1 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: [hep-ph] 3rd Workshop on High-p T Physics at LHC Tokaj, 16 March, 2008

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 Q 0 2 obey DGLAP scale evolution equations of pQCD: Calculable in pQCD

3 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 {a i } found { f i (x,{a j }) } at Q 0, model independent DGLAP Comparison with data at various x & Q noVary {a j } { f i (x) } at Q>Q 0 Min(chi 2 ) ? Impose sum rules

4 Difficulties in extracting nonperturbative input for PDFs at fixed Q data not at one fixed Q 2 but correlated in x and Q 2 - 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 Q 2 ! ▪ A-dependence [under control], spatial dependence [open question],… perturbative nonperturbative f i/A (x,Q 2 ) = f i/p (x,Q 2 ) /

5 1.EKS98 (Eskola, Kolhinen, Ruuskanen, Salgado) [ hep-ph/ ,hep-ph/ ] - 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/ ,hep-ph/ ; HKN_NLO hep-ph] - automated chi 2 minimization - first uncertainty estimates for the nPDFs 3. nDS (de Florian, Sassot) [hep-ph/ ] - first NLO global analysis for nPDFs 4. EPS08 (Eskola, Paukkunen, Salgado) [ hep-ph] - first global analysis with RHIC data included Global analyses for… Free proton PDFs: CTEQ, MRST, GRV,… Nuclear PDFs:

6 EKS98: ▪ pioneering analysis Nucl. Phys. B535 (1998) 351, [hep-ph/ ] ▪ (x, Q 2,A)-dependent modifications; parametrization for general use: Eur. Phys. J. C9 (1999) 61 [hep-ph/ ] gluons sea quarks valence quarks Got the Q 2 -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/ ] - discussed the need to include RHIC data in the global analysis - Need stronger gluon shadowing at x<0.03 ? - Uncertainty estimates tied to the fit function forms valence sea F2(A)/F2(D) gluons

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~ Improve the chi 2 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 Define the PDFs of bound protons w.r.t. the known free proton PDFs: PDFs of the bound neutrons from isospin symmetry: u n/A =d p/A, d n/A =u p/A Similarly to EKS98, parametrize initial distributions at Q 0 =1.3 GeV in terms of three different initial modifications R i (x,Q 0 ): valence, sea & gluons piecewise construction: Sum rules imposed baryon # conservation  constrains mainly valence momentum conservation  constrains mainly gluons EPS08 framework = similar to EKS98

10 - A-dependence is in the parameters e.g. y a =y a (C) (A/12) p(ya) - new: more flexible small-x fit function, with no saturation of shadowing f A /f p ~ x -dA /x -dP  0 when x  0 (dA<dP) EPS08 framework

11 - [almost] no constraints for large-x sea&gluon modifications  fix gluons to valence R V 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 chi 2 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 p T >2 GeV #datapoints = 627

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

14 New elements in EPS08 – improvements in chi 2 minimization 1.Weights w N 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 σ norm given by the experiment – similar procedure used also by CTEQ: - f N is determined by minimizing the chi 2 N for each data set N, i.e. for each parameter-set candidate during the overall chi 2 minimization - ”penalty factor” (…) 2 accounts for the fact that f N =1 should be the optimal value  the normalization given by the experiment usual definition now define

15 The results from EPS08

16 DIS & EPS08

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

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: f N ≠ 1 ! PHENIX σ norm =10% STAR σ norm =17%

20 EPS08 and forward-rapidity negative hadron RHIC data: Good agreement obtained for p T >2 GeV From the EPS08 fit f N =1.02 not a big effect BRAHMS σ norm =5% here f N =0

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

22 Comparison with earlier global analyses Much more gluon shadowing in EPS08 -- correspondingly more antishadowing EPS08: chi 2 /N = 0.71 EKPS

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> chi 2 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 p T >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 - p T <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 - Gluon shadowing still under debate…  use EPS08 parallel with EKS98