Nuclear Modifications of Parton Distribution Functions

1. Nuclear Modifications ofParton Distribution Functions shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/ Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) Collaborators: Masanori Hirai (Juntendo) Takahiro Nagai (GUAS) Ref. Phys. Rev. C 76 (2007) 065207. Workshop on Description of Lepton-Nucleus Reactions KEK, Tsukuba, December 22, 2007 December 22, 2007

2. Contents (1) Introduction Motivation Comments on parton distribution functions (PDFs) in the nucleon (2) Determination of PDFs in Nuclei Analysis method LO and NLO results and their comparisons  Summary

3. Motivations for studying structure functions and 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.

4. (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  New structure functions and new investigations at  factory!

5. Nuclear PDFs in neutrino reactions CCFR and NuTeV: 56Fe target Nuclear effects are important in extracting nucleonic PDFs. (2) Oscillation experiments Nuclear corrections in 16O Low Q2 data: High Q2(PDFs)  Low Q2 is needed. (Quark-hadron duality) (3) Neutrino Factory New investigations with proton and deuteron targets, so that nuclear modifications could be studied by measuring A/D ratios.

6. Parton Distribution Functions (PDFs) in the Nucleon PDFs from http://durpdg.dur.ac.uk/hepdata/pdf.html  factory Valence-quark distributions are determined from data including CCFR and NuTeV ones with the iron target. It should be worth investigating them for the real nucleon at a neutrino factory.

7. CTEQ5M1 MRS2001 CTEQ5M1 CTEQ5HJ MRS2001 PDF uncertainty CTEQ6 (J. Pumplin et al.), JHEP 0207 (2002) 012

8. Parton Distribution Functionsin “Nuclei”

9. Status of PDF determinations Unpolarized PDFs in the nucleon    Investigated by 3 major groups (CTEQ, GRV, MRST).Well studied from small x to large x in the wide range of Q2.The details are known.(Recent studies: NNLO, QED, error analysis, , …)“Polarized” PDFs in the nucleon Investigated by several groups (GS, GRSV, LSS, AAC, BB, …).Available data are limited (DIS) at this stage. (recent: HERMES, Jlab, COMPASS)New data from RHIC Future: J-PARC, eRHIC, eLIC, GSI…PDFs in “nuclei”  Investigated by only a few groups. Details are not so investigated!Available data are limited (inclusive DIS, Drell-Yan). New data from RHIC, LHC, Jlab, NuTeV Future: Fermilab, J-PARC, eRHIC, eLIC, GSI… J-PARC = Japan Proton Accelerator Research Complex

10. Situation of data for nuclear PDFs Available data for nuclear PDFs Jlab at large x Neutrino factory: ~10 years later ? (CCFR, NuTeV) Small-x, high-energy electron facility? RHIC, LHC, J-PARC RHIC, LHC Table from MRST, hep/ph-9803445 RHIC, LHC

11. (from H1 and ZEUS, hep-ex/0502008) F2 data for the proton Current nuclear data are kinematically limited. F2 & Drell-Yan data for nuclei region of nuclear data

12. 1.2 EMC NMC 1.1 E139 E665 1 0.9 0.8 0.7 0.001 0.01 0.1 1 Nuclear modification Nuclear modification of F2A /F2D is well known in electron/muon scattering. Fermi motion original EMC finding shadowing x sea quark valence quark

13. Binding Model

14. 0.98 0.20 Because the peak shifts slightly (1 0.98), nuclear modification of F2 is created. Fermi motion binding

