Possible studies of structure functions at JLab Shunzo Kumano High Energy Accelerator Research Organization (KEK) Graduate University for Advanced Studies (GUAS) http://research.kek.jp/people/kumanos/ Our codes are available for Nuclear PDFs: http://research.kek.jp/people/kumanos/nuclp.html Polarized PDFs: http://spin.riken.bnl.gov/aac/ Fragmentation functions: http://research.kek.jp/people/kumanos/ffs.html Q2 evolutions: http://research.kek.jp/people/kumanos/program.html Workshop on the Jefferson Laboratory Upgrade to 12 GeV Sept. 14 - Nov. 20, 2009, INT, Seattle, USA http://www.int.washington.edu/PROGRAMS/09-3.html November 5, 2009 1

Outline Three different topics. I will stop when time runs out. 1. Nuclear modifications of R = FL / FT at large x We (M. Ericson and SK) insist that nuclear modifications of R = FL / FT should exist at large x. 2. From nucleon-spin crisis to tensor-structure crisis (?) Tensor structure functions of spin-1 hadrons (b1, b2, …). 3. ∆ g(x) determination by accurate g1 measurements Accurate g1 by JLab E07-011  NLO gluon term in g1 could be determined.

Nuclear modifications of R = FL / FT at large x Ref. M. Ericson and SK, Phys. Rev. C 67 (2003) 022201.

' Nuclear effect on R = FL / FT by HERMES L, T X p RA /RD Q2 (GeV2) HERMES, K. Ackerstaff el al., PL B 475 (2000) 386; Erratum, PL B567 (2003) 339 [hep-ex/0210067; hep-ex/0210068]. p X ' L, T (2000) (2003) Q2 (GeV2) RA /RD

Nuclear effects on R by CCFR/NuTeV U.-K. Yang et al., PRL 87 (2001) 251802. CCFR HERMES SLAC note No significant deviation is measured from the nucleon case ( ). No large nuclear modification of R is observed in +Fe ! (note: CCF/NuTeV target is Fe)

M. Ericson and SK, Phys. Rev. C 67 (2003) 022201  Submitted (Nov. 30, 2002) just after the HERMES correction paper (Oct. 31, 2002).  Nuclear modifications of transverse-longitudinal ratio do exist in medium and large-x regions, although the modifications do not seem to exist at small x within experimental errors according to the revised HERMES paper.  Mechanisms (1) Transverse nucleon motion  T-L admixture of nucleon structure functions. (2) Binding and Fermi-motion effects in the spectral function.

Formalism Projection operators of W1A and W2A Longitudinal and transverse components

Formalism (continued)

Results R x x admixture effects 10 GeV Q = 100 10 GeV Q = 100 0.1 0.2 0.3 0.4 0.6 0.8 1 x R 14 N 10 GeV 2 Q = 100 0.95 1 1.05 1.1 0.2 0.4 0.6 0.8 x without L-T mixing 10 GeV 2 Q = 100 admixture effects

After the HERMES (CCFR/NuTeV) re-analysis, people tend to lose interest in the nuclear effect on R. However, we claim that nuclear modification should exist in medium and large-x regions. Physical origins  transverse-longitudinal admixture due to the transverse Fermi motion  binding and Fermi motion effects in the spectral function In the kinematical region of our prediction, data does not exist. Need future experimental investigations at JLab, EIC,  factory, …

Almost same for p an d, but at 0.04 < x < 0.32. JLab measurements in 2007 • V. Tvaskis et al., PRL 98 (2007) 142301. • Lingyan Zhu (Hampton Univ), personal communications (2009). Badelek, Kwiecinski, Stasto (1997) E99-118 MRST-2004 GRV-1995 Almost same for p an d, but at 0.04 < x < 0.32. In any case, nuclear modifications should be small for the deuteron. Importance of future JLab measurements for heavier nuclei, especially at large x (>0.4).

From nucleon-spin crisis to tensor-structure crisis (?) Refs. F. E. Close and SK, Phys. Rev. D 42 (1990) 2377, M. Hino and SK, Phys. Rev. D 59 (1999) 094026; D 60 (1999) 054018, SK and M. Miyama, Phys. Lett. B 497 (2000) 149, T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.

