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3rd Workshop on High-p T Physics at LHC Tokaj, 16 March, 2008

3rd Workshop on High-p T Physics at LHC Tokaj, 16 March, 2008. EPS08 - An improved global analysis of nuclear PDFs including RHIC data Kari J. Eskola Department of Physics, University of Jyväskylä Helsinki Institute of Physics KJE, Hannu Paukkunen , Carlos Salgado, arXiv:0802.0139 [hep-ph].

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3rd Workshop on High-p T Physics at LHC Tokaj, 16 March, 2008

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  1. 3rd Workshop on High-pT Physics at LHC Tokaj, 16 March, 2008 EPS08 - An improved global analysis of nuclear PDFs including RHIC dataKari J. EskolaDepartment of Physics, University of JyväskyläHelsinki Institute of PhysicsKJE, Hannu Paukkunen, Carlos Salgado,arXiv:0802.0139 [hep-ph]

  2. Collinear QCD factorization & PDFs Inclusive hard process cross sections in hadronic and nuclear collisions, e.g. A+B  k+l + anything (LO below) : • Parton Distribution Functions • number density distributions (in LO at least) • universal = process-independent, specific to A and B • contain nonpertubative input at an initial scale Q02 • obey DGLAP scale evolution equations of pQCD: Calculable in pQCD

  3. DGLAP Comparison with data at various x & Q { fi(x) } at Q>Q0 Min(chi2) ? Global analysis of PDFs = DGLAP-evolved PDFs + constraints from hard pQCD process data + constraints from sum rules (momentum, charge, baryon#) Procedure: iterate until best fit, best set of initial parameters {ai} found { fi(x,{aj}) } at Q0, model independent Vary {aj} no Impose sum rules

  4. / fi/A(x,Q2) = fi/p(x,Q2) • Difficulties in extracting nonperturbative input for PDFs at fixed Q02 • - data not at one fixed Q2 but correlated in x and Q2 • kinematic ranges & data precision vary from one experiment to another • how to account for systematic uncertainties, for overall-normalization errors? • nPDF analysis more complicated than free proton PDFs: • ▪ not enough data at small x & perturbative Q2! • ▪ A-dependence [under control], spatial dependence [open question],… perturbative nonperturbative

  5. Global analyses for… EKS98 (Eskola, Kolhinen, Ruuskanen, Salgado) [hep-ph/9802350,hep-ph/9807297] - 1st global analysis for nPDFs - very good fits to nuclear DIS & DY data obtained with sum rules imposed – it works! 2. HKN, HKM (Hirai, Kumano, Nagai, Miyama) [LO hep-ph/0103208,hep-ph/0404093; HKN_NLO 0709.3038 hep-ph] - automated chi2 minimization - first uncertainty estimates for the nPDFs 3. nDS (de Florian, Sassot) [hep-ph/0311227] - first NLO global analysis for nPDFs 4. EPS08 (Eskola, Paukkunen, Salgado) [0802.0139 hep-ph] - first global analysis with RHIC data included Free proton PDFs: CTEQ, MRST, GRV,… Nuclear PDFs:

  6. EKS98: ▪ pioneering analysisNucl. Phys. B535 (1998) 351, [hep-ph/9802350] ▪ (x, Q2,A)-dependent modifications; parametrization for general use: Eur. Phys. J. C9 (1999) 61 [hep-ph/9807297] gluons sea quarks valence quarks Got the Q2-slopes right!

  7. Last year in the High-pT LHC workshop in Jyväskylä: - reported uncertainty estimates for EKS98-type of global analysis, with automated chi2 minimization and DIS&DY data [EKPS, hep-ph/0703104] - discussed the need to include RHIC data in the global analysis valence sea gluons F2(A)/F2(D) - Need stronger gluon shadowing at x<0.03 ? - Uncertainty estimates tied to the fit function forms

  8. Now, for the EPS08 1. Include RHIC high-pT pion & negative-h data from d+Au - forward-rapidity data  constrained region extended down to x~10-3 2. Improve the chi2 minimization procedure - introduce weighting of different data sets  emphasize the constraints for gluons - account for given overall normalization errors of the data 3. Answer Q: Can the strong gluon shadowing suggested by BRAHMS forward data be accommodated together with the DIS&DY data in a global DGLAP analysis? = can a good global fit still be obtained? = can the nuclear effects be factorized into the nPDFs?

