1. Determination of nuclear PDFs in the EIC era (Status of NPDFs and our requests to EIC experimentalists)
Shunzo Kumano
High Energy Accelerator Research Organization (KEK)
Graduate University for Advanced Studies (GUAS)
Our nuclear PDF page
Workshop on
Physics at a High Energy Electron Ion Collider
October , 2009, INT, Seattle, USA
October 20, 2009 1

2. Requested tasks (try to reply in the end of my talk)
Physics case for a "stage-I" electron-ion collider (EIC):
polarized 2-5 GeV electrons  250 GeV polarized protons
or 100 GeV/nucleon light and heavy ions.
• What are the "headline" physics issues that could be addressed
by a stage-I machine?
• In which ways can it add to studies performed at Jlab 12 GeV
and at RHIC?
• What are the key processes, cross sections, kinematical regions,
event rates?
• What is the status of the required theoretical tools?
• What are the machine and detector parameters required to meet
these physics goals and to maximize the benefit for the high energy EIC?

3. Kinematics x "stage-I" EIC: 2-5 GeV electron  100 (250) GeV nucleon
500
0.001
0.01
0.1 Q 2
(GeV2) )
NMC (F A /F D
SLAC
EMC
E665
BCDMS
HERMES A'
E772/E886 DY
F2 & Drell-Yan data
for nuclei
Stage-I EIC coverage
Our requests:
• Accurate measurements of
Q2 dependence of F2A / F2D.
• FLA measurements.
Accurate gluon distributions
in nuclei!

4. Contents Introduction • Motivations
• Typical data for modifications in F2 and Drell-Yan
2. PDFs in the nucleon
• A recent global analysis (just a brief explanation)
3. Determination of PDFs in nuclei
• Recent global analyses
Comparisons of various analysis results
• Difficulty in determining gluon modifications
4. Summary

5. Introduction

6. Motivations for studying parton distribution functions
To establish QCD
Perturbative QCD
• In principle, theoretically established in many processes.
(There are still issues on small-x physics.)
• Experimentally confirmed (unpolarized, polarised ?)
Non-perturbative QCD (PDFs)
• Theoretical models: Bag, Soliton, …
(It is important that we have intuitive pictures of the nucleon.)
• Lattice QCD
Theoretical non-pQCD calculations are not accurate enough.
 Determination of the PDFs from experimental data.

7. (2) For discussing any high-energy reactions, accurate PDFs
are needed.
 origin of nucleon spin: quark- and gluon-spin contributions
 exotic events at large Q2: physics of beyond current framework
 heavy-ion reactions: quark-hadron matter
 neutrino oscillations: nuclear effects in n + 16O
 cosmology: ultra-high-energy cosmic rays

8. Nuclear modifications of structure function F2
Anti-shadowing
Fermi motion
of the nucleon
Nuclear binding
(+ Nucleon modification)
Shadowing

9. Drell-Yan and Antiquark Distributions
Drell-Yan cross-section ratio
is roughly equal to antiquark ratio.
The Fermilab E772 Drell-Yan data suggested that nuclear
modification of antiquark distributions should be small
in the region, x≈0.1.

10. Recent Global Analysis for Parton Distribution Functions
in the Nucleon
J. Blümlein’s talk
at this workshop

11. Recent papers on unpolarized PDFs
It is likely that I miss some papers!
CTEQ (uncertainties) D. Stump (J. Pumplin) et al., Phys. Rev. D65 (2001) &
(CTEQ6) D. Pumplin et al., JHEP, 0207 (2002) 012; 0506 (2005) 080;
0602 (2006) 032; 0702 (2007) 053; PRD78 (2008)
(charm) PR D75 (2007) ;
(strange) PRL 93 (2004) ; Eur. Phys. J. C40 (2005) 145; JHEP 0704 (2007) 089.
GRV (GRV98) M. Glück, E. Reya, and A. Vogt, Eur. Phys. J. C5 (1998) 461.
(GJR08) M. Glück, P. Jimenez-Delgado, and E. Reya, Eur. Phys. J. C53 (2008) 355.
MRST A. D. Martin, R. G. Roberts, W. J. Stirling, and R. S. Thorne,
(MRST2001, 2002, 20033) Eur. Phys. J. C23 (2002) 73; Eur. Phys. J. C28 (2003) 455;
(theoretical errors) Eur. Phys. J. C35 (2004) 325;
(2004) PL B604 (2004) 61; (QED) Eur. Phys. J. C39 (2005) 155; PL B636 (2006) 259;
(2006) PRD73 (2006) ; PL B652 (2007) 292.
(2009) Eur. Phys. J. C63 (2009) 189.
Alekhin S. I. Alekhin, PRD68 (2003) ; D74 (2006)
BB J. Blümlein and H. Böttcher, Nucl. Phys. B774 (2007)
S. Alekhin, J. Blumlein, S. Klein, S. Moch, arXiv: [hep-ph].
NNPDF S. Forte et al., JHEP 0205 (2002) 062; 0503 (2005) 080; 0703 (2007) 039.
H C. Adloff et al., Eur. Phys. J. C 21 (2001) 33; C30 (2003) 1.
ZEUS S. Chekanov et al., PRD67 (2003) ; Eur. Phys. J. C42 (2005) 1.
Recent upgrades.
Recent activities  uncertainties  NNLO  QED  s – s  charm  for LHC

12. Parton distribution functions are determined by fitting various
experimental data.

13. Recent improvements on data set
NuTeV, CHORAS
NuTeV
CHORAS
HERA
Tevatron
HERA
Tevatron
A. D. Martin, W. J. Stirling, R. S. Thorne,
and G. Watt, Eur. Phys. J. C63 (2009) 189.

