Recent Advances in Precision QCD Predictions and PDF Uncertainties for LHC Physics

1. DIS08: progress in pdfs • why precision pdfs? • recent developments* • current issues and prospects James Stirling IPPP, Durham University * See also SF WG and also PDF4LHC Meeting, CERN, Feb 08

2. DIS93 March 1993 Durham, UK DIS08

3. DIS93

4. pdfs for LHC • high precision (SM and BSM) cross section predictions require precision pdfs: th = pdf + … • improved signal and background predictions → easier to spot new physics deviations • ‘standard candle’ processes (e.g. Z) to • check formalism (factorisation, DGLAP, …) • measure machine luminosity? • learning more about pdfs from LHC measurements. e.g. • high-ET jets → gluon? • W+,W–,Z0→ quarks? • forward DY → small x? • … DIS08

5. where X=W, Z, H, high-ET jets, … and  known • to some fixed order in pQCD and EW • in some leading logarithm approximation (LL, NLL, …) to all orders via resummation ^ QCD factorization theorem for short-distance inclusive processes full NNLO pQCD, supplemented by NNLL and electroweak corrections where appropriate, is the goal for LHC

6. M proton proton x1P x2P DGLAP evolution momentum fractions x1 and x2determined by mass and rapidity of X xdependence of f(x,Q2) determined by fit to data, Q2 dependence determined by DGLAP equations: full NNLO DGLAP now known, also with small x, QED etc improvements DIS08

7. how important is pdf precision? • Example 1: σ(MH=120 GeV) @ LHC σpdf  ±3%, σptNNL0  ± 10% σptNNLL  ± 8% →σtheory  ± 9% • Example 2: σ(Z0) @ LHC σpdf  ±3%, σptNNL0  ± 2% →σtheory  ± 4% • Example 3: quantitative limits on New Physics depend on pdfs Catani et al, hep-ph/0306211 Campbell, Huston, S (2007)

8. sensitivity of dijet cross section at LHC to large extra dimensions • LED accelerate the running of αS as the compactification scale Mcis approached • sensitivity attentuated by pdf uncertainties in SM prediction Ferrag (ATLAS), hep-ph/0407303 DIS08

9. pdf overview… DIS08

10. Who? Alekhin, CTEQ, MRST/MSTW, H1, ZEUS, GGK, Botje, GRV, BFP, NNPDF, … http://durpdg.dur.ac.uk/hepdata/pdf.html pdfs from global fits Formalism LO, NLO, … DGLAP MSbar factorisation Q02 functional form @ Q02 sea quark (a)symmetry etc. fi (x,Q2) fi (x,Q2) αS(MZ ) Data DIS (SLAC, BCDMS, NMC, E665, CCFR, H1, ZEUS, … ) Drell-Yan (E605, E772, E866, …) High ET jets (CDF, D0) W rapidity asymmetry (CDF, D0) N dimuon (CCFR, NuTeV) etc. LHAPDFv5.3 @ CEDAR HepForge DIS08

11. typical data ingredients of a global pdf fit DIS08

12. summary of DIS data + neutrino FT DIS data Note: must impose cuts on DIS data to ensure validity of leading-twist DGLAP formalism in the global analysis, typically: Q2 > 2 - 4 GeV2 W2 = (1-x)/xQ2 > 10 - 15 GeV2 DIS08

13. strange earliest pdf fits had SU(3) symmetry: later relaxed to include (constant) strange suppression (cf. fragmentation): with  = 0.4 – 0.5 nowadays, dimuon production in N DIS (CCFR, NuTeV) allows ‘direct’ determination: in the range 0.01 < x < 0.4 data seem to prefer DIS08

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15. charm, bottom considered sufficiently massive to allow pQCD treatment: distinguish two regimes: (i) include full mH dependence to get correct threshold behaviour (ii) treat as ~massless partons to resum Snlogn(Q2/mH2) via DGLAP FFNS: OK for (i) only ZM-VFNS: OK for (ii) only consistentGM(=general mass)-VFNSnow available(e.g. ACOT(), RT) definition of these is tricky and non-unique (ambiguity in assignment of O(mH2//Q2) contributions), and the implementation of improved treatment can have big effect on light partons (correction, not uncertainty!) → see talks in SF + HF Working Groups DIS08

16. pdf uncertainties • most groups produce ‘pdfs with errors’ • typically, 30-40 ‘error’ sets based on a ‘best fit’ set to reflect ±1variation of all the parameters* {Ai,ai,…,αS} inherent in the fit • these reflect the uncertainties on the data used in the global fit (e.g. F2  ±3% →u ±3%) • however, there are also systematic pdf uncertainties reflecting theoretical assumptions/prejudices in the way the global fit is set up and performed * e.g. DIS08

17. why do ‘best fit’ pdfs and errors differ? • different data sets in fit • different subselection of data • different treatment of exp. sys. errors • different choice of • pQCD order (in DGLAP and cross sections) • factorisation/renormalisation scheme/scale • Q02 • parametric form Axa(1-x)b[..] etc (and implicit extrapolation) • αS • treatment of heavy flavours • theoretical assumptions about x→0,1 behaviour • theoretical assumptions about sea flavour symmetry • tolerance to define  fi • evolution, cross section codes, rounding errors (removable differences!) this applies to both CTEQ vs. MRST vs. … and to CTEQ: 6.1 → 6.5 → ... → see talks in SF + HF Working Groups!

