NNLO PDFs in 3 flavor scheme and collider data S.Alekhin (DESY & IHEP, Protvino) In collaboration with J.Blümlein and S.Moch INT, Seattle, 19 Oct 2010
The ABKM fit ingredients DATA: QCD: DIS NC inclusive DIS μμ CC production fixed-target DY Tevatron Run II jets NNLO evolution NNLO massless DIS and DY coefficient functions NLO+ massive DIS coefficient function - FFNS NLO+ jet production corrections - 5-flavor scheme Deuteron corrections in DIS: Fermi motion off-shell effects Power corrections in DIS: target mass effects dynamical twist-4(6) terms sa, Blümlein, Klein, Moch PRD 81, 014032 (2010) 2
The heavy quark electro production The dominant mechanism is photon-gluon fusion, contributes up to 30% to the inclusive structure functions. The massive coefficient functions are known up to the NLO. Witten NPB 104, 445 (1976) Laenen, Riemersma, Smith, van Neerven NPB 392, 162 (1993) FFNS Only 3 light flavors in the initial state are considered. Accurate at Q~mc At large Q the fixed-order results are insufficient due to big logs ~lnn(q/mc) must be resummed Involved high-order calculations. The full NNLO corrections are missed inconsistency in the NNLO PDF fits. ZMVFNS Collins, Tung NPB 278, 934 (1986) At Q >> mc the heavy quarks are considered as massless the NNLO evolution and the coefficient functions up to N3LO are ready The big logs ~lnn(q/mc) are in a natural way resummed in the QCD evolution Matching conditions for the 3(4)-flavor and the 4(5)-flavor massless theories A smooth matching with the FFNS in the limit of Q mc must be provided 3
BMSN prescription for the GMVFNS Buza, Matiounine, Smith, van Neerven EPJC 1, 301 (1998) FFNS: massive coef. functions, 3-flavor PDFs ZMVFNS: massless coeff. functions, 4-flavor PDFs ASYMP: asymptotic expansion of massive coef. functions (Q»mc), 3-flavor PDFs Smooth matching with FFNS without additional parameters All coefficients are in MSbar scheme Somewhat involved technically FONLL prescription for DIS ~ BMSN with the 4-flavor PDFs Forte, Laenen, Nason, Rojo NPB 834, 116 (2010) sa, Blümlein, Klein, Moch PRD 81, 014032 (2010) In the NLO the FFNS is sufficient for description of the realistic DIS data the big logs appear in the high order corrections to the massive coefficient functions Glück, Reya, Stratmann NPB 422, 37 (1994) 4
Towards to the massive NNLO corrections At small x and small Q the main contribution comes from η<1 due to the gluon distribution shape threshold production, similarly. The large logs ~ ln2n (β) can be resummed in all orders, this gives a good approximation to the exact NNLO expression at small β with the tower of large logs. At large η this approximation is out control, suppressed by factor of ~1/η. η=s/4m2-1 Laenen, Moch PRD 59, 034027 (1999) At large Q the full NNLO corrections are necessary calculations in progress, stay tuned! Bierenbaum, Blümlein, Klein NPB 829, 417 (2009) [hep-ph 1008.0792] β= 1-4m2/s Lo Presti, Kawamura, Moch, Vogt [hep-ph 1008.0951] 5
FFNS versus semi inclusive HERA data The FFNS predictions with account of the threshold NNLO corrections are in a good agreement with the charm-production HERA data at small and moderate Q. For the b-quark production agreement is even better, the threshold approximation is applicable for wider kinematics. H1prelim-09-171 ZEUS-prel-09-015 DESY-10-047 6
