Post on 09-Jan-2016
description
Transverse Spin and TMDs
Jian-ping Chen, Jefferson LabEIC Workshop at INT09, Oct.19-23, 2009
Introduction: why do we care about transverse structure?
Current status: What have we learned?
Near-future perspective: What do we expect before EIC?
Ultimate goal: What can EIC contribute?
Acknowledgement: Some plots from H. Avagyan, H. Gao, X. Jiang, X. Qian, …
Introduction
Why do we care about transverse structure?
Strong Interaction and QCD• Strong interaction, running coupling ~1 -- QCD: accepted theory for strong interaction -- asymptotic freedom (2004 Nobel) perturbation calculation works at high energy -- interaction significant at intermediate energy quark-gluon correlations -- interaction strong at low energy (nucleon size)
confinement
theoretical tools: pQCD (co-linear factorization), OPE, Lattice QCD, AdS/CFT, …
• A major challenge in fundamental physics: Understand QCD in all regions, including strong
(confinement) region E
s
Nucleon (Hadron) Structure• Colors are confined in hadronic system
• Hadron: ideal lab to study QCD
• Nucleon = u u d + sea + gluons• Mass, charge, magnetic moment, spin, axial charge, tensor charge • Decomposition of each of the above fundamental quantities
Mass: ~1 GeV, but u/d quark mass only a few MeV each! Momentum: total quarks only carry ~ 50% Spin: ½, total quarks contribution only ~30% Spin Sum Rule
Orbital Angular Momentum Relations to GPDs and TMDs Tensor charge Transverse sum rule?
• Partons and gluon field are in-separable • Multi-parton correlations are important• Beyond co-linear factorization• Multi-dimensional structure and distributions Transverse dimension is crucial for complete understanding of nucleon
structure and QCD, and help shed light in understanding confinement
Three Decades of Spin Structure Study• 1980s: EMC (CERN) + early SLAC quark contribution to proton spin is very small = (12+-9+-14)% ! ‘spin crisis’ (Ellis-Jaffe sum rule violated)
• 1990s: SLAC, SMC (CERN), HERMES (DESY) = 20-30% the rest: gluon and quark orbital angular momentum
A+=0 (light-cone) gauge (½) + Lq+ G + Lg=1/2 (Jaffe)
gauge invariant (½) + Lq + JG =1/2 (Ji) A new decomposition (X. Chen, et. al.) Bjorken Sum Rule verified to <10% level
• 2000s: COMPASS (CERN), HERMES, RHIC-Spin, JLab, … : ~ 30%;G probably small?, orbital angular momentum important? Transversity and Transverse-Momentum Dependent Distributions Generalized Parton Distributions Orbital angular Momentum
Current Status
What have we learned?
Transversity and TMDs
• 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 integrating 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)
“Leading-Twist” TMD Quark Distributions
Quark
Nucleon
Unpol.
Long.
Trans.
Unpol. Long. Trans.
Multi-dimension Distributions
GPDs/IPDsH(x,rT),E(x,rT),..
d2kT
d2kT
TMD PDFs f1u(x,kT),
.. h1u(x,kT)
Gauge invariant definition (Belitsky,Ji,Yuan 2003)Universality of kT-dependent PDFs (Collins,Metz 2003)Factorization for small kT. (Ji,Ma,Yuan 2005)
Wpu(k,rT) “Mother” Wigner distributions
d2 r T
PDFs f1u(x), .. h1
u(x)
quark polarization
Access TMDs through Hard Processes
Partonic scattering amplitude
Fragmentation amplitude
Distribution amplitude
proton
lepton lepton
pionproton
proton lepton
antilepton
Drell-Yan
BNLJPARC
FNAL
EIC
SIDIS
electron
positron
pion
pion
e–e+ to pions
s=20 GeV, pT=0.5-2.0 GeV/c�0 – E704, PLB261 (1991) 201.�+/- - E704, PLB264 (1991) 462.
Xpp Single Spin Asymmetries in
Large transverse single-spin effects were observed at RHIC, at much higher CM energies.