18. MRST: Q02 = 1 GeV2,Qcut2 = 2 GeV2 xg = Axa(1–x)b(1+Cx0.5+Dx) – Exc(1-x)d • CTEQ6.1: Q02 = 1.69 GeV2,Qcut2 = 4 GeV2 xg = Axa(1–x)becx(1+Cx)d DIS08

19. MRST2001 CTEQ6.1 Alekhin02 % uncertainty in the gluon distribution at Q2 = 5 GeV2 DIS08

20. extrapolation errors theoretical insight/guess: f ~ A x as x → 0 theoretical insight/guess: f ~ ± A x as x → 0 no theoretical insight: f ~ ??? as x → 0 DIS08

21. Malik, CDF Hays, D0 impact of jet data on fits • a distinguishing feature of pdf sets is whether they use (MRST/MSTW, CTEQ,…) or do not use (H1, ZEUS, Alekhin, NNPF,…) Tevatron jet data in the fit: the impact is on the high-x gluon • the (still) missing ingredient is the full NNLO pQCD correction to the cross section, but not expected to have much impact in practice • note that large-mass pN Drell-Yan also probes the gluon indirectly via g → q qbar generation of sea antiquarks at high x DIS08

22. progress from the various pdf groups Nadolsky Pumplin Olness • CTEQ (Michigan State – Hawaii – Washington) • 6.1 → 6.5 (2006) → 6.6 (2008) • LO, NLO • 6.5: first implementation of GM-VFNS “SACOT-” (was ZM-VFNS)  significant impact on c,b compensating impact on u,dchanges in(W,Z) • more sophisticated treatment of strange, antistrange, allowed to have (approx.) independent shapes, i.e. no longer • studies of intrinsic charm • MSTW (Durham – UCL) • 2006: MST + Roberts (MRST) → MST + Watts (MSTW) • LO, NLO, NNLO • MRST2006: NNLO update (i) with errors, (ii) with much improved GM-VFNS treatment of charm, bottom • MSTW2008: new data, inc. CHORUS N, NuTeV , HERA DIS+jet; more sophisticated treatment of strange, antistrange, allowed to have (approx.) independent shapes, DY @ NNLO; better treatment of tolerance/errors Watt Thorne DIS08

23. recent progress… DIS08

24. progress from the various pdf groups • Alekhin et al • Alekhin (2002)→ Alekhin-Melnikov-Petriello (2006) → Alekhin-Kulagin-Petti (2007) • LO, NLO. NNLO • A = SLAC, BCDMS, NMC, E665, H1, ZEUS • AMP, AKP = + DY E605 p, E866 p/d + CHORUS inclusive N CHORUS + CCFR, NuTeV dimuon N • H1 and ZEUS • use restricted data sets: H12003 = H1 (CC+NC) + BCDMS, ZEUS2005 = ZEUS only, inc JET • no Tevatron jet data, so softer high-x gluons compared to MSTW, CTEQ • different error treatments: ZEUS offset vs. H1 Hessian For detailed H1/ZEUS/CTEQ/MSTW comparison see A M Cooper-Sarkar talk at PDF4LHC, Feb 2008 • Neural Net (NNPDF) collaboration • Ball, Del Debbio, Ubiali (Edinburgh), Forte, Piccione (Milano), Latorre (Barcelona), Rojo-Chacon (LPTHE - Paris) • use NN technology to avoid choice of parametric form at Q02 • so far, fit 5 singlet, non-singlet + gluon combinations to restricted (DIS) data set Alekhin Feltesse Sarkar Rojo-Chacon DIS08

25. CTEQ 6.1M effect of more independent strange, from 6.1M to 6.6M effect of ZM-VFNS → GM-VFNS on light quarks DIS08

26. Alekhin et al • reduction in uncertainty on high-x sea antiquarks due to inclusion of fixed target Drell-Yan data in the global fit • note also size of “scale dependence” uncertainties, reduced at NNLO but still significant DIS08

27. MSTW • s-sbar now non-zero (central value) • overall larger s+sbar suppression compared to light quarks • only in NLO fit (no NNLO correction yet) DIS08