15. Shadowing Models: Vector-Meson-Dominance (VMD) type

16. EMC (European Muon Collaboration) effect Theoretical Description

17. References There are only a few papers on the parametrization of nuclear PDFs!  Need much more works. (EKRS) K. J. Eskola, V. J. Kolhinen, and P. V. Ruuskanen, Nucl. Phys. B535 (1998) 351; K. J. Eskola, V. J. Kolhinen, and C. A. Salgado, Eur. Phys. J. C9 (1999) 61. K. J. Eskola et al., JHEP 0705 (2007) 002. (HKM, HKN) M. Hirai, SK, M. Miyama, Phys. Rev. D64 (2001) 034003; M. Hirai, SK, T.-H. Nagai, Phys. Rev. C70 (2004) 044905; M. Hirai, SK, T.-H. Nagai, Phys. Rev. C76 (2007) 065207. (DS) D. de Florian and R. Sassot, Phys. Rev. D69 (2004) 074028. 2 analysis See also S. A. Kulagin and R. Petti, Nucl. Phys. A765 (2006) 126 (2006); L. Frankfurt, V. Guzey, and M. Strikman, Phys. Rev. D71 (2005) 054001. The recent HKN report (KEK-TH-1013) is explained in this talk.

18. NLO Determination of Nuclear Parton Distribution Functions by M. Hirai, SK, T.-H. Nagai arXiv:0709.3038 [hep-ph] Phys. Rev. C 76 (2007) 065207 NPDF codes can be obtained from http://research.kek.jp/people/kumanos/nuclp.html Related refs. M. Hirai, SK, M. Miyama, Phys. Rev. D64 (2001) 034003; M. Hirai, SK, T.-H. Nagai, Phys. Rev. C70 (2004) 044905.

19. New points (1) Both LO and NLO global analyses (LO = Leading Order of s, NLO = Next to Leading Order) Estimation of NPDF uncertainties both in NLO and LO • Roles of NLO terms in the global analysis • Better determination of gluon distributions (NLO terms) (2) Discussions on deuteron modifications Comparison with F2D/F2p data • Deuteron modifications should be important in Gottfried sum, RHIC d-Au collisions, …; however, they are not well studied. •Note:Nuclear effects in the deuteron are partially contained in the “nucleonic” PDFs.

20. Experimental data: total number = 1241 (1) F2A / F2D 896 data NMC:p, He, Li, C, Ca SLAC:He, Be, C, Al, Ca, Fe, Ag, Au EMC: C, Ca, Cu, Sn E665: C, Ca, Xe, Pb BCDMS: N, Fe HERMES: N, Kr (2) F2A / F2A’ 293 data NMC: Be / C, Al / C, Ca / C, Fe / C, Sn / C, Pb / C, C / Li, Ca / Li (3) DYA / DYA’ 52 data E772: C / D, Ca / D, Fe / D, W / D E866: Fe / Be, W / Be

21. Functional form Nuclear PDFs “per nucleon” If there were no nuclear modification Isospin symmetry： Take account of nuclear effects by wi (x, A) at Q2=1 GeV2 (Q02 )

22. x Functional form of wi (x, A) A simple function = cubic polynomial Three constraints

23. Analysis conditions · Nucleonic PDFs: MRST98[ QCD = 174 MeV (LO), 300 MeV (NLO) ] · Total number of parameter：12 · Total number of data： 1241 ( Q2≧1 GeV2 ) 896 (F2A/F2D) + 293 (F2A/F2A´) + 52 (Drell-Yan) · Subroutine for 2 analysis： CERN-Minuit 2min (/d.o.f.) = 1653.3 (1.35) ….. LO = 1485.9 (1.21) ….. NLO · Error estimate： Hessian method

24. NLO improvement NLO disimprovement 2 values in LO and NLO Total 2improvements in NLO. NLO improvements mainly in light nuclei; however, disimprovements for Drell-Yan data.

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

26. Comparison with F2A/F2D data: Light nuclei

27. Comparison with F2A/F2D data: Heavy nuclei

28. 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.

29. Scaling Violation and Gluon Distributions dominant term at small x Q2 dependence of F2 is proportional to the gluon distribution. No experimental consensus of Q2 dependence!  GA(x) determination is difficult.