References on tensor structure function b1 Theoretical formalism for polarized electron-deuteron deep inelastic scattering P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571. [ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ] HERMES experimental result A. Airapetian et al., Phys. Rev. Lett. 95 (2005) 242001. Our works Sum rule for b1 F. E. Close and SK, Phys. Rev. D 42 (1990) 2377. Projections to F1, F2, g1, g2, b1, …, b4 from W  T.-Y. Kimura and SK, Phys. Rev. D 78 (2008) 117505.

Motivation  Spin structure of the spin-1/2 nucleon Nucleon spin puzzle: This issue is not solved yet, but it is rather well studied theoretically and experimentally.  Spin-1 hadrons (e.g. deuteron) Tensor-structure puzzle (???) There are some theoretical studies especially on tensor structure in electron-deuteron deep inelastic scattering.  HERMES experimental results A few investigations have been done for polarized proton-deuteron processes.  J-PARC, COMPASS, U70, GSI-FAIR, RHIC … experiment ?

Structure function b1 in a simple example Spin-1 particles (deuteron, mesons) b1 = 0 b1  0: New field of high-energy spin physics with orbital angular momenta. only in S-wave The b1 probes a dynamical aspect of hadron structure beyond simple expectations of a naive quark model. Description of tensor structure by quark-gluon degrees of freedom

Electron scattering from a spin-1 hadron P. Hoodbhoy, R. L. Jaffe, and A. Manohar, NP B312 (1989) 571. [ L. L. Frankfurt and M. I. Strikman, NP A405 (1983) 557. ]

Projections to F1, F2, …, b4 from W T.-Y. Kimura and SK, PRD 78 (2008) 117505.

Structure Functions Parton Model

Sum rule for b1 Elastic amplitude in a parton model F.E.Close and SK, PRD42, 2377 (1990). Elastic amplitude in a parton model

Macroscopically If the sum-rule violation is shown by experiment, it suggests antiquark tensor polarization.

HERMES results on b1 deuteron positron 27.6 GeV/c A. Airapetian et al. (HERMES), PRL 95 (2005) 242001. deuteron positron 27.6 GeV/c Drell-Yan experiments probe these antiquark distributions.

Actual experimental proposals at J-PARC: P04, P24 Antiquark distributions  +  –  q E866 E906 J-PARC  It should be possible to use polarized proton-deuteron Drell-Yan processes to measure the tensor polarized distributions.

References for tensor structure in Drell-Yan • General formalism for polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons M. Hino and SK, Phys. Rev. D59 (1999) 094026. • Parton-model analysis of polarized Drell-Yan processes M. Hino and SK, Phys. Rev. D60 (1999) 054018. • An application: Possible extraction of polarized light-antiquark distributions from Drell-Yan SK and M. Miyama, Phys. Lett. B497 (2000) 149. Comments on the situation • There was a feasibility study for polarized deuteron beam at RHIC: E. D. Courant, BNL-report (1998). • No actual experimental progress with hadron facilities. • Future: J-PARC, COMPASS, U70, GSI-FAIR, RHIC, …

Spin asymmetries in the parton model Unpolarized cross section Spin asymmetries

Possibly, opening of tensor-structure crisis at JLab!? Possible JLab measurements HERMES (2005) See P. Hoodbhoy et al., NP B312 (1989) 571. Possible JLab measurements in this x region. • HERMES data have large errors  Important contribution from JLab. See also a theoretical model by G. A. Miller, in Topical Conference on Electronuclear physics with Internal Targets, edited by R. G. Arnold (World Scientific, 1990). Possibly, opening of tensor-structure crisis at JLab!?

Determination of gluon polarization by accurate g1 measurements Refs. AAC (Asymmetry Analysis Collaboration), Y. Goto et al., Phys. Rev. D 62 (2000) 034017; M. Hirai, SK, N. Saito, Phys. Rev. D 69 (2004) 054021; 74 (2006) 014015; M. Hirai, SK, Nucl. Phys. B 813 (2009) 106.

Nucleon Spin Nucleon Spin: Naïve Quark Model QCD Sea-quarks and gluons? Orbital angular momenta ? Electron / muon scattering Almost none of nucleon spin is carried by quarks! Recent data indicate DG is small at x ~ 0.1. Future experiments Nucleon Spin:

F. Kunne (COMPASS), AIP Conf. Proc. 1149 (2009) 321. Gluon polarization from lepton scattering F. Kunne (COMPASS), AIP Conf. Proc. 1149 (2009) 321.