28. NNPDF • datasets included in the analysis • preliminary results for pdf combinations at Q02 and comparison to MRST, CTEQ, Alekhin DIS08

29. improved LO pdfs • conventional wisdom is to match pQCD order of pdfs with that of MEs • but, in practice, • LO = PDFs(LO)  ME(LO) can be different from NLO = PDFs(NLO)  ME(NLO), in both shape and normalisation • LO pdfs have very poor 2 in (LO) global fit (no surprise: NLO corrections at large and small x are significant and preferred by the data) • momentum conservation limits how much additional glue can be added to LO partons to compensate for missing NLO pQCD corrections (e.g. to get correct evolution rate of small-x quarks) • therefore relax momentum conservation and redo LO fit; study the impact of this on 2, partons and cross sections • e.g. Thorne & Shertsnev 2007: LO* partons • 2: 3066/2235 → 2691/2235, mom consv: 100% → 113% DIS08

30.  transverse momentum distribution in H → production at LHC comparison of gluons at high Q2 DIS08 Thorne, Shertsnev

31. looking ahead… DIS08

32. Thorne Kollar Antunovic Chekelian FL • an independent measurement of the small-x gluon • a test of the assumptions in the DGLAP LT pQCD analysis of small-x F2 • visible instability in MSTW analysis (impact of negative gluon and large NNLO coefficient function) • higher–order ln(1/x) and higher-twist contributions could be important MSTW

33. pQCD FL predictions DIS08

34. impact of LHC measurements on pdfs • the standard candles: central (W,Z,tt,jets) as a probe and test of pdfs in the x ~ 10 -2±1, Q2 ~ 104-6 GeV2range where most New Physics is expected (H, SUSY, ….) → ongoing studies of uncertainties and correlations • forward production of (relatively) low-mass states (e.g. *,W,Z,dijets) to access partons at x<<1 (and x~1) DIS08

35. (W,Z) @ LHC • in understanding differences between (W,Z) predictions from different pdf sets (due to the pdfs, not choice of pQCD order, e/w parameters, etc) a number of factors are important, particularly • the rate of evolution from the Q2 of the fitted DIS data, to Q2 ~ 104 GeV2 (driven by S, gluon) • the mix of quark flavours: F2and (W,Z) probe different combinations of u,d,s,c,b • precise measurement of cross section ratios at LHC (e.g. (W+)/(W-),(W±)/(Z)) will allow these subtle effects to be explored further DIS08

36. LHC Tevatron DIS08

37. impact on (W,Z) @ LHC • CTEQ: 6.6 ~ 6.5 > 6.1 due to changes in treatment of s,c,b • reasonable agreement between all sets (that fit HERA data) • care needed in comparing results from NLO/NNLO/NNLL-NLO calculations CTEQ DIS08

38. impact on (W,Z) @ LHC (Tevatron) • MRST/MSTW NNLO: 2008 ~ 2006 > 2004 mainly due to changes in treatment of charm • NLO: CTEQ6.6 2% higher than MSTW 2008, because of slight differences in quark (u,d,s,c) pdfs, difference within quoted uncertainty MSTW DIS08

39. MSTW2008(NLO) vs. CTEQ6.6 DIS08

40. LHCb → detect forward, low pT muons from DIS08

41. Impact of 1 fb-1 LHCb data for forward Z and * (M = 14 GeV) production on the gluon distribution uncertainty McNulty Thorne DIS08

42. summary and issues… • pdf sets continue to converge; main difference now is inclusion of Tevatron jet data → high-x gluon • GM-VFNS accepted as standard for c,b; nice agreement with HERA F2c,b… but must not forget possible contributions from intrinsic heavy flavour • urgently need NNLO pp→jet+Xfor a full NNLO pdf global fit - but impact on current pseudo-NNLO analysis not expected to be large • focus now on predictions and uncertainties for standard candle LHC cross sections DIS08

43. summary and issues…contd. • strange pdf: no direct measurement for x < 10-2 but ~20% of (W±,Z) is due to strange in this region • intrinsic heavy flavours? • Note: Brodsky, Goldhaber, Kopeliovich, Schmidt [arXiv:0707.4658] forward Higgs production at LHC from intrinsic bb→ H • LHCb can access a new small-x domain • is fixed–order DGLAP adequate to describe new FL data from HERA? If not, what else is needed and what (if any) are implications for LHC phenomenology? DIS08

44. extra slides

45. high-x gluon from high ET jets data • both MSTW and CTEQ use Tevatron jets data to determine the gluon pdf at large x • the errors on the gluon therefore reflect the measured cross section uncertainties DIS08

46. pdfs with errors…. CTEQ gluon distribution uncertainty using Hessian Method output = best fit set + 2Np error sets Hessian Matrix “best fit” parameters DIS08

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