Structure Functions in the Nucleon Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) April 25 – 26, 2008 (Talk on April 26) Ultra-high energy cosmic rays and hadron structure 2008 KEK, Tsukuba, Japan

Contents 1.Introduction Parton Distribution Functions (PDFs) Relevant kinematical regions for ultra-high energy Relevant kinematical regions for ultra-high energy cosmic ray interactions with atmospheric nuclei cosmic ray interactions with atmospheric nuclei 2.Current Situation PDFs in the nucleon PDFs in the nucleon Nuclear PDFs Nuclear PDFs Fragmentation functions Fragmentation functions 3. Summary

Introduction

Typical Air Shower Model (SENECA) My talk is on this “hard” part. Soft interactions are discussed yesterday. workshop

In a shower model (e.g. SIBYLL) R. S. Fletcher, T. K. Gaisser, P. Lipari, and T. Stanev, Phys. Rev. D 50 (1994) 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 x 1 and small x 2 should affect simulation results of the air shower.

Soft and Hard processes My talk is on hard processes. Nuclear PDFs at small x (N, O) Nuclear PDFs at small x (N, O) Nucleonic and Nuclear PDFs at large x (p, …, Fe) Nucleonic and Nuclear PDFs at large x (p, …, Fe) Fragmentation functions Fragmentation functions SoftHard ~1 GeV Hard scale (e.g. transverse momentum p T ) ResonancesPartons pQCD + Parton Distribution Functions (PDFs) (+ Fragmentation Functions) (R. Engel) p, …, Fe N, O Most energetic particles (namely large x F ) contribute mainly to subsequent shower development.

Quark momentum distributions If the proton consists of three quarks and if they carry equal momenta x 11/3 Quarks interact by gluon exchange within the proton.  Momentum could be transferred. gluon x 11/3 momentum distribution Momentum distribution is spread. Meaning of x (= parton momentum / parent-hadron momentum)

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

Scaling violation (Q 2 dependence) ZEUS, Eur. Phys. J. C21 (2001) 443. small Q 2 large Q 2 As Q 2 becomes large, the virtual  starts to probe the gluon, quark, and antiquark “clouds”. DGLAP (Dokshitzer, Gribov, Lipatov, Altarelli, Parisi) Q 2 corresponds to “spatial resolution”.

Description of hard hadron interactions It is important to understand: Gluon distributions at small x (N, O), Gluon distributions at small x (N, O), Quark distributions at large x (p, …, Fe), Quark distributions at large x (p, …, Fe), Fragmentation functions Fragmentation functions Parton distribution functions Parton interactions (pQCD) Fragmentation functions A 1 (p, …, or Fe) A 2 (N or O) Cosmic ray Atmosphere

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

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

Momentum fraction x in the forward region

Parton Distribution Functions in the Nucleon

Motivations for studying PDFs (1)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.

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

Recent papers on unpolarized PDFs 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; (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) 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) ; hep-ph/ Alekhin S. I. Alekhin, PRD68 (2003) ; D74 (2006) BB J. Blümlein and H. Böttcher, Nucl. Phys. B774 (2007) 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. It is likely that I miss some papers! Recent activities  uncertainties  NNLO  QED  s – s  charm

Parton distribution functions are determined by fitting various experimental data.

Available data for determining PDFs (Ref. MRST, hep/ph ) Used data for MRST01 (Ref. MRST, hep/ph )

N X q p  W   –  Determination of each distribution Valence quark

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

Gluon scaling violation of F 2 jet production K. Prytz, Phys. Lett. B311 (1993) 286.

Unpolarized Parton Distribution Functions (PDFs) in the nucleon The PDFs could be obtained from Valence-quark distributions Gluon distribution / 5

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

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. CCFR, NuTeV experiments Huge Fe target (690 ton) … “Nucleonic” PDFs have been obtained by assuming that nuclear corrections are the same as those in the charged-lepton (e,  ) scattering. M. Tzanov et al. (NuTeV), Phys. Rev. D 74 (2006)

Nuclear corrections in iron (A=56, Z=26) Charged-lepton scattering Neutrino scattering Base-1 remove CCFR data incorporate deuteron corrections incorporate deuteron corrections Base-2 corresponds to CTEQ6.1M with s≠sbar include CCFR data include CCFR data Charged-lepton correction factors are applied. Charged-lepton correction factors are applied. s≠sbar 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. Large uncertainties on possible nuclear corrections I. Schienbein et al. (CTEQ), PRD 77 (2008)

Nuclear Parton Distribution Functions

EMC NMC E139 E665 q-qbar fluctuation of photon (+ recombination) Nuclear binding (+ Nucleon modification) Fermi motion of the nucleon x Explained in Saito’s talk Could affect cosmic-ray studies Nuclear modifications of structure function F 2

Experimental data: total number = 1241 (1) F 2 A / F 2 D 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) F 2 A / F 2 A ’ 293 data NMC: Be / C, Al / C, Ca / C, Fe / C, Sn / C, Pb / C, C / Li, Ca / Li (3)  DY A /  DY A’ 52 data E772: C / D, Ca / D, Fe / D, W / D E866: Fe / Be, W / Be

Functional form If there were no nuclear modification Isospin symmetry ： Take account of nuclear effects by w i (x, A) Nuclear PDFs “per nucleon” at Q 2 =1 GeV 2 (  Q 0 2 )

Comparison with F 2 Ca /F 2 D &  DY pCa /  DY pD data (R exp -R theo )/R theo at the same Q 2 points R= F 2 Ca /F 2 D,  DY pCa /  DY pD NLO analysis LO analysis

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

Fragmentation Functions

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

Momentum (energy) sum rule Favored and disfavored fragmentation functions

Experimental data for pion # of data TASSO TCP HRS TOPAZ SLD SLD [light quark] SLD [ c quark] SLD [ b quark] ALEPH OPAL DELPHI DELPHI [light quark] DELPHI [ b quark] 12,14,22,30,34, Total number of data ： 264 Typical data for pion

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

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

Our works related to this talk (1) Nuclear PDFs M. Hirai, SK, and M. Miyama, Phys. Rev. D 64 (2001) ; M. Hirai, SK, and M. Miyama, Phys. Rev. D 64 (2001) ; M. Hirai, SK, and T.-H. Nagai, Phys. Rev. C 70 (2004) ; M. Hirai, SK, and T.-H. Nagai, Phys. Rev. C 70 (2004) ; C 76 (2007) C 76 (2007) (2) Fragmentation functions M. Hirai, SK, T.-H. Nagai, and K. Sudoh, Phys. Rev. D75 (2007) M. Hirai, SK, T.-H. Nagai, and K. Sudoh, Phys. Rev. D75 (2007) (3)Hadron Physics at J-PARC SK, Nucl. Phys. A782 (2007) 442. SK, Nucl. Phys. A782 (2007) 442.

Summary Communications between cosmic-ray physicists and hadron physicists are needed for developing a reliable interaction model. 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 small x (LHC)  Nucleonic and Nuclear PDFs at large x (JLab, J-PARC, …)  Fragmentation functions (Belle, …)

The End