1 Global reanalysis of nuclear PDFs Kari J. Eskola, Department of Physics, University of Jyväskylä Helsinki Institute of Physics hep-ph/ , in collaboration with Vesa Kolhinen, Hannu Paukkunen, Carlos Salgado High-p T Physics at LHC, Jyväskylä, 24 March, 2007

2 URHIC Theory group at Jyväskylä (JYFL & HIP) Seniors Vesa Ruuskanen, prof. emer Kari J. Eskola, prof ( – ) Kimmo Tuominen, doc. Postdocs T. Renk, V. Kolhinen Graduate students T. Kähärä H. Niemi H. Paukkunen Undergraduate students J. Auvinen M. Heikinheimo T. Karavirta P. Mäkinen

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 inpendent 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 Free proton PDFs: CTEQ, MRST, GRV,… Nuclear PDFs: 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) [hep-ph/ ,hep-ph/ ] - automated chi 2 minimization - uncertainty estimates 3. nDS (de Florian, Sassot) [hep-ph/ ] - first NLO global analysis for nPDFs Global analyses for…

5 Goals of our reanalysis, hep-ph/ Improve the old EKS98 global analysis by - Automating chi2 minimization (in EKS98 fits done by eye only) - Improve chi2 over EKS98 (difficult...)? - Obtain uncertainty estimates on the EKS98-type nuclear modifications of PDFs Study whether DIS&DY data support stronger gluon shadowing -- BRAHMS data would seem to suggest stronger shadowing than in EKS98, HKN, nDS

6 Define the PDFs of bound protons w.r.t. the known free proton PDFs: PDFs of the bound neutrons from isospin symmetry As in EKS98, parametrize initial distributions at Q 0 =1.3 GeV in terms of three different initial modifications R i (x,Q 0 ) for valence, sea & gluons piecewise construction; functional forms simpler than in EKS98 Sum rules imposed baryon # conservation  constrain valence momentum conservation  constrain gluons The framework = EKS98

7 xaxa yoyo yaya xexe yeye β xsxs A-dependence is in the parameters, e.g. y a =y a (C) (A/12) p ya

8 No constraints for large-x sea&gluons modifications  fix their modifications to that of valence Lots of manual labour to figure out which parameters are important!  Minimize chi2 for 16 free fit parameters

9 The data used DIS: l+A SLAC-E-139 NMC 95, 95re, 96 E665 Drell-Yan in p+A E772 E866 #datapoints = 514

10 DIS; A/C A-systematics

11 DIS; A/D

12 Drell Yan in p+A; A/D DY in p+A; A/Be

13 Constraints for gluons from the first 3 panels of F2(Sn)/F2(C): Small-x Q 2 -dependence nicely reproduced if R G A (x,Q 0 ) ~1 at x~ If gluon shadowing at x ~ 0.01 is clearly stronger than sea quark shadowing, then log Q-slope of F2(Sn)/F2(C) becomes small or even negative… Based on the chi 2 s obtained in global analysis, we do not find support for strong gluon shadowing from DIS&DY data. However… stronger gluon shadowing does not lead to much worse overall chi2 – the gluon constraint from current DIS & DY data is not very stringent…

14 Comparison with other global analyses: chi 2

15 Comparison with other global analyses

16 Estimated uncertainties on initial modifications (Hessian method, from Minuit): analyzed small-x and large-x errors separately EKS98 works very well  new parametrization not needed! gluon and sea quark shadowings function-form dependent,  the uncertainties shown are lower limits  stronger gluon shadowing at x<0.03 ?? ( since still Chi 2 /N<1)

17 Support for stronger gluon shadowing from BRAHMS d+Au data? Next steps for us - include these data in global analysis - NLO analysis

18 Extra slides….

19 Comparison with other global analyses: log Q2 slopes of F2(Sn)/F2(C)

20