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Parton Distributions at High x J. P. Chen, Jefferson Lab DNP Town Meeting, Rutgers, Jan. 12-14, 2007 Introduction Unpolarized Parton Distribution at High x Polarized Parton Distributions at High x New Vista: Transversity at High x Summary

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Unpolarized and Polarized Structure Functions

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Unpolarized Parton Distributions (CTEQ6) After 40 years DIS experiments, unpolarized structure of the nucleon reasonably well understood. High x valence quark dominating

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NLO Polarized Parton Distributions (AAC06)

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Why Are PDFs at High x Important? Valence quark dominance: simpler picture -- direct comparison with nucleon structure models SU(6) symmetry, broken SU(6), diquark x 1 region amenable to pQCD analysis -- hadron helicity conservation? Clean connection with QCD, via lattice moments Input for search for physics beyond the Standard Model at high energy collider -- evolution: high x at low Q 2 low x at high Q 2 -- small uncertainties amplified -- example: HERA ‘anomaly’ (1998) Input to nuclear, high energy and astrophysics calculations

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Predictions for High x Nucleon ModelF 2 n /F 2 p d/u u/u d/d A1nA1n A1pA1p SU(6)2/31/22/3-1/305/9 Scalar diquark1/401-1/311 pQCD3/71/51111 Proton Wavefunction (Spin and Flavor Symmetric) 11 110 )( 3 2 )( 3 1 )( 3 1 )( 18 1 )( 2 1 SS SSS uud d udu u up

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Unpolarized Parton Distribution at High x and Moments of Structure Functions

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d/u Extraction from F 2 n /F 2 p No ‘free’ neutron target (life time ~ 12 minutes) -- deuteron (or 3 He) used as ‘effective’ neutron target However, deuteron is a nucleus, F2d ≠ F2p + F2n Nuclear effects (nuclear binding, Fermi motion, shadowing) obscure neutron structure information -- ‘nuclear EMC effect’

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Unpolarized Neutron to Proton ratio

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Mirror symmetry of A=3 nuclei Extract F 2 n /F 2 p from ratio of 3 He/ 3 H structure functions Super ratio R = ratio of ”EMC ratios” for 3 He and 3 H Calculated to within 1% Most systematic and theoretical uncertainties cancel Nearly free neutron target by tagging low-momentum proton from deuteron at backward angles Small p (70-100 MeV/c) Minimize on-shell extrapolation (neutron only 7 MeV off-shell) Backward angles ( pq > 110 o ) Minimize final state interactions Spectator tagging DIS from A=3 nuclei

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Unpolarized Neutron to Proton Ratio Hall A 11 GeV with HRS BONUS at Hall B 11 GeV with CLAS12

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At high x F 2 p High-x PDFs - p Scattering = dudu F 2 p - xF 3 p = 4xu F 2 p + xF 3 p = 4xu Unprecedented valence / sea separation MINER A Main INjector ExpeRiment for v-A MINERvA is a compact, fully active neutrino detector designed to study neutrino-nucleus interactions with unprecedented detail MINERvA is unique in worldwide program Opportunity for precision neutrino interaction measurements Wide range of neutrino energies MINERvA Schedule –late 2007-2008: construction begins –2009: complete construction, installation Helium target approved. H/D still need approval.

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Separated Structure Functions at Large x and Duality Data from JLab Hall C E94-110 The resonance region is, on average, well described by NNLO QCD fits. The result is a smooth transition from Quark Model Excitations to a Parton Model description, or a smooth quark-hadron transition. F2F2F2F2 FLFLFLFL F1F1F1F1

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F 2, F 1 in excellent agreement with NNLO + TM above Q 2 = 2 GeV 2 Remove known HT, the elastic, and duality works down to Q 2 = 0.5 GeV 2 The case looks different for F L F L related to the gluon contribution n = 2 Cornwall-Norton Moments F2F2F2F2 FLFLFLFL 2xF 1

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Extracting d-bar/-ubar From Drell-Yan Scattering (E866/E906) Ratio of Drell-Yan cross sections Fermilab E906/Drell-Yan will extend these measurements and reduce statistical uncertainty.