14. MSTW-2008 uv dv g A. D. Martin, W. J. Stirling, R. S. Thorne,
and G. Watt, Eur. Phys. J. C63 (2009) 189. uv dv g

15. Longitudinal structure function FL
Gluon distributions
(MSTW)
Large x
Gluon distributions still have large uncertainties at small- and large-x regions.
Small x
Longitudinal structure function FL

16. Determination of Nuclear Parton Distribution Functions

17. Recent global analyses on nuclear PDFs
It is likely that I miss some papers!
EPS09
K. J. Eskola, H. Paukkunen, and C. A. Salgado, JHEP 04 (2009) 065.
Charged-lepton DIS, DY, p0 production in dAu.
SYKMOO08
I. Schienbein, J. Y. Yu, C. Keppel, J. G. Morfin, F. I. Olness,
and J. F. Owens, Phys. Rev. D 77 (2008)
Neutrino DIS (only NuTeV data).
HKN07
M. Hirai, S. Kumano, and T. -H. Nagai, Phys. Rev. C 76 (2007)
Charged-lepton DIS, DY.
DS04
D. de Florian and R. Sassot, Phys. Rev. D 69 (2004)
See also L. Frankfurt, V. Guzey, and M. Strikman, Phys. Rev. D 71 (2005) ;
S. A. Kulagin and R. Petti, Phys. Rev. D 76 (2007)

18. Global nuclear PDF analysis18

19. Data set for nuclear PDF analyses
HKN07, PRC 76
(2007)
• Charged-lepton DIS, DY
0.005 < x < 0.8, 1 < Q2 < 113 GeV2
• p0 production from d-Au collision
• Neutrino DIS (NuTeV/CCFR): < x < 0.75
Analysis results: total c2 / d.o.f. (# of parameter)
EPS09: (17)
HKN07: (12)
DS06: (18)
SYKMOO08-A: 1.37 [n data] 19

20. Functional form of initial distributions at Q0220

21. Comparison with F2Ca/F2D & DYpCa/ DYpD data
LO analysis
NLO analysis
(Rexp-Rtheo)/Rtheo at the same Q2 points
R= F2Ca/F2D, DYpCa/ DYpD

22. Q2 dependence The differences between LO and NLO
become obvious only at small x.
• Experimental data are not accurate enough
to find the differences.
 Determination of gluon distributions
(NLO terms) is not possible.
• The uncertainties become smaller in NLO
at small x.
Only NLO uncertainty bands are shown.

23. Nuclear PDFs

24. and future experiments
HKN07 results
and future experiments
Fermilab
J-PARC
RHIC
LHC
EIC
HKN07, PRC 76 (2007)
JLab
Factory
MINARA
Fermilab
J-PARC
GSI
RHIC
LHC
EIC

25. Comparison of nuclear PDFs
Different analysis results are consistent with each other
because they are roughly within uncertainty bands.
Valence quark: Well determined except at small x.
Antiquark: Determined at small x, Large uncertainties at medium and large x.
Gluon: Large uncertainties in the whole-x region.
Valence
Sea
Gluon
EPS09
HKN07
DS04
EPS09 (K. J. Eskola et al.), JHEP 04 (2009) 065 25

26. Why is it so difficult to determine nuclear gluon distributions?

27. x Current nuclear data are kinematically limited. F2 data
(from H1 and ZEUS, hep-ex/ )
F2 data
for the proton x 1 10
100
500
0.001
0.01
0.1 Q 2
(GeV2) )
NMC (F A /F D
SLAC
EMC
E665
BCDMS
HERMES A'
E772/E886 DY
F2 & Drell-Yan data
for nuclei
region of nuclear data

28. Scaling violation and Gluon distributions
dominant term at small x
K. Prytz, PLB 311 (1993) 286.
Q2 dependence of F2 is proportional
to the gluon distribution.
No experimental consensus of
Q2 dependence!
 gA(x) determination is difficult.

29. Summary I
Nuclear PDFs
Valence quark: Well determined except at small x.
Antiquark: Determined at small x, Large uncertainties at medium and large x.
Gluon: Large uncertainties in the whole-x region
The antiquark modifications at medium x should be clarified by Fermilab-P906
and other hadron-beam projects (J-PARC?).
 EIC can contribute to determination of gluon shadowing at x~10–3.

30. Summary II: Short reply to the requests
"stage-I" EIC: 2-5 GeV electrons  250 GeV protons or 100 GeV/nucleon ions
• What are the "headline" physics issues that could be addressed
by a stage-I machine?
Determination of gluon shadowing.
• In which ways can it add to studies performed at Jlab 12 GeV and at RHIC?
gA(x ~ 10–3) cannot be determined at both facilities. (RHIC forward?)
• What are the key processes, cross sections, kinematical regions, event rates?
Accurate Q2 dependence measurements of F2A / F2D.
FLA measurements, …
• What is the status of the required theoretical tools?
Theoretical tools (pQCD) are well established at NLO (even NNLO).
There may be an issue of standard DGLAP evolution at small x.
• What are the machine and detector parameters required to meet
these physics goals and to maximize the benefit for the high energy EIC? ?

31. The End
The End