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Structure Functions in the Nucleon

Structure Functions in the Nucleon. Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS). shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/. Ultra-high energy cosmic rays and hadron structure 2008 KEK, Tsukuba, Japan

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Structure Functions in the Nucleon

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  1. Structure Functions in the Nucleon Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) shunzo.kumano@kek.jp http://research.kek.jp/people/kumanos/ Ultra-high energy cosmic rays and hadron structure 2008 KEK, Tsukuba, Japan http://www-conf.kek.jp/hadron08/crhs08/ April 25 – 26, 2008 (Talk on April 26)

  2. Contents Introduction • Parton Distribution Functions (PDFs) • Relevant kinematical regions for ultra-high energy cosmic ray interactions with atmospheric nuclei Current Situation • PDFs in the nucleon • Nuclear PDFs • Fragmentation functions 3. Summary

  3. Introduction

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

  5. In a 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) • Nucleonic and Nuclear PDFs at large x (p, …, Fe) • Fragmentation functions

  7. x 1/3 1 gluon x 1/3 1 Meaning of x (= parton momentum / parent-hadron momentum) Quark momentum distributions If the proton consists of three quarks and if they carry equal momenta momentum distribution Quarks interact by gluon exchange within the proton. 　　　　　 Momentum could be transferred. Momentum distribution is spread.

  8. momentum distribution Sea quark x ~ 0.2 1 Valence quark Valence and sea quarks A quark-antiquark pair is created through gluon. This quark is called “sea quark”.

  9. 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”.

  10. Parton interactions (pQCD) Fragmentation functions Cosmic ray A1 (p, …, or Fe) Parton distribution functions Atmosphere A2 (N or O) Description of hard hadron interactions It is important to understand: • Gluon distributions at small x (N, O), • Quark distributions at large x (p, …, Fe), • Fragmentation functions

  11. HERA RHIC LHC J-PARC High-energy hadron facilities and high-energy cosmic rays Ultra-high energy cosmic rays are related to physics small-x physics (LHC) and large-x physics (JLab, J-PARC(?)). (R. Engel, International School on AstroParticle Physics, June 30th - July 9th, 2005, Belgirate, Italy )

  12. Hadron facilities Ultra-high energy cosmic ray interactions could be related to LHC & JLab, J-PARC (?) physics. Large-x facility Small-x facility

  13. Momentum fraction x in the forward region

  14. Parton Distribution Functions in the Nucleon

  15. Motivations for studying PDFs To establish QCD Perturbative QCD • In principle, theoretically established in many processes. (There are still issues on resummations and small-x physics.) • Experimentally confirmed (unpolarized, polarized ?) Non-perturbative QCD (PDFs) • Theoretical models: Bag, Soliton, … (It is important that we have intuitive pictures of the nucleon.) • Lattice: Reliable x-distributions have not been obtained.  Determination of the PDFs from experimental data.

  16. (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

  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; (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. --- no update 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; hep-ph/0706.0459. 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; ZEUS S. Chekanov et al., 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) Used data for MRST01 (Ref. MRST, hep/ph-0110215)

  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. 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

  24. 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”

  25. … Huge Fe target (690 ton) Issue of q(x) in the “nucleon” at large x from -Fe (≠nucleon) scattering Most people believe that valence-quark distributions are well determined, but it may not. M. Tzanov et al. (NuTeV), Phys. Rev. D 74 (2006) 012008. CCFR, NuTeV experiments “Nucleonic” PDFs have been obtained by assuming that nuclear corrections are the same as those in the charged-lepton (e, ) scattering.

  26. Nuclear corrections in iron (A=56, Z=26) Large uncertainties on possible nuclear corrections Charged-lepton scattering I. Schienbein et al. (CTEQ), PRD 77 (2008) 054013. Neutrino scattering Base-1 • remove CCFR data • incorporate deuteron corrections Base-2 corresponds to CTEQ6.1M with s≠sbar • include CCFR data Charged-lepton correction factors are applied. • s≠sbar Using current nucleonic PDFs, they (and MRST) obtained very different corrections from charged-lepton data. However, it depends on the analysis method for determining nucleonic (≠nuclear) PDFs.

  27. Nuclear Parton Distribution Functions http://research.kek.jp/people/kumanos/nuclp.html

  28. 1.2 EMC NMC 1.1 E139 Fermi motion of the nucleon E665 1 0.9 Could affect cosmic-ray studies 0.8 0.7 0.001 0.01 0.1 1 x Nuclear binding (+ Nucleon modification) q-qbar fluctuation of photon (+ recombination) Nuclear modifications of structure function F2 Explained in Saito’s talk

  29. 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

  30. 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 )

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

  32. J-PARC E866 JLab E906 • Factory MINARA Results & Future experiments Fermilab J-PARC J-PARC proposalJ. Chiba et al. (2006) RHIC LHC eLIC eRHIC Fermilab J-PARC GSI RHIC LHC eLIC eRHIC (HKN07)

  33. Fragmentation Functions http://research.kek.jp/people/kumanos/ffs.html

  34. 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

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

  36. Experimental data for pion Total number of data：264 Typical data for pion

  37. Fragmentation functions Global analysis results Gluon and light-quark fragmentation functions have large uncertainties. Large differences between the functions of various analysis groups.

  38. PDG2007 Expected Belle data The Belle will provide accurate fragmentation functions at low energy in the near future. R. Seidl (RIKE-BNL), talk at ECT* in February, 2008

  39. Our works related to this talk (1) Nuclear PDFs M. Hirai, SK, and M. Miyama, Phys. Rev. D 64 (2001) 034003; M. Hirai, SK, and T.-H. Nagai, Phys. Rev. C 70 (2004) 044905; C 76 (2007) 065207. (2) Fragmentation functions M. Hirai, SK, T.-H. Nagai, and K. Sudoh, Phys. Rev. D75 (2007) 094009. Hadron Physics at J-PARC SK, Nucl. Phys. A782 (2007) 442.

  40. Summary Hard interactions are discussed in my talk. In order to understand the shower profile, namely to determine energy and composition of primary cosmic rays, it should be important to study  Nucleonic and Nuclear PDFs at small x (LHC)  Nucleonic and Nuclear PDFs at large x (JLab, J-PARC, …)  Fragmentation functions (Belle, …) Communications between cosmic-ray physicists and hadron physicists are needed for developing a reliable interaction model.

  41. The End The End

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