• In collinear picture, the QCD predict small SSAs with transversely polarized protons colliding at high energies.
Kane, Pumplin, Repko ‘78
FermiLab E-704
FNAL
BELLE: Collins function measurements
BELLE: Asymmetries in e+e-→h1h2X (H┴1 H┴
1)_
Efremov et al. Phys.Rev.D. 73,094025 (2006)
positivity limit1
Belle detectorKEKB
Asymmetric collider8GeV e- + 3.5GeV e+
Direct indication of non-0 Collins fragmentation !
Separation of Collins, Sivers and pretzelocity effects through angular dependence in SIDIS
1( , )
sin( ) sin( )
sin(3 )
l lUT h S
h SSiverCollins
Pretzelosi
UT
tyU
sUT h S
h ST
N NA
P N
A
A
N
A
1
1 1
1
1 1
sin( )
sin(3 )
sin( )Co
PretzelosityU
SiversUT
llins
T h S T
h S
UT
UT h S
TU
UT
TA
H
f
A
D
A h H
h
AUTsin() from transv. pol. H target
`Collins‘ moments
• Non-zero Collins asymmetry
• Assume q(x) from model, then
H1_unfav ~ -H1_fav
• H1 from Belle (arXiv:0805:2975)
`Sivers‘ moments
•Sivers function nonzero (+) orbital angular momentum of quarks
•Regular flagmentation functions
Collins Moments for Kaon
S. Gliske’s talk at DNP09
Sivers Moments for Kaon
Collins asymmetries from COMPASS deuteron
Phys. Lett. B 673 (2009) 127-135
u and d cancellation?
Sivers asymmetries from COMPASS deuteron
Transversity Distributions
A global fit to the HERMES p, COMPASS d and BELLE e+e- data by the Torino group (Anselmino et al.).
PRD 75, 054032 (2007)
PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008 F. BradamanteF. Bradamante
Collins asymmetry – proton datacomparison with M. Anselmino et al. predictionsPRD 75, 054032 (2007)
Franco BradamanteTransverse2008, Beijing
PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008PKU-RBRC Workshop on Transverse Spin Physics, June 30, 2008 F. BradamanteF. Bradamante
Sivers asymmetry – proton datacomparison with the most recent predictions from M. Anselmino et al. (arXiv 0805.2677) Franco Bradamante
Transverse2008, Beijing
2-d (x-PT) Collins Moments
S. Gliske’s talk at DNP09
2-d (x-PT) Sivers Moments
Other TMDs
xB
COMPASS 2002-2004arXiv:0705.2402
Pretzelocityg1T
E06-010 Single Target-Spin Asymmetry in Semi-Inclusive n↑(e,e′π+/-) Reaction on a Transversely Polarized 3He Target
Collins
Sivers
First measurement on the neutron with polarized 3He
With good PID, Kaon data for free
Collins, Sivers, Pretzelocity and g1
T
7 PhD Students
Completed data taking 2/09
Exceeded PAC approved goal
Summary of Current Status
• Large single spin asymmetry in pp->X• Collins Asymmetries
- sizable for the proton (HERMES and COMPASS) large at high x,- and has opposite sign unfavored Collins fragmentation as large as favored (opposite sign)? - consistent with 0 for the deuteron (COMPASS)
• Sivers Asymmetries - non-zero for + from proton (HERMES), consistent with zero (COMPASS)? - consistent with zero for - from proton and for all channels from deuteron - large for K+ ?
• Collins Fragmentation from Belle
• Global Fits/models by Anselmino et al., Yuan et al. and …
• First neutron measurement from Hall A 6 GeV (E06-010)
• Very active theoretical and experimental study RHIC-spin, JLab (6 GeV and 12 GeV), Belle, FAIR, J-PARC, … EIC
Near-future Perspective
What do we expect before EIC?
