQ is so by def’n) • Note that this has implications for MC tuning, i.e. Tune A uses CTEQ5L • need tunes for NLO pdf’s …but at the end of the day this is still LO physics; There’s no substitute for honest-to-god NLO. 11

12. Rick Field at TeV4LHC: CTEQ6.1 Tune I used LHAPDF! See the next talk by Craig Group! 12

13. W + jets at NLO • Currently are working (B. Cooper, A. Messina, D. Waters, J. Dittmann) to obtain W + jets cross sections that can be compared directly to NLO • correct for UE and hadronization but not out of cone • Hadronization+UE corrections for 0.4 cone different than for 0.7 cone (used for inclusive jet analysis) • from Ken Hatakeyama R=0..4 R=0.7 13

14. We can’t help with the VBF Higgs discovery channel at the Tevatron but we can look at the rates for central jet emission in W/Z + jet(s) events Cross section larger for W + jets so that is primary investigation Will compare measured cross sections to LO +PS predictions and to fixed order (LO and NLO) predictions from MCFM In particular, are interested in comparing to CKKW cross sections generated by Steve Mrenna Predictions will be extrapolated to the LHC Tevatron W + jets studies 14

15. Comparisons • Look at probability for 3rd jet to be emitted as a function of the rapidity separation of the tagging jets • Relatively flat probability, stable with CKKW scale (not shown) • Bracketed by two predictions for MCFM using mW and <pTjet> as scales • MCFM predicts a slight decrease in the ratio as the tagging jet rapidity separation increases • CKKW and ALGEN+Herwig 3p agrees with the data • ALPGEN+Herwig 3p too high for this kinematic region MCFM pTjet MCFM mW 15

16. Summary • NLO predictions for Method 2 are more reliable than LO • HT is not a good variable to use if you’re expecting similar behavior at NLO (i.e. real world) as at LO • of course, best numbers for heavy flavor fractions are given by direct measurement; it will be interesting to compare these to the theory predictions and to better understand the factor of 1.5 • A lot of theory tools out there (and more on the way); up to use to make use of them 16