Heavy quark mass definition The running c-quark mass MSTW ABKM JR CTEQ PDG mc(gev) 1.40 1.5 1.3 1.3 mb(gev) 4.75 4.5 4.2 4.5 1.66 4.79 mc=mc(mc)[1+as(mc)d1+as2(mc)d2+...] The choice of μr=mc is motivated by the DIS data kinematic better perturbative convergence and reduced scale dependence The global fits are sensitive to the heavy quark masses, the values depend on the order The values of pole masses mc,b used by different groups are systematically lower than the PDF values From the fit to inclusive DIS data with the running muss definition of semiinclusive SFs mc(mc)=1.15±0.11 GeV (NNLO, prel.), in good agreement with the PDG can be fixed at the PDF value to improve the PDF accuracy Re-expansion of the pole-mass coefficient functions in terms of mc(mc) sa, Moch in progress 7
Modeling of the GMVFNS in global PDF fits Thorne, Tung [hep-ph 0903.3861] ZMVFNS Thorne [hep-ph 1006.5925] A unique set of PDFs used: The 3-flavor PDFs at Q<mc, the 4-flavor PDFs at Q>mc (step at Q=mc for the case of NNLO). The MSbar coefficient functions are modified in order to suppress too fast rise of F2 at small Q (and compensate a step in PDFs) ACOT, Thorne-Roberts, Thorne, ACOT(χ)... Different prescriptions give equally good quality of the fit since variation in the scheme is compensated by variation of PDFs. The hadronic cross sections are sensitive to the choice of the GMVFNS parameters. The factorization scheme, which corresponds to a particular prescription is not necessarily commonly used MSbar scheme. Big uncertainties in the candle cross sections CTEQ Collaboration PRD 78, 013004 (2008) 8
FFNS in the global PDF fit FFNS GMVFNS The 4- and 5-flavor PDFs can be generated from the 3-flavor PDFs using the matching conditions. In this way the collider data can be added to the DIS in the PDF fit performed on the FFNS footing At small scale the gluons obtained in the FFNS fit are bigger than ones obtained in the GMVFN fit (negative gluons?). H1prelim-10-045 FFNS GMVFNS sa, Blümlein, Klein, Moch PRD 81, 014032 (2010) The 4- and 5-flavor PDFs have to be evolved starting from the matching scale effect is nonnegligible at large scales. Martin, Stirling, Thorne PLB 652, 292 (2007) 9
Impact of the jet data on gluons The NNLO corrections to jet production are cumbersome (non-trivial subtraction of the IR singularities), only the e+e- case has been solved recently. Weinzierl, Gehrmann-De Ridder, Gehrmann, Glower, Heinrich The fragmentation function uncertainties. FastNLO tool allows to employ full NLO corrections in the PDF fit. Kluge, Rabberitz, Wobbisch [hep-ph 0609285] Radescu ICHEP 2010 The Tevatron Run I data overshoot the DIS-based predictions large gluon distributions and big value of strong coupling constant. The Run II data go lower no tension with DIS, impact of the jet data on gluons is greatly reduced. αs(mz)=0.1161±0.0045(exp.) (NLO) D0 Collaboration [hep-ex 1006.2855] MSTW EPJC 63, 189 (2009) 10
Run II D0 dijet data in the ABKM fit D0 Collaboration PRL 101, 062001 (2008) The NLO ABKM09 predictions compared with the D0 Run II dijet data: 5-flavor PDFs generated from the 3-flavor ones, μr= μf=mjj Impact of the data on ABKM PDFs is marginal ABKM describes jet data better than the truly global fits based on the Run II data?? 11
Run II D0 inclusive data in the ABKM fit D0 Collaboration PRL 101, 062001 (2008) Before the fit After the fit After the fit The NLO variant of the ABKM09 fit with the D0 Run II inclusive midpoint data included (uncertainty due to missing NNLO corrections) Mixed scheme: 3-flavor PDFs for the DIS and 5-flavor PDFs for jets, μf=et The value of χ2 for D0 data is 104/110 jet data can be easily combined with others 12
Run II D0 inclusive data in the ABKM fit (cont'd) Higgs@LHC Higgs@Tevatron Impact of the D0 data is somewhat bigger than 1σ variation of the scales reduces significance of the data (work in progress) what is the proper selection of the jet data? Run I data give even bigger large-x gluons Potential impact of the precise DIS data looks promising EIC, JLAB@12 and other forthcoming facilities 13
