Markus Wobisch Louisiana Tech University for the D0 Collaboration

1. Measurement of angular correlations of jets at √s = 1.96 TeV and determination of the strong coupling at high momentum transfers Markus Wobisch Louisiana Tech University for the D0 Collaboration Fermilab Joint Experimental-Theoretical Seminar May 18, 2012

2. Outline • Introduction- Physics of hadron collisionsas and PDFs- What we have learned from jets in Run II so far • A new multi-jet observable- Angular correlations of jets- Definition & examples- Measurement procedure & experimental results • Determination of as- Study the running of as at high momentum transfers

3. Introduction jet jet Jet production in hadron collisions

4. Introduction jet jet Jet production in hadron collisions Parton distribution functions (PDFs) of the hadrons

5. Introduction jet jet Jet production in hadron collisions pQCD matrix elements Parton distribution functions (PDFs) of the hadrons

6. Introduction jet jet Jet production in hadron collisions pQCD matrix elements Parton distribution functions (PDFs) of the hadrons Strong coupling constant as

7. . jet jet Strong coupling constant as

8. Strong Coupling as S. Bethke, arXiv:0908.1135 Experimental evidence: as depends on momentum transfer Q  as(Q) Running of as:as(Q) decreases with Q  tested up to 208 GeV (LEP e+e- data) Not yet at scales > 208 GeV

9. as and the Renormalization Group Equation as(mR): depends on mRthe renormalization scale Observables must be independent of mR RGE Renormalization Group Equation RGE relates as(Q0) at one scale Q0to as(Q) at any other scale Q RGE predicts all as(Q) curves which are possible

10. as and the Renormalization Group Equation as(mR): depends on mRthe renormalization scale Observables must be independent of mR RGE Renormalization Group Equation RGE relates as(Q0) at one scale Q0to as(Q) at any other scale Q RGE predicts all as(Q) curves which are possible Agreement: label curves by as(mR=MZ)

11. Testing pQCD experimental tests  two aspects: 1. • Which is the right as(Q) curve? • Determine as(MZ) • Comparison of as(MZ) results for different processes  check universality • (this usually assumes the RGE)  This analysis 2. • Is the running of as(Q) correctly predicted? • Test RGE prediction of the running of as(Q)

12. as(Q) beyond 208 GeV ?  so far tested up to Q= 208 GeV Running of as(Q) could be modified for scales Q > m0e.g. by extra dimensions here: m0 = 200 GeV and n=1,2,3 extra dim.(n=0  Standard Model) This analysis: study as(Q) for Q  400 GeV

13. . jet jet pQCD matrix elements

14. pQCD matrix elements Computed in a perturbative expansion in as using the Feynman rules Known to NLO in as for 2-jet and 3-jet production LO pQCD matrix elements for 22 processes

15. . jet jet Parton distribution functions (PDFs) of the hadrons

16. PDF knowledge PDFs are determined in global analyses: CTEQ, MSTW, NNPDF

17. PDF knowledge PDFs are determined in global analyses: CTEQ, MSTW, NNPDF Most experimental constraints on PDFs are from data at lower scales

18. PDF knowledge PDFs are determined in global analyses: CTEQ, MSTW, NNPDF Most experimental constraints on PDFs are from data at lower scales DGLAP PDF knowledge at high scales from “DGLAP” evolution  uses RGE foras(Q) DGLAP:Dokshitzer–Gribov–Lipatov–Altarelli–Parisi

19. as(Q) for Q>208 GeV (?)  Two results from inclusive jet cross section data

20. as results from inclusive jet cross section data CDF Collaboration, T. Affolder et al., Phys. Rev. Lett. 88, 042001 (2002) B. Malaescu, P. Starovoitov, arXiv:1203.5416 From ATLAS inclusive jet cross section data Statements: “Test running over 40 < ET < 440 GeV” “Test running up to pT  600 GeV”

21. as results from inclusive jet cross section data Statements: “Test running over 40 < ET < 440 GeV” “Test running up to pT  600 GeV”  Not really!because analyses use PDFsfor which DGLAP evolutionis already done under assumption of running as(Q) according to the RGE • RGE was already assumed • Not an independent test

22. Run II jet results – so far

23. What we have learned fromjets in Run II so far • Test: Standard Model vs. New Physics • Constraining PDFs and as 22 • Testing pQCD at higher orders • Further PDF constraints • Study multi-jet ratios 23 • New result: • Measurement of a new multi-jet observable • More reliable determination of as at high pT

24. Do we see QCD dynamics – or …? New particle resonances in dijet mass spectrum Tails of new high-energy phenomena in dijet angular distribution large y small y

25. Do we see QCD dynamics – or …? dijet mass spectrum dijet angular distributions Limits on new resonances Limits on quark compositeness and extra spatial dimensions  No indications for New Physics

26. . ConstrainingPDFs and as  Inclusive jet cross section  Dijet mass cross section

27. PDF sensitivity Theory: pQCD @NLO is reliable (±10%)  sensitivity to PDFs  unique: high-x gluon xT

28. Inclusive jet pT / dijet mass pT (GeV)  Both data sets are sensitive to as and the PDFs

29. Three-jet mass spectrum: O(as3) Phys. Lett. B (2011) • 2-jet cross section: • O(as2) x PDF2 • (correlation of a and • gluon density) • 3-jet cross section: • O(as3) x PDF2 • analyze 2-jet and 3-jet cross sections: •  decorrelate asand gluon density in PDF fits • additional PDF constraints from 3-jet mass data

30. Run II jets in MSTW2008 PDF fit MSTW2008 paper (Fig 52. / see also Figs. 51, 53) • Tevatron jet data affect gluon for x > 0.2 – 0.3 • (so far only inclusive jet data have been used in PDF fits)