  9. EPS08 framework = similar to EKS98 • Define the PDFs of bound protons w.r.t. the known free proton PDFs: • PDFs of the bound neutrons from isospin symmetry: un/A=dp/A, dn/A=up/A • Similarly to EKS98, parametrize initial distributions at Q0=1.3 GeV • in terms of three different initial modifications Ri(x,Q0): • valence, sea & gluons • piecewise construction: • Sum rules imposed • baryon # conservation  constrains mainly valence • momentum conservation  constrains mainly gluons

  10. EPS08 framework • A-dependence is in the parameters e.g. ya=ya(C) (A/12) p(ya) • new:more flexible small-x fit function, with nosaturation of shadowing • fA/fp ~ x-dA/x-dP 0 when x0 (dA<dP)

  11. [almost] no constraints for large-x sea&gluon modifications •  fix gluons to valence RV in the EMC-effect region [support from (yet unpublished) PHENIX photon data in Au+Au] • - Fast DGLAP solver now our own [HannuP] -- earlier we used CTEQ’s • - Lots of manual labour to figure out which parameters are important [HannuP] ! •  Minimize chi2 for 15 free fit parameters

  12. The data used in EPS08 DIS: l+A (484 points) SLAC-E-139 NMC 95, 95re, 96 + EMC - leave E665 out Drell-Yan in p+A (92) E772 E866 + new input RHIC pi and h- in d+Au (51) BRAHMS, fwd PHENIX, mid-rap. STAR, mid-rap. Include only the region pT>2 GeV #datapoints = 627

  13. Inclusive single hadron production at high pT: selection of RHIC data KKP pQCD: p+pbar, pp: LO pQCD with K(s) works ~OK [KJE & H. Honkanen, hep-ph/0205048 ] d+Au at RHIC: To avoid the Cronin effect complications with protons (assumed to be related to hadronization), we include in the EPS08 fit onlypion data, and fwd-rap. h- data We also exclude the region qT< 2 GeV from the global fit at pT< 2 GeV too steep slopes - also at NLO; FF uncertainties ?

  14. New elements in EPS08 – improvements in chi2 minimization usual definition now define • Weights wN for data sets N • with these, we emphasize those data sets which provide important • constraints but whose number of data points is small • 2.Treatment of the additional overall normalization errors σnorm • given by the experiment – similar procedure used also by CTEQ: • - fNis determined by minimizing the chi2N for each data set N, i.e. for each • parameter-setcandidate during the overall chi2 minimization • - ”penalty factor” (…)2 accounts for the fact that fN=1 should be • the optimal value  the normalization given by the experiment

  15. The results from EPS08

  16. DIS & EPS08

  17. > 0 Constraints for gluons from the first 3 panels of F2(Sn)/F2(C) in DIS EPS08 has the strongest gluon shadowing which still agrees with the F2 Q2-slopes !

  18. DY & EPS08

  19. EPS08 and RHIC pion data from d+Au: good agreement obtained when the given additional overall-normalization errors are accounted for: fN ≠ 1 ! PHENIX σnorm=10% STAR σnorm=17%

  20. EPS08 and forward-rapidity negative hadron RHIC data: Good agreement obtained for pT>2 GeV BRAHMS σnorm=5% here fN=0 From the EPS08 fit fN=1.02 not a big effect

  21. The EPS08 nuclear effects at the initial scale Q=1.3 GeV Unconstrained region Note the strong gluon shadowing! Constrained region

  22. Comparison with earlier global analyses Much more gluon shadowing in EPS08 -- correspondingly more antishadowing EKPS EPS08: chi2/N = 0.71

  23. Conclusions • RHIC data now in the global analysis of nPDFs, for the 1st time • the constrained x-region has been extended from x>0.01 to x>0.001 • chi2 analysis improved by introducing • + weights for data sets • + treatment of overall normalization errors • very good agreement obtained with DIS and DY data, • and also with the pT>2 GeV RHIC pion data at midrapidity • and with h- data at fwd rapidity • universal nPDFs and factorization seem OK - treatment of normalization errors led to a good simultaneous agreement w. PHENIX and STAR pion data - pT<2 GeV region in hadron production in d+Au at RHIC still difficult  need FF improvements, impact parameter dependent nPDFs,…

  24. thanks to the weights given to the RHIC data, the EPS08 results • correspond to the strongest shadowing which is still in agreement • with the Q2-slopes of F2 measured at DIS • gluon shadowing in EPS08 is much stronger than in earlier global • analyses! • More data needed ! • next: include RHIC photons from Au+Au • hope to have D production in d+Au at RHIC • hope for a p+Pb program at LHC, too • - EPS08 now available at http://www.jyu.fi/science/laitokset/fysiikka/en/research/highenergy/urhic/nPDFs • Gluon shadowing still under debate… •  use EPS08 parallel with EKS98

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