30. Nuclear PDFs

31. PDFs in 40Ca and uncertainties • Some NLO improvements, but not significant ones. • Impossible to determine gluon modifications. • Antiquark distributions are not determined at large x. • Flavor separation is needed for antiquarks   factory • Confirmation of valence modifications at small x   factory

32. Summary on nuclear-PDF determination in NLO LO and NLO analysis for the nuclear PDFs and their uncertainties. • Better determination of GA(x) is usually expected in NLO.  However, the NLO improvement is not very clear due to inaccurate measurement of Q2 dependence.  The gluon modifications are also not determined well even in NLO. Deuteron modifications • At most 0.5%~2%; however, be careful that deuteron effects could be contained in the PDFs of the nucleon. NPDF codes at http://research.kek.jp/people/kumanos/nuclp.html.  Comparison with (and analysis including) NuTeV nuclear corrections in future! Small NuTeV nuclear corrections!? (J. F. Owens et al., PRD75, 054030 (2007); J. G. Morfin@WIN07) Neutrino factory should be important for finding nuclear medium effects in the valence-quark and (flavor-separated) antiquark distributions.

33. Extra

34. Nuclear corrections in iron (A=56, Z=26) KP (Kulagin, Petti) Nuclear PDFs from neutrino deep inelastic scattering, I. Schienbein, J. Y. Yu, C. Keppel, J. G. Morfin, F. Olness, and J. F. Owens (CTEQ Collaboration), arXiv:0710.4897v1 [hep-ph]. Sumamry

36. 0.18 fm 0.40 fm x

37. this analysis CTEQ, (F. Olness et al., Eur. Phys. J. C40 (2005) 145) H.-L. Lai et al., JHEP 04 (2007) 089. The 2007 paper includes the final NuTeV data for dimuons.

38. best fit

39. NuTeV analysis The NuTeV result is not much different from CTEQ onealthough it used to differ in hep-ex/0405037.

40. Global analysis for determiningfragmentation functionsand their uncertainties Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/ with M. Hirai (TokyoTech), T.-H. Nagai (GUAS), K. Sudoh (KEK) Reference: Phys. Rev. D75 (2007) 094009.

41. Contents (1) Introduction to fragmentation functions (FFs)  Definition of FFs  Motivation for determining FFs (2) Determination of FFs  Analysis method  Results  Comparison with other parameterizations (3) Summary

42. Introduction

43. e+ , Z q h e– q Fragmentation Function Fragmentation: hadron production from a quark, antiquark, or gluon Fragmentation function is defined by Variable z • Hadron energy / Beam energy • Hadron energy / Primary quark energy A fragmentation process occurs from quarks, antiquarks, and gluons, so that Fh is expressed by their individual contributions: Non-perturbative (determined from experiments) Calculated in perturbative QCD

44. Momentum (energy) sum rule Favored and disfavored fragmentation functions

45. Status of determining fragmentation functions Parton Distribution Functions (PDFs), Fragmentation Functions (FFs) Uncertainty ranges of determined fragmentation functions were not estimated, although there are such studies in nucleonic and nuclear PDFs. The large differences indicate that the determined FFs have much ambiguities.

46. Situation of fragmentation functions There are two widely used fragmentation functions by Kretzer and KKP. An updated version of KKP is AKK. (Kretzer) S. Kretzer, PRD 62 (2000) 054001 (KKP) B. A. Kniehl, G. Kramer, B. Pötter, NPB 582 (2000) 514 (AKK) S. Albino, B.A. Kniehl, G. Kramer, NPB 725 (2005) 181 The functions of Kretzer and KKP (AKK) are very different.

47. Purposes of investigating fragmentation functions Semi-inclusive reactions have been used for investigating ・origin of proton spin Quark, antiquark, and gluon contributions to proton spin (flavor separation, gluon polarization) ・properties of quark-hadron matters Nuclear modification (recombination, energy loss, …)

48. Determination of fragmentation function and their uncertainties M. Hirai, SK, T.-H. Nagai, K. Sudoh Phys. Rev. D75 (2007) 094009. Determination of Fragmentation Functions A code for calculating the FFs is available at http://research.kek.jp/people/kumanos/ffs.html

49. New aspects in our analysis • Determination of fragmentation functions (FFs) and their uncertainties in LO and NLO. • Discuss NLO improvement in comparison with LO by considering the uncertainties. (Namely, roles of NLO terms in the determination of FFs) • Comparison with other parametrizations • Avoid assumptions on parameters as much as we can, Avoid contradiction to the momentum sum rule • SLD (2004) data are included.

50. Comparison with other analyses