Gluon polarization from RHIC π0 production (Torii’s talk at Pacific-Spin05) Parton distribution functions Parton interactions Fragmentation functions Gluonic processes dominate. Determination of ∆g however with uncertainties of gluon fragmentation functions. Uncertainty range of gluon fragmentation functions in LO. (See the next page.) In the NLO, the range is smaller.

Comparison of fragmentation functions in pion (KKP) Kniehl, Kramer, Pötter (AKK) Albino, Kniehl, Kramer (HKNS) Hirai, Kumano, Nagai, Sudoh (DSS) de Florian, Sassot, Stratmann NLO • Gluon and light-quark fragmentation functions have large uncertainties, but they are within the uncertainty bands. The functions of KKP, Kretzer, AKK, DSS, and HKNS are consistent with each other. All the parametrizations agree in charm and bottom functions. M. Hirai, SK, T.-H. Nagai, K. Sudoh, PRD75 (2007) 094009. A code is available at http://research.kek.jp/people/kumanos/ffs.html

AAC codes for polarized PDFs: http://spin.riken.bnl.gov/aac/ Global analyses of polarized PDFs: Asymmetry Analysis Collaboration (AAC) AAC codes for polarized PDFs: http://spin.riken.bnl.gov/aac/ 2000 version (AAC00) Y. Goto et al., PRD 62 (2000) 034017. - Q2 dependence of A1, positivity - q at small and large x   issue 2004 version (AAC03) M. Hirai, SK, N. Saito, PRD 69 (2004) 054021. - uncertainty estimation (very large g uncertainty, impact of accurate g1p (E155)) - error correlation between g and q 2006 version (AAC06) M. Hirai, SK, N. Saito, PRD 74 (2006) 014015. - include RHIC-Spin 0 (g uncertainty is significantly reduced) - g at large x ? (from Q2 difference between HERMES and COMPASS) - g < 0 solution 2008 version (AAC08) M. Hirai, SK, NPB 813 (2009) 106. - impact of g by JLab E07-011 ? (g uncertainty could be significantly reduced.) Today’s talk

General method for determining polarized PDFs Leading Order (LO) Next to Leading Order (NLO) Unpolarized PDFs

Constraint on ∆ g(x) from current g1 data

Gluon polarization at large x AAC, PRD74 (2006) 014015: Analysis without higher-twist effects NLO This term is terminated. CG=0 x=0.001 x=0.3 x=0.05

However, it may be higher-twist effect. LSS, PRD73 (2006) 034023. Leading Twist (LT) Higher Twist (HT) LT fit LT+HT fit LT+HT fit, only LT term is shown At this stage, we cannot conclude that the difference between the HERMES and COMPASS data should be 100% HT or HT+g(large x)>0, or 100% g(large x)>0 effects.

Obtained polarized PDFs by AAC06 Gluon polarization tends to be positive at large x.

Constraint on ∆ g(x) from future g1 data: Effects of E07-011 at JLab 12 GeV

3 data sets for global analyses of polarized PDFs Current DIS (g1) RHIC p0 (run 5) JLab E07-011 (g1) A Included — B C Expected E07-011 data Set A: Only DIS data for the determination of polarized PDFs [Dg(x)] Set B: Effects of collider data sets p0 production [Run-5 PHENIX, PRD76, 051106R (2007)] Set C: Effect of DIS accurate g1 data by JLab E07-011. g1 measurements [E. Brash, et al., JLab experiment E07-011; X. Jiang, personal communications.] 38

Effects of expected JLab E07-011 data “positive” “node” x Two initial functions for∆ g(x): positive, node Positive Node Gluon Reduction of uncertainties for ∆ g(x) by E07-011 Antiquark

∆ g(x) with PHENIX run-5 or JLab E07-011 data Note: π0 data are from run-5 although it may not be a good idea to compare future data with past ones. Significant improvements JLab-E07-011 is comparable to RHIC run-5 π0 in determining ∆ g(x) if gluon fragmentation errors are neglected.

Why such a large improvement of ∆ g(x) by E07-011 data?

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