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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
Unpolarized and Polarized Structure Functions
Unpolarized Parton Distributions (CTEQ6)• After 40 years DIS experiments, unpolarized structure of the nucleon reasonably
well understood.• High x valence quark dominating
NLO Polarized Parton Distributions (AAC06)
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
Predictions for High x
Nucleon Model F2n/F2
p d/u u/u d/d A1n A1
p
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
Proton Wavefunction (Spin and Flavor Symmetric)
11
110
)(3
2)(
3
1
)(3
1)(
18
1)(
2
1
SS
SSS
uuduud
uduuduudup
Unpolarized Parton Distribution at High x
and Moments of Structure Functions
d/u Extraction from F2n/F2
p
• 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’
Unpolarized Neutron to Proton ratioUnpolarized Neutron to Proton ratio
Unpolarized Neutron to Proton ratioUnpolarized Neutron to Proton ratio
• Mirror symmetry of A=3 nuclei Extract F2
n/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 (pq> 110o)
Minimize final state interactions
Spectator tagging
DIS from A=3 nuclei
Unpolarized Neutron to Proton Ratio
Hall A 11 GeV with HRSBONUS at Hall B 11 GeV with CLAS12
At high x
F2p
F2p
High-x PDFs- p Scattering
=d
u
F2p - xF3
p = 4xu
F2p + xF3
p = 4xu Unprecedented valence / sea separation
MINERAMain 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.
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.
FF22
FFLL
FF11
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
n = 2 Cornwall-Norton Momentsn = 2 Cornwall-Norton Moments
FF22
FFLL
2xF2xF11
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.
Semi-Inclusive DIS at 11 GeV JLab
x
x
Valence Quark Spin Structure
A1 at high x and flavor decomposition
Polarized quarks as x--> 1
SU(6) symmetry: A1
p = 5/9 A1n = 0 d/u=1/2
∆u/u = 2/3 ∆d/d = -1/3 Broken SU(6) via scalar diquark
dominance
A1p 1 A1
n 1 d/u 0 ∆u/u 1 ∆d/d -1/3
Broken SU(6) via helicity conservation
A1p 1 A1
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 A1
World data for A1 World data for A1
Proton Neutron
Precision A1n at High x from Hall A
E99-117
• First precision A1
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, …
A1p/A1
d Results from CLAS
xbj
A 1p
HF perturbed QM
World Data parm Q2 = 10 GeV2
Spin 3/2 suppression Helicity 3/2 suppression
Symmetric Q Wave function
SLAC - E143
SMC
HERMES
SLAC - E155
CLAS-EG1b Q2 = 1.0 - 4.52 GeV2
SU(6)
pQCD
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1xbj
A 1d ( D
-sta
te c
orre
cted
) HF perturbed QM
World Data Parm + d WF Q2 = 4.2 GeV2
World Data parm Q2 = 10 GeV2
Spin 3/2 suppression
Helicity 3/2 suppression
Symmetric Q Wave function suppression
SLAC - E143
SMC
HERMES
SLAC - E155
CLAS-EG1b Q2 = 1.0 - 4.52 GeV2
SU(6)
pQCD
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Proton
Deuteron
Naïve Extraction of Polarized Quark Distributions
• Combining A1n and A1
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
A1p at 11 GeV
Projections for JLab at 11 GeV
A1n at 11
GeV
u and d at JLab 11 GeV
Flavor decomposition with SIDISFlavor decomposition with SIDIS
Polarized Sea
JLab @11 GeV
Duality in Spin-Structure: Hall A E01-012 Results
• g1/g2 and A1/A2 (3He/n) in resonance region, 1 < Q2 < 4 GeV2
• Study quark-hadron duality in spin structure. • Access even higher x region?
A13He (Resonance vs DIS) 1
n resonance comparison with pdfs
xQ2
d2: Quark-gluon Correlations and Color Polarizabilities
d2: color polarizability, q-g correlations
Wandzura-Wilczek relation
• d2: 2nd moment, twist-3 matrix element, q-g correlations
• Color polarizability, benchmark test of Lattice QCD
1
21
21
22 ),(),(),(
x
WW
y
dyQygQxgQxg
1
0
22
21
2
1
0
22
22
222
)],(3),(2[
)],(),([3)(
dxQxgQxgx
dxQxgQxgxQd WW
Proton Results: d2p (Hall C and SLAC)
d2p
Q2
Neutron Results: d2n (Hall A and SLAC)
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)
Transversity at High x
Semi-inclusive Deep Inelastic Scattering
Transversity• Three twist-2 quark distributions:
• Momentum distributions: q(x,Q2) = q↑(x) + q↓(x)• Longitudinal spin distributions: Δq(x,Q2) = q↑(x) - q↓(x)• Transversity distributions: δq(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 : δq, 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 (+/-) and Sivers (+) moments• COMPASS measurement on d: consistent with zero
E06-010/06-011 Single Target-Spin Asymmetry in Semi-Inclusive n↑(e,e′π+/-) Reaction on a Transversely Polarized 3He Target
Collins
Sivers
First neutron measurement planned at 6 GeV JLab
JLab 12 GeV with large accpetance: precision measurement of transversity and tensor charge
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
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