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Semi-Inclusive DIS at 11 GeV JLab x x

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Valence Quark Spin Structure A 1 at high x and flavor decomposition

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Polarized quarks as x--> 1 SU(6) symmetry: A 1 p = 5/9 A 1 n = 0 d/u=1/2 ∆u/u = 2/3 ∆d/d = -1/3 Broken SU(6) via scalar diquark dominance A 1 p 1 A 1 n 1 d/u 0 ∆u/u 1 ∆d/d -1/3 Broken SU(6) via helicity conservation A 1 p 1 A 1 n 1 d/u 1/5 ∆u/u 1 ∆d/d 1 Note that ∆q/q as x--> 1 is more sensitive to spin-flavor symmetry breaking effects than A 1

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World data for A 1 Proton Neutron

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Precision A 1 n at High x from Hall A E99-117 First precision A 1 n data at high x Extracting valence quark spin distributions Test our fundamental understanding of valence quark picture SU(6) symmetry Valence quark models pQCD (with HHC) predictions Quark orbital angular momentum Crucial input for pQCD fit to PDF PRL 92, 012004 (2004) PRC 70, 065207 (2004) Physics News Update, Science Now, Science News, Physics Today Update, APS-DNP web, …

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A 1 p /A 1 d Results from CLAS Proton Deuteron

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Naïve Extraction of Polarized Quark Distributions Combining A 1 n and A 1 p results Valence quark dominating at high x u quark spin as expected d quark spin stays negative! Disagree with pQCD model calculations assuming HHC (hadron helicity conservation) Quark orbital angular momentum Consistent with valence quark models and pQCD PDF fits without HHC constraint

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A 1 p at 11 GeV Projections for JLab at 11 GeV A 1 n at 11 GeV

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u and d at JLab 11 GeV Flavor decomposition with SIDIS Polarized Sea JLab @11 GeV

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Duality in Spin-Structure: Hall A E01-012 Results g 1 /g 2 and A 1 /A 2 ( 3 He/n) in resonance region, 1 < Q 2 < 4 GeV 2 Study quark-hadron duality in spin structure. Access even higher x region? A 1 3He (Resonance vs DIS) 1 n resonance comparison with pdfs x Q2Q2

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d 2 : Quark-gluon Correlations and Color Polarizabilities

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d 2 : color polarizability, q-g correlations Wandzura-Wilczek relation d 2 : 2 nd moment, twist-3 matrix element, q-g correlations Color polarizability, benchmark test of Lattice QCD

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Proton Results: d 2 p (Hall C and SLAC) d2pd2p Q2Q2

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Neutron Results: d 2 n (Hall A and SLAC)

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Planned d 2 n with JLab 6 GeV and 12 GeV Projections with planned 6 GeV and 12 GeV experiments Improved Lattice Calculation (QCDSF, hep-lat/0506017)

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Transversity at High x Semi-inclusive Deep Inelastic Scattering

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Transversity Three twist-2 quark distributions: Momentum distributions: q(x,Q 2 ) = q ↑ (x) + q ↓ (x) Longitudinal spin distributions: Δq(x,Q 2 ) = q ↑ (x) - q ↓ (x) Transversity distributions: δq(x,Q 2 ) = q ┴ (x) - q ┬ (x) It takes two chiral-odd objects to measure transversity Semi-inclusive DIS Chiral-odd distributions function (transversity) Chiral-odd fragmentation function (Collins function) TMDs: (without integration over P T ) Distribution functions depends on x, k ┴ and Q 2 : δq, f 1T ┴ (x, k ┴,Q 2 ), … Fragmentation functions depends on z, p ┴ and Q 2 : D, H 1 (x,p ┴,Q 2 ) Measured asymmetries depends on x, z, P ┴ and Q 2 : Collins, Sivers, … (k ┴, p ┴ and P ┴ are related) HERMES measurement on p: non-zero Collins ( +/ -) and Sivers ( +) moments COMPASS measurement on d: consistent with zero

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E06-010/06-011 Single Target-Spin Asymmetry in Semi-Inclusive n ↑ (e,e′π +/- ) Reaction on a Transversely Polarized 3 He Target Collins Sivers First neutron measurement planned at 6 GeV JLab JLab 12 GeV with large accpetance: precision measurement of transversity and tensor charge

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Summary High x is a clean region to understand valence quark structure Good progress in the last 5-10 years JLab 12 GeV will make unique contributions to high-x PDF study Unpolarized PDFs at high x d/u at high x: 3 He/ 3 H, BONUS, PV-DIS Duality, F L, neutrino reactions, sea quarks Polarized PDFs at high x A 1 at high x: valence structure, flavor decomposition d 2 : color polarizability, test Lattice QCD Transversity at high x New dimension JLab 12 GeV will make significant contributions Next decade: Complete a chapter on unpolarized and polarized PDF study at high x Open a new chapter on transversity study

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