31. D0 as(pT) from Run II inclusive jet cross section data jet jet pT (GeV)  Avoid potential inconsistencies

32. PDFs and input data MSTW2008 paper (Fig 52. / see also Figs. 51, 53) Currently: Main constraints on high-x gluon density come from Tevatron jet data Goal: Minimize correlations between data and PDF uncertainties  Restrict as analysis to kinematic regions where impact of Tevatron data for PDFs is small.  Tevatron jet data don’t affect gluon for x < 0.2 – 0.3

33. Data Sample for as analysis 22 (out of 110) inclusive jet cross section data pointshave small contributions from x > 0.2 – 0.3  Data points at 50 < pT< 145 GeV  Input in as analysis Restriction to 50 < pT< 145 GeV avoids pT regions in which RGE has not yet been tested! (no circular argument here) pT (GeV)

34. Strong Coupling Constant • Use best theory prediction: NLO + 2-loop threshold corrections(Kidonakis/Owens) with MSTW2008NNLO PDFs • Most precise result from a hadron collider • Consistent with HERA results and world average

35. Going further … … towards testing in the RGE at higher momentum transfers Should not use cross section data (Don’t want to rely on PDF information) • Better use cross section ratios…

36. Cancelling PDFs in Ratios Goal: test pQCD (and as) independent of PDFs  Ratios of cross sections for 3-jet and 2-jet observables as R = • Sensitive to as (3-jets: as3 / 2-jets: as2) • Significantly reduced PDF sensitivity

37. Cancelling PDFs in Ratios • However: no complete PDF cancellations • Slightly different x-coverage in numerator/denominator • Slightly different contributions from different partonicsubprocesses as R = • Therefore: • residal PDF uncertainties • Residual dependence of the RGE  But significant improvement w.r.t. cross sections

38. R3/2 =s3-jet / s2-jet R3/2 = s3-jet / s2-jet as

39. Dijet Azimuthal Decorrelations 1/sdijet * dsdijet / dDfdijet as PRL 94, 221801 (2005) Dfdijet angle between the two leading pT jets more inclusive than R3/2  don’t need to tag 3rd jet

40. . A new observable • RDR: Angular correlations of jets • Definition • Measurement

41. New Observable: RDR RDR average number of neighboring jets for jets from an inclusive jets sample as “Angular Correlations of Jets” • Depends on 3 variables: • inclusive jet pT • distance DR to neighbor jet in (Df,Dy) • neighbor jet pT-nbr requirement

42. New Observable: RDR 1. Start with central inclusive jet sample (|y|<1) • Loop over all inclusive jetsFor each inclusive jet: count No. of neighboring jets- in distance DR in (Df,Dy) - with pTnbr > pTminnbr • Ratio: sum of all neighboring jets / total number of inclusive jets average number of neighboring jets RDR(pT, DR,pTminnbr) Note: for DR < p  only contributions from (at least) 3-jet events  RDR looks at any jet and any neighboring jet … more inclusive than R3/2 (require to tag three leading jets) … more inclusive than RDf (require to tag two leading jets)

43. RDR : examples For simplicity: All jets have the same pT and we study DR < 2p/3 • Two inclusive jets  add “2” to denominator • None has a neighbor  “0” to numerator If all events were like this  RDR = 0 • Three inclusive jets  add “3” to denominator • Two have one neighbor  add “2” to numerator If all events were like this  RDR = 2/3 • Four inclusive jets  add “4” to denominator • Each has one neighbor  add “4” to numerator If all events were like this  RDR = 1

44. RDR : analysis phase space Measure triple differentially: RDR(pT, DR, pT-nbr) • Phase space for RDR(pT, DR, pT-nbr) measurement: • Central inclusive jets: |y| < 1 • Inclusive jets in pT range: 50 < pT < 450 GeV • 4 different pT requirements for neighbor jet: pT-nbr> 30, 50, 70, 90 GeV • Jet-jet distances in 3 ranges of DR: 1.4 – 1.8 – 2.2 – 2.6 (<< p) • Criteria: • inclusive jet pT requirements ( high trigger efficiencies) • y, DR requirements such that (ymax + DRmax) < 3.6 ( in acceptance) • DR such that always DR> 2 * Rcone ( no overlapping jet cones) • pT-nbr requirements from soft to hard

45. Presentation of RDR Average number of neighbor jets within DR to an inclusive jet  Measure dependence of RDRon (pT, DR, pT-nbr-min)

46. RDR in theory Theory properties • Next slides show that RDRis theoretically well-behaved: • Small PDF uncertainties / small PDF set dependence • Small k-factor (k = NLO/LO) • Small renormalization/factorization scale dependencies • Small non-perturbative corrections

47. RDR PDF sensitivity • MSTW 68% C.L. PDF uncertainty: 2-3% • MSTW2008, CT10, NNPDFv2.1 agree better than 3%  PDF sensitivity is weak

48. RDR scale dep. / k-factor • inverse of k-Factor: LO/NLO (dotted line)  close to unity • Scale dependence (solid lines)  small (5-10%)

49. RDR non-pert corrections • Product of correction • factors for: • Hadronization • Underlying event • Small (<10%, typically 3-5%) • “old” and “new” PYTHIA tunes agree well at high pT

50. Measurement Experimental procedure • following closely the D0 inclusive jet cross section measurement: • Run / Event / Jet selection - good vertex in central tracking acceptance  pT reconstruction- cut on missing pT to avoid cosmics- jet ID requirements to avoid noise jets and electron/photon • Choices of inclusive jet triggers & trigger turn-ons