Combined NC HERA data in the PDF fit H1 ans ZEUS Collaborations JHEP 1001, 109 (2010) sa, Blümlein, Moch [hep-ph/1007.3657] The systematic uncertainties are very detailed (114 sources are studied); the total errors in data do not exceed 2% at small Q The value of χ2 is about 1.2 with account of the correlations The data go somewhat above the fit what happens with even more precise Run II data? 14
Gluon distribution at small x sa, Blümlein, Moch [hep-ph/1007.3657] The slope on Q for the combined HERA RunI data is in good agreement with the predictions based on the earlier PDFs The general normalization is higher than before some tension in the momentum sum rule; more flexible shape of the PDFs at small x is necessary The small-x quarks are enhanced The small-x gluons are suppressed; the effect is more pronounced for the NNLO variant of the fit 15
αs from DIS and other processes αs(mz)=0.1135±0.0014 (NNLO) αs(mz)=0.1179±0.0016 (NLO) sa, Blümlein, Klein, Moch PRD 81, 014032 (2010) αs(mz)=0.1147±0.0012 (NNLO) sa, Blümlein, Moch [hep-ph/1007.3657] From the Tevatron jet data αs(mz)=0.1161±0.0045 (NLO) D0 Collaboration [hep-ex 1006.2855] From the world e+e- data on trust αs(mz)=0.1135±0.0002(exp.)±0.0005(had.) ±0.0009(pert..) (NNLO)+power corr. Abbate, Fickinger,Hoang, Mateu, Steward [hep-ph 1006.3080] Nice agreement with DIS values Blümlein, Böttcher [hep-ph 1005.3113] αs(mz)=0.1171±0.0014 (NNLO) MSTW EPJC 63, 189 (2009) 16
NMC data in the PDF fit NMC Collaboration NPB 483, 3 (1997) The muon beam experiment at CERN with the beam energies of 90, 120, 200, and 280 GeV and partial overlap of the samples Fills gap in kinematics of the SLAC and HERA data at Q2< 10 GeV2; provides a valuable constraint on the gluon distribution at x>0.001 At x<0.012 the structure function R is extracted from the data; at x>0.012 it as taken as R1990 ( empiric parameterization of the SLAC data motivated by QCD and Including the high-twist terms at large x) Whitlow et al. PLB 282, 475 (1992) 17
Value of R from the QCD fit RQCD obtained in the ABKM09 NNLO fit to the cross sections is in good agreement with R1990 at x > 0.012 similar set of data is used in both fits The value of RNMC at x<0.012 is quite different from R1990 at x > 0.012; Moreover it does not depend on Q2, in contrast with RQCD the QCD fits based on the F2 extracted with the use of RNMC are inconsistent In the NNLO variant of ABKM fit based on the NMC data on F2 the value of αs(mz)=0.1175, in good agreement to the MSTW NNLO value and bigger than the default ABKM value by +0.0028. In the NLO case the shift is smaller, +0.0010 18
Gluon distribution, αs, and the candle c.s. The cumulative effect of the wrong treatment of the NMC data is 10-20%, this reduces significantly the spread in the ABKM and MSTW predictions. Important issue for the interpretation of the Tevatron data Baglio, Djouadi [hep-ph 1003.4266] sa, Blümlein, Klein, Moch PRD 81, 014032 (2010) The gluon distribution is correlated with αs effect is accumulated in the c.s., some 20-30 % for the gluon-initiated processes as Higgs and top-quark production 19
Summary The inclusive Tevatron jet data added to ABKM fit the truly global PDFs Moderate impact on the gluons (scale uncertainty) Selection of the data is unclear: RunI / RunII / inclusive / dijet additional uncertainty The combined inclusive HERA data included Improved small-x gluon distribution αs(mz)=0.1147±0.0012 (NNLO) Running mass definition implemented for heavy-quark DIS Good agreement with the PDG value of the c-quark mass Impact of the NMC data interpretation on the Tevatron Higgs rate Consolidation of the different predictions