Spin Structure: Puzzles and Progress

1
Spin Structure Puzzles and Progress

• J. P. Chen, Jefferson Lab
• Hall A Collaboration Meeting, Jan. 4-5, 2007

• Introduction Spin Crises or Puzzles
• Spin Sum Rules (Generalized) GDH, Bjorken,
  B-C,
• Polarizabilities Spin (dLT puzzle), Color
  (q-g correlations)
• Higher-twist Effects (q-g, q-q correlations)
• Duality in Spin Structure
• Polarized Parton Distributions at High-x
• New Vista Transversity and TMDs
• Summary

2
Nucleon Structure and QCD

• Success of the Standard Model
• electro-weak and QCD in high energy
  (short distance) region tested
• Major challenges
• -- understand QCD in the strong
  interaction region (distance of the nucleon size)
• -- understand the nucleon structure
• Strong interaction, running coupling 1
• -- asymptotic freedom (2004 Nobel)
• perturbation calculation works at
  high energy
• -- interaction significant at intermediate
  energy
• quark-gluon correlations
• -- confinement
• interaction strong at low energy
• coherent hadron
• -- Chiral symmetry
• -- theoretical tools pQCD, OPE, Lattice
  QCD, ChPT
• Spin Structure Study new dimensions
• -- study QCD and nucleon structure

3
Spin and Magnetic Moment (of electron)

• 1921 Otto Stern and Walther Gerlach
• Ag molecular-beam passing through
  inhomogeneous magnetic field
• split into two beams
• Ag atom has a magnetic moment
• Bohr magneton of the electron me
  e?/2mec
• 1925 Uhlenbeck and Goudsmit
• spin internal property, like angular momentum
• electron spin Se1/2 ? two
  eigenstates - 1/2
• Dirac
• relativistic effect spin ?? magnetic moment
• electron is point-like particle (no internal
  structure observed so far)

4
Anomalous Magnetic Moment (of Proton)

• 1933 Otto Stern
• Magnetic moment of the proton
• -- expected mpe?/2mpc (since
  Sp1/2)
• -- measured mpe?/2mpc(1kp) ! first
  spin crisis
• anomalous magnetic moment (a.m.m) kp 1.5
  - 10
• 1943 Nobel Prize awarded to Stern
• for development of the molecular beam
  method and
• the discovery of the magnetic moment of
  protons
• now kp1.792847386 -
  0.000000063
• and kn-1.91304275 -
  0.00000045

5
A.M.M and Its Implications

• Anomalous magnetic moment is an evidence for
  an internal structure
• ? finite size
• Finite size ? Form factors
• Dirac form factor normal relativistic
  effect
• Pauli form factor relate to a.m.m. part
• Finite size ? ? Excitation spectrum
• GDH Sum Rule
• relates a.m.m. to integral of excitation
  spectrum

6
Theoretical Explanation of A.M.M.

• 1930s-1950s Pion cloud models
• kp/kn -1/7 too small
• 1960s Quark models
• SU(3)color x SU(6)spin-flavor Symmetry
• kp/kn -1.5 very close to
  experiment -1.46
• small corrections due to orbital angular
  momentum
• 1990s Lattice QCD
• kp1.85-0.22, kn -1.44-0.11
• 2000s multi-dimension structure of nucleon
• A.M.M lt -- gt related to GPDs, TMDs
• through quark orbital
  angular momentum

7
Spin Crisis or Spin Puzzle

• 1980s EMC (CERN) early SLAC (E80/E130)
• quark contribution to proton spin is very
  small
• DS (12-9-14) ! spin
  crisis
• (Ellis-Jaffe sum rule violated)
• 1990s SLAC (E142/E143/E154/E155), SMC (CERN),
  HERMES (DESY)
• DS 20-30
• the rest gluons (DG) and quark orbital
  angular momentum (L)
• (½)DS DG L 1/2
• Bjorken Sum Rule verified to 5-10 level
• 2000s COMPASS (CERN), RHIC-Spin, HERMES, JLab,
  
• DS 30 DG small, L is probably
  significant
• GDH and B-C sum rules, spin polarizabilities
• Higher-twist effects q-g correlations
• Transverse spin

