Parton Distributions at High x

1
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

2
Unpolarized and Polarized Structure Functions

3
Unpolarized Parton Distributions (CTEQ6)

• After 40 years DIS experiments, unpolarized
  structure of the nucleon reasonably well
  understood.
• High x ? valence quark dominating

4
NLO Polarized Parton Distributions (AAC06)

5
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 Q2 ? low x at
  high Q2
• -- small uncertainties amplified
• -- example HERA anomaly (1998)
• Input to nuclear, high energy and astrophysics
  calculations

6
Predictions for High x
Proton Wavefunction (Spin and Flavor Symmetric)

Nucleon Model F2n/F2p d/u Du/u Dd/d A1n A1p
SU(6) 2/3 1/2 2/3 -1/3 0 5/9
Scalar diquark 1/4 0 1 -1/3 1 1
pQCD 3/7 1/5 1 1 1 1
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Unpolarized Parton Distribution at High x
and Moments of Structure Functions
8
d/u Extraction from F2n/F2p

• No free neutron target (life time 12 minutes)
• -- deuteron (or 3He) 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

9
Unpolarized Neutron to Proton ratio
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Unpolarized Neutron to Proton ratio
DIS from A3 nuclei
Spectator tagging

• Mirror symmetry of A3 nuclei
• Extract F2n/F2p from ratio of 3He/3H structure
  functions
• Super ratio
• R ratio of EMC ratios for 3He and 3H
  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 (qpqgt 110o)
• Minimize final state interactions

11
Unpolarized Neutron to Proton Ratio
Hall A 11 GeV with HRS
BONUS at Hall B 11 GeV with CLAS12
12
High-x PDFsn - p Scattering
MINERnAMain INjector ExpeRiment for v-A
At high x
F2np - xF3np 4xu
F2np F2np
d u

F2np xF3np 4xu
Unprecedented valence / sea separation

• 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
F2

• 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.

F1
FL
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n 2 Cornwall-Norton Moments

• F2, F1 in excellent agreement with NNLO TM
  above Q2 2 GeV2
• Remove known HT, the elastic, and duality works
  down to Q2 0.5 GeV2
• The case looks different for FL
• FL related to the gluon contribution

F2
2xF1
FL
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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.

16
Semi-Inclusive DIS at 11 GeV JLab
x
x
17
Valence Quark Spin Structure
A1 at high x and flavor decomposition
18
Polarized quarks as x--gt 1
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World data for A1
Proton
Neutron
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Precision A1n at High x from Hall AE99-117

• First precision A1n 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,

21
A1p/A1d Results from CLAS

Proton
Deuteron
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Naïve Extraction of Polarized Quark Distributions

• Combining A1n and A1p 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

23
Projections for JLab at 11 GeV
A1n at 11 GeV
A1p at 11 GeV
24
Flavor decomposition with SIDIS
Du and Dd at JLab 11 GeV
Polarized Sea
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Duality in Spin-Structure Hall A E01-012 Results

• g1/g2 and A1/A2 (3He/n) in resonance region,
  1 lt Q2 lt 4 GeV2
• Study quark-hadron duality in spin structure.
• Access even higher x region?

A13He (Resonance vs DIS)
G1n resonance comparison with pdfs
Q2
x
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d2 Quark-gluon Correlations and Color
Polarizabilities

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d2 color polarizability, q-g correlations

• d2 2nd moment, twist-3 matrix element, q-g
  correlations
• Color polarizability, benchmark test of Lattice
  QCD

• Wandzura-Wilczek relation

28
Proton Results d2p (Hall C and SLAC)
d2p
Q2
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Neutron Results d2n (Hall A and SLAC)
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Planned d2n 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,Q2) q?(x) q?(x)
• Longitudinal spin distributions ?q(x,Q2) q?(x)
  - q?(x)
• Transversity distributions dq(x,Q2) 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 PT)
• Distribution functions depends on x, k- and Q2
  dq, f1T- (x,k- ,Q2),
• Fragmentation functions depends on z, p- and Q2
  D, H1(x,p- ,Q2)
• Measured asymmetries depends on x, z, P- and Q2
  Collins, Sivers,
• (k-, p- and P- are related)
• HERMES measurement on p non-zero Collins (p/p-)
  and Sivers (p) 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'p/-) Reaction on a
Transversely Polarized 3He Target
Collins
First neutron measurement planned at 6 GeV JLab
JLab 12 GeV with large accpetance precision
measurement of transversity and tensor charge
Sivers
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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 3He/3H, BONUS, PV-DIS
• Duality, FL, neutrino reactions, sea quarks
• Polarized PDFs at high x
• A1 at high x valence structure, flavor
  decomposition
• d2 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