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Introduction to Parton Distribution Functions in the Nucleon and Nuclei

Introduction to Parton Distribution Functions in the Nucleon and Nuclei. Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS). shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/. Meeting on New Interaction Code

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Introduction to Parton Distribution Functions in the Nucleon and Nuclei

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  1. Introduction to Parton Distribution Functions in the Nucleon and Nuclei Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/ Meeting on New Interaction Code For Cosmic Air Shower ICRR, Kashiwa, Japan http://cosmos.n.kanagawa-u.ac.jp/newCode/ December 26, 2008

  2. Contents Introduction • Parton Distribution Functions (PDFs) in air-shower model • Deep inelastic scattering and Parton picture Determination of PDFs • PDFs in the nucleon Global analysis Comments on higher-twist effects • Nuclear PDFs Mechanisms for nuclear modifications Our global analysis, Comparison with other analyses 3. Summary

  3. Introduction

  4. Typical Air Shower Model (SENECA) Soft interactions My talk is on this “hard” part. http://th.physik.uni-frankfurt.de/~drescher/SENECA/

  5. In an air-shower model (e.g. SIBYLL) R. S. Fletcher, T. K. Gaisser, P. Lipari, and T. Stanev, Phys. Rev. D 50 (1994) 5710. High-energy part is described by the following cross sections SIBYLL (1994): PDFs by Eichten-Hinchliffe-Lane-Quigg (EHLQ) in 1984 The PDFs at large x1 and small x2 should affect simulation results of the air shower.

  6. Soft Hard Hard scale (e.g. transverse momentum pT ) Resonances ~1 GeV Partons pQCD + Parton Distribution Functions (PDFs) (+ Fragmentation Functions) p, …, Fe N, O (R. Engel) Soft and Hard processes My talk is on hard processes. Most energetic particles (namely large xF ) contribute mainly to subsequent shower development. • Nuclear PDFs at small x (N, O) --- LHC • Nucleonic and Nuclear PDFs at large x (p, …, Fe) --- JLab, J-PARC • Fragmentation functions --- Belle, Babar

  7. N, O p, …, Fe Momentum fraction x in the forward region

  8. Deep Inelastic Lepton-Nucleon Scattering andParton Picture

  9. Kinematics of e+pe’+X z

  10. proton momentum: p Meaning of x consider the frame where the proton is moving fast x= momentum fraction carried by the struck parton For example, x=0.5 means that the struck parton carries 50% momentum of the proton.

  11. Kinematical range of x: 0 ≤ x ≤ 1 for the nucleon

  12. Meaning of Q2 Breit frame is defined as the frame in which exchanged boson is completely spacelike: q=(0, 0, 0, q). Laboratory frame Breit frame q0=0: photon does not transfer any energy Spatial resolution = reduced wavelength Q2 corresponds to the “spatial resolution” in the Breit frame.

  13. Bjorken scaling Example of electron-proton scattering data at SLAC (1972). W2=F2 x= 0.25 Structure function F2 is independent of Q2. (Bjorken scaling) Q2 (GeV2/c2) It means that F2 does not change even if the spatial resolution is increased.  existence of small particles which cannot be resolved: This point-like particle was named “parton”. parton  quark, gluon

  14. Scaling violation (Q2 dependence) DGLAP (Dokshitzer, Gribov, Lipatov, Altarelli, Parisi) small Q2 large Q2 ZEUS, Eur. Phys. J. C21 (2001) 443. Q2 corresponds to “spatial resolution”. As Q2 becomes large, the virtual starts to probe the gluon, quark, and antiquark “clouds”.

  15. Parton Distribution Functions in the Nucleon

  16. Related web sites Parton distribution functions (PDFs), Experimental data: ・http://durpdg.dur.ac.uk/HEPDATA/ CTEQ: ・http://www.phys.psu.edu/~cteq/ Our activities: ・ Nuclear PDFs, Q2 evolution codes, Fragmentation functions http://research.kek.jp/people/kumanos/

