Global reanalysis of nuclear PDFs

1. Global reanalysis of nuclear PDFs Kari J. Eskola, Department of Physics, University of Jyväskylä Helsinki Institute of Physics hep-ph/0703104, in collaboration with Vesa Kolhinen, Hannu Paukkunen, Carlos Salgado High-pT Physics at LHC, Jyväskylä, 24 March, 2007

2. URHIC Theory group at Jyväskylä (JYFL & HIP) Seniors Vesa Ruuskanen, prof. emer Kari J. Eskola, prof (1.4.07 – ) 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. 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 inpendent Vary {aj} no Impose sum rules

4. Global analyses for… Free proton PDFs: CTEQ, MRST, GRV,… Nuclear PDFs: 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) [hep-ph/0103208,hep-ph/0404093] - automated chi2 minimization - uncertainty estimates 3. nDS (de Florian, Sassot) [hep-ph/0311227] - first NLO global analysis for nPDFs

5. Goals of our reanalysis, hep-ph/0703104 • 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. The framework = EKS98 • 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 Q0=1.3 GeV • in terms of three different initial modifications Ri(x,Q0) for • valence, sea & gluons • piecewise construction; functional forms simpler than in EKS98 • Sum rules imposed • baryon # conservation  constrain valence • momentum conservation  constrain gluons

7. xa xs ya yo β ye A-dependence is in the parameters, e.g. ya=ya(C) (A/12)pya xe

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

13. Constraints for gluons from the first 3 panels of F2(Sn)/F2(C): Small-x Q2-dependence nicely reproduced if RGA(x,Q0) ~1 at x~0.03-0.04. 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 chi2s 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: chi2

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 Chi2/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)