Collins and Sivers SSAs with CLAS @ 6 GeV JLab
CLAS with a transversely polarized proton target will allow measurements of Collins and Sivers asymmetries in the large-x region
Anselmino et al Vogelsang & YuanSchweitzer et al
Precision Study of Transversity and TMDs
• From exploration to precision study• Transversity: fundamental PDFs, tensor charge• TMDs provide 3-d structure information of the nucleon• Learn about quark orbital angular momentum• Multi-dimensional mapping of TMDs
• 3-d (x,z,P┴ )
• Q2 dependence • Multi-facilities, global effort
• Precision high statistics• high luminosity and large acceptance
CHL-2CHL-2
Upgrade magnets Upgrade magnets and power suppliesand power supplies
Enhance equipment in Enhance equipment in existing hallsexisting halls
6 GeV CEBAF1112Add new hallAdd new hall
12 GeV Upgrade Kinematical Reach
• Reach a broad DIS region • Precision SIDIS for
transversity and TMDs• Experimental study/test of
factorization • Decisive inclusive DIS
measurements at high-x• Study GPDs
Solenoid detector for SIDIS at 11 GeVProposed for PVDIS at 11 GeV
FGEMx4
LGEMx4 LSGas Cherenkov
HG
Aerogel
GEMx2
SH
PS
Z[cm]
Y[cm
]
Yoke
Coil
3HeTarget
3-d Mapping of Collins/Sivers Asymmetries at JLab 12 GeV
With A Large Acceptance Solenoid Detector (L=1036)
• Both + and -
• For one z bin
(0.5-0.55)
• Will obtain 8
z bins (0.3-0.7)
• Upgraded PID for K+ and K-
Power of SOLid
Discussion• Unprecedented precision 3-d mapping of SSA
• Collins and Sivers• +, - and K+, K-
• Study factorization with x and z-dependences • Study PT dependence• With similar quality SIDIS data on the proton and data from e+e-
• extract transversity and fragmentation functions for both u and d quarks• determine tensor charge• study TMDs for valence quarks• study quark orbital angular momentum
• Combining with world data, especially data from high energy facilities (future EIC)• study Q2 evolution (need theoretical development)• sea and gluon TMDs (more surprises are waiting?)
• Global efforts (experimentalists and theorists), global analysis• Precision information on multi-dimension nucleon structure
Ultimate Goal
What can EIC contribute?
Transverse Structure Study with EIC
• Much large kinematical reach Much higher Q2 range, clearly into hard scattering region
Wide Q2 range, study Q2 evolution and high-twist effects Much higher PT range, into high PT region and overlap region Much lower x range, study sea TMDs Reach current fragmentation region for flavor study (pions, Kaons, nucleons, …)
• Ultimate understanding of nucleon structure with complete 4-d (x,z,PT,Q2) mapping Model independent extractions of transversity and TMDs through global analysis Determination of tensor charge
• Study, test and understand QCD• Special universality: Sivers(SIDIS) = - Sivers(Drell-Yan)• Study QCD beyond co-linear approximation, study parton correlations• Shed light on QCD in strong region (confinement)
Sivers effect: Pion electroproduction100 days at L=1033 MEIC (4x60 GeV) (Harut Avakian)
Sivers effect: Kaon electroproduction
EIC
CLAS12
(Harut Avakian)
Summary
• Why transverse dimension? Complete understanding of nucleon structure Transverse momentum dependence - strong quark-gluon correlations Key to understanding QCD in all regions, including confinement region
• What have we learned? Non-zero Collins and Sivers asymmetries for pions and Kaons Non-favored Collins fragmentation functions as important as favored ones HERMES and COMPASS Collins asymmetries consistent, HERMES and COMPASS Sivers results on the proton might be different? First measurements of Collins and Sivers asymmetry on the neutron Explorations on other TMDs: Boer-Mulders, Pretzelocity and g1
T
Model dependent extractions of transversity, Sivers and Collins functions • What do we expect before EIC?
• Precision 3-d (x,z,PT) mapping of TMDs • What can EIC contribute?
• Ultimate coverage in kinematics, complete 4-d (x,z,PT,Q2) mapping• Lead to breakthrough in full understanding of nucleon structure and QCD