8

9

F2 2xF1 g2 0
10
Unpolarized and Polarized Structure functions

11
Unpolarized Parton Distributions (CTEQ6)

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

12
NLO Polarized Parton Distributions (AAC06)

13
JLab Spin Structure Experiments

• Inclusive, Low-Intermediate Q2
• JLab Hall A neutron/3He, longitudinal and
  transverse
• Generalized GDH, E94-110, Q2 range 0.1 - 1 GeV2
• Small Angle GDH, E97-110, Q2 range 0.02 0.3
  GeV2
• E97-113 g2n at Q2 of 0.5-1.5 GeV2, higher-twist
• E99-117 A1n at high x,
• Spin Duality (E01-012) Q2 from 1-4 GeV2
• JLab Hall B proton/deuteron, longitudinal
• EG1a/EG1b, Q2 range 0.05 - 4 GeV2
• EG4 Q2 range 0.015 0.5 GeV2
• JLab Hall C proton/deuteron, longitudinal and
  transverse
• RSS ltQ2gt 1.3 GeV2
• Semi-inclusive
• transversity, flavor decomposition,.

14
Jefferson Lab Experimental Halls
6 GeV pol. e beam Pol85, 100mA
HallA two HRS Hall
BCLAS Hall C HMSSOS
15
Hall A polarized 3He target

• Both longitudinal,
• transverse and vertical
• Luminosity1036 (1/s)
• (best in the world)
• High in-beam polarization
• gt 50
• Effective polarized
• neutron target
• 7 completed experiments
• 5 approved with 6 GeV JLab
• 3 approved with 12 GeV (A/C)

16
Hall B/C Polarized proton/deuteron target

• Polarized NH3/ND3 targets
• Dynamical Nuclear Polarization
• In-beam average polarization
• 70-80 for p
• 20-40 for d
• Luminosity up to 1035 (Hall C)
• 1034 (Hall B)

17
Spin Sum Rules and Polarizabilities
Moments of Spin Structure Functions
18
Gerasimov-Drell-Hearn Sum RuleCircularly
polarized photon on longitudinally polarized
nucleon

• A fundamental relation between the nucleon spin
  structure and its anomalous magnetic moment
• Based on general physics principles
• Lorentz invariance, gauge invariance ? low
  energy theorem
• unitarity ? optical theorem
• casuality ? unsubtracted dispersion relation
• applied to forward Compton
  amplitude
• First measurement on proton up to 800 MeV (Mainz)
  and up to 3 GeV (Bonn)
• agree with GDH with assumptions for
  contributions from un-measured regions

19
Generalized GDH Sum Rule

• Many approaches Anselmino, Ioffe, Burkert,
  Drechsel,
• Ji and Osborne, a rigorous generalization
• Forward Virtual-Virtual Compton Scattering
  Amplitudes S1(Q2,n), S2(Q2, n)
• (or alternatively, gTT(Q2,n), gLT(Q2,n))
• Same assumptions no-subtraction dispersion
  relation
• optical theorem
• (low energy
  theorem)
• Generalized GDH Sum Rule
• For v0

20
Connecting GDH with Bjorken Sum Rules

• Q2-evolution of GDH Sum Rule provides a bridge
  linking strong QCD to pQCD
• Bjorken and GDH sum rules are two limiting cases
• High Q2, Operator Product Expansion
  S1(p-n) gA ? Bjorken
• Q2 ? 0, Low Energy Theorem
  S1 k2 ? GDH
• Operator Product Expansion of higher twists gt
  1 GeV2
• Intermediate region Lattice QCD calculations
• Chiral Perturbation Theory lt 0.1 GeV2?
• Calculations Bernard, Hemmert, Meissner,
  RBcPT with D
• Ji, Kao, Osborne Kao, Spitzenberg,
  Vanderhaeghen, HBcPT

21
Sum Rules and Polarizabilities

• Drechsel, Pasquini, Vanderhaeghen, Phys. Rep.
  378,99 (2003)
• Drechsel, Tiator, Annu. Rev. Nucl. Part.
  Sci. 54, 69 (2004)
• Chen, Deur, Meziani, Mod. Phy. Lett. A 20,
  2745 (2005)
• Consider Forward Spin-flip VVCS Amplitude
  (or )
• low energy expansion

dispersion relation
expand RHS, term-by-term ? GDH sum,
polarizability,
22
JLab E94-010Neutron spin structure moments and
sum rules at Low Q2 Spokespersons G. Cates, J.
P. Chen, Z.-E. Meziani PhD Students A. Deur,
P. Djawotho, S. Jensen, I. Kominis, K. Slifer
GDH integral on neutron