  17. Recent activities  uncertainties  NNLO  QED  s–s  charm 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) 14012 & 14013. (CTEQ6) D. Pumplin et al., JHEP, 0207 (2002) 012; 0506 (2005) 080; 0602 (2006) 032; 0702 (2007) 053; PRD78 (2008) 013004. (charm) PR D75 (2007) 054029; (strange)PRL 93 (2004) 041802; 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) 054019; PL B652 (2007) 292. (2008) arXiv:0806.4890 Alekhin S. I. Alekhin, PRD68 (2003) 014002; D74 (2006) 054033. BB J. Blümlein and H. Böttcher, Nucl. Phys. B774 (2007) 182-207. NNPDF S. Forte et al., JHEP 0205 (2002) 062; 0503 (2005) 080; 0703 (2007) 039. H1 C. Adloff et al., Eur. Phys. J. C 21 (2001) 33; C30 (2003) 1. ZEUS S. Chekanov et al., PRD67 (2003) 012007; Eur. Phys. J. C42 (2005) 1.

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

  19. Available data for determining PDFs (Ref. MRST, hep/ph-9803445)

  20. X m q –  W p N n m Determination of each distribution Valence quark

  21. Sea quark e/ scattering Drell-Yan (lepton-pair production) projectile target

  22. Gluon scaling violation of F2 K. Prytz, Phys. Lett. B311 (1993) 286. jet production

  23. Global Analysis for PDFs

  24. Outline of analysis 1. Express x-dependent PDFs with parameters at a fixed Q2 ( Q02) * Choice of Q02 2. Evolve the PDFs to experimental Q2 data points * Q2 evolution methods 3. Convolute with coefficient functions to calculate observables 4. Determine 2in comparison with data 5. Repeat 2, 3, and 4 processes until minimal 2 is obtained

  25. Unpolarized Parton Distribution Functions (PDFs) in the nucleon The PDFs could be obtained from http://durpdg.dur.ac.uk/hepdata/pdf.html Gluon distribution / 5 Valence-quark distributions

  26. CTEQ5M1 MRS2001 CTEQ5HJ PDF uncertainty q(x) at large x u d CTEQ6 (J. Pumplin et al.), JHEP 0207 (2002) 012 g (unknown)2 for cosmic-ray studies There are also large nuclear corrections in these regions. g(x) at small x “gluon saturation”

  27. Comments onHigher-Twist Effects

  28. Higher-twist effects by CTEQ in 2002 CTEQ (J. Pumplin et al.), JHEP 07 (2002) 012. error estimate ?

  29. proton deuteron Higher-twist effects by BB in 2008 J. Blüemlein, H. Böttcher, Phys. Lett. B 662 (2008) 336.

  30. Higher-twist effects by BB in 2008

  31. For extracting reliable higher-twist effects Full analysis is needed! “Full” means at least  Parametrization and fit also for the HT terms  Uncertainty range of a determined HT function together with target-mass corrections and higher-order effects.

  32. Nuclear Parton Distribution Functions

  33. Brief Introduction toNuclear Modifications ofParton Distribution Functions

  34. 1.2 EMC NMC 1.1 E139 E665 1 0.9 Could affect cosmic-ray studies 0.8 0.7 0.001 0.01 0.1 1 Shadowing (qq fluctuation of photon) Nuclear modifications of structure function F2 Fermi motion of the nucleon D. F. Geesaman, K. Saito, A. W. Thomas, Ann. Rev. Nucl. Part. Sci. 45 (1995)337. x Nuclear binding (+ Nucleon modification)

  35. q k Quark (a) p Hadron (T) P Nucleus (A) EMC (European Muon Collaboration) effect Theoretical Description

  36. Binding Model

  37. 0.98 0.20 Because the peak shifts slightly (1 0.98), nuclear modification of F2 is created. Fermi motion binding

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

  39. Determination of Nuclear Parton Distribution Functions

  40. 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

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

  42. 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; 0807 (2008) 102. (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 HKN07 analysis is explained in this talk.

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

  44. 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

  45. 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 )

  46. x Functional form of wi (x, A) Note: The region x > 1 cannot be described by this parametrization. A simple function = cubic polynomial Three constraints

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

  48. Nuclear PDFs

  49. Nuclear PDFs and uncertainties Fermilab J-PARC GSI Future experiments • Some NLO improvements, but not significant ones. • Impossible to determine gluon modifications. • Antiquark distributions are not determined at large x. RHIC LHC LHeC eLIC eRHIC JLab J-PARC? GSI? • Factory MINARA RHIC LHC LHeC eLIC eRHIC

  50. Comparison withOther Global Analyses

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