• Q2 evolution of spin structure moments and sum
  rules
• (generalized GDH, Bjorken and B-C sum rules)
• transition from quark-gluon to hadron
• Check cPT calculations
• Results published in five PRL/PLB
• New results on 3He

Q2
PRL 89 (2002) 242301
23
New Hall A 3He Results (preliminary)

• Q2 evolution of moments of 3He spin structure
  functions
• Test Chiral Perturbation Theory predictions at
  low Q2
• need cPT calculations for 3He

• GDH integral IA

G1
2
24
G2 1st moment of g2 for 3He and neutron

• Q2 evolution of G23He and G2n
• B-C sum rule satisfied within uncertainties

G23He
G2n
E94-010, PRL 92 (2004) 022301
E94-010, preliminary
25
Hall B EG1b Preliminary Results G1p Plots from
G. Dodgespokespersons V. Burkert, D. Crabb, G.
Dodge, S. Kuhn, R. Minehart, M. Taiuti
G1p
EG1b preliminary and EG1a, PRL 91 222002 (2003)
26
Moments of neuton and p-nplots from A. Deur
neutron
p-n
Hall B EG1b preliminary and Hall A E94-010 PRL 92
(2004) 022301
EG1b preliminary and Hall A Hall B EG1a PRL
93 (2004) 212001
27
Generalized Spin Polarizabilities

• Consider Spin-flip VVCS amplitudes gTT(Q2,n),
  gLT(Q2,n)
• Low-energy expansion, the O(n3)term gives
• generalized forward spin polarizability, g0
  , and
• generalized longitudinal-tranverse spin
  polarizability, dLT

28
Neutron Spin Polarizabilities

• ChPT expected to work at low Q2 (up to 0.1
  GeV2?)
• g0 sensitive to resonance, dLT insensitive to D
  resonance
• E94-010 results PRL 93 (2004) 152301
• RB ChPT calculation with resonance for g0 agree
  with data at Q20.1 GeV2
• Significant disagreement between data and both
  ChPT calculations for dLT
• Good agreement with MAID model predictions
• g0
  dLT

Q2

Q2

29
Summary of Comparison with cPT

• IAn G1P
  G1n G1p-n
  g0n dLTn
• Q2 (GeV2) 0.1 0.1 0.05 0.1
  0.05 0.16 0.05 0.1 0.1
• HBcPT (NL) poor poor good poor good
  good good poor bad
• RBcPT(NL)/D good fair fair fair good
  poor fair good bad
• Q2 0.1 GeV2 is too high for HBcPT? 0.05 is good?
• RBcPT(NL) with D reasonable to Q2 0.1?
• dLT puzzle dLT not sensitive to D, one of the
  best quantities to test cPT,
• it disagrees with neither
  calculations by several hundred !
• Very low Q2 data on n(3He), p and d available
  soon (E97-110, EG4)
• Need NNL O(P5)? Kao et al. are working on that.
• A challenge to cPT theorists.

30
JLab E97-110GDH Sum Rule and Spin Structure of
3He and Neutron with Nearly Real Photons
Spokespersons J. P. Chen, A. Deur, F. Garibaldi
PhD Students J. Singh, V. Sulkosky, J. Yuan

• Measured generalized GDH at Q2 near zero for 3He
  and neutron
• Slope at Q2 0
• Benchmark test of ChPT
• Data taken in 2003
• Analysis underway
• Preliminary asymmetries and cross sections
  available
• See J. Singhs talk

31
Hall B EG4 Projected ResultsSpokespersons M.
Battaglieri, R. De Vita, A. Deur, M. Ripani

• Extend to very low Q2 of 0.015 GeV2
• longitudinal polarization
• ? g1p, g1d
• Benchmark test of cPT
• Data taking in 2006.

32
dLT Puzzle

• Possible reasons for dLT puzzle discussions with
  theorists
• B. Holstein A real challenge to (cPT)
  theorists!
• Ulf-G. Meissner Dont know now. Need to work
  on it.
• T. Hemmert Speculation Short range effects
  beyond pN?
• Kochelev/Vanderhaegen t-channel axial vector
  meson
• 
  exchange? Isoscalar in nature?
• C. Weiss An efffect of QCD vacuum structure?
• To solve the puzzle and to understand the nature
  of the problem, need isospin separation
• ? need measurement on proton
• Does the discrepancy also exists for proton?
• New proposal to measure dLT on proton
  (K. Slifers talk)

33
Hall C RSS Preliminary Results on G1p and
G2pfrom K. Slifer (Spokesperons M. Jones, O.
Rondon)

• Q21.3 GeV2, G1p consistent with Hall B results
• G2p 0, satisfy B-C sum
  rule

G1p G2p
34
Hall A E01-012 Preliminary Results G1n

• Spokesperson N. Liyanage, J. P. Chen,
  S. Choi, PhD Student P. Solvignon
• g1/g2 and A1/A2 (3He/n) in resonance region,
  1 lt Q2 lt 4 GeV2
• Study quark-hadron duality in spin structure.
  P. Solvignons talk

G1n
G1n resonance comparison with pdfs
Q2
Q2
35
g2, d2 and f2 Higher Twists Quark-gluon
Correlations and Color Polarizabilities

36
Nucleon Structure Beyond Simple Parton Models

• Interaction important at intermediate to low Q2
• quantify the interaction
• 1st step beyond parton models
  quark-gluon correlations
• how to measure q-g correlations?
• In QCD framework Operator Product Expansion
• ? 1/Q expansion (twist expansion)
• twist t is related to (mass dimension
  spin)
• mt contains twist-t matrix elements
  

37
Twist-2 and Twist-3
-- twist-3 quark-gluon correlations -- one gluon
one additional 1/Q

• -- twist-2 parton (quark, gluon) distributions
• -- no interactions

38
g2 twist-3, q-g correlations

• experiments transversely polarized target
• SLAC E155x, (p/d)
• JLab Hall A (n), C (p/d)
• g2 leading twist related to g1 by
  Wandzura-Wilczek relation

• g2 - g2WW a clean way to access twist-3
  contribution
• quantify q-g correlations

39
Jefferson Lab Hall A E97-103
Precision Measurement of g2n(x,Q2) Search for
Higher Twist Effects
T. Averett, W. Korsch (spokespersons) K.
Kramer (Ph.D. student)

• Improve g2n precision by an order of magnitude.
• Measure higher twist ? quark-gluon correlations.
• JLab Hall A Collaboration, K. Kramer et al.,
  PRL (2006)

40
E97-103 results g2n vs. Q2

• measured g2n consistently higher than g2ww
  positive twist-3
• higher twist effects significant below Q21 GeV2
• Models (color curves) predict small or negative
  twist-3

Bag Model Soliton Models
41
Color Polarizability d2 (twist-3)

• 2nd moment of g2-g2WW
• d2 twist-3 matrix element

Color polarizabilities cE,cB are linear
combination of d2 and f2 q-g correlations
Provide a benchmark test of Lattice QCD at high
Q2 cPT and Model (MAID) at low Q2 Avoid
issue of low-x extrapolation
42
Measurement on proton d2p (Hall C and SLAC)
d2p
Q2
43
Measurements on neutron d2n (Hall A and SLAC)
44
Planned d2n with JLab 6 GeV and 12 GeV(from B.
Sawatzky)

• Projections with planned 6 GeV and 12 GeV
  experiments
• Improved Lattice Calculation (QCDSF,
  hep-lat/0506017)

45
JLab 12 GeV Projection for x2g2n

• Solenoid (100 hours)
• SHMSHMS (500 hours) (W. Korsch)

46
d2n with JLab 12 GeV

• Projection with Solenoid, Statistical only
• Improved Lattice Calculation (QCDSF,
  hep-lat/0506017)

47
Twist-4 Extraction and Color Polarizabilities

• JLab world neutron data, higher-twist effects
  extracted
• m4 (0.019-0.024)M2
• m6 (-0.019-0.017)M2
• Twist-4 term
• m4 M2/9 (a24d24f2)
• SLAC E155x d20.0079(48)
• f2 0.034-0.043 (total)
• or f2 0.033-0.005 (stat.)
• Color polarizabilities
• cE 0.033-0.029
• cB -0.001-0.016
• p and p-n (eg1 E94-010)
• f2 -0.160-0.179 (p)
• -0.136-0.109 (p-n)
• f2 can be accessed through parity

48
Valence Quark Spin Structure
A1 at high x and flavor decomposition
49
JLab E99-117 Precision Measurement of A1n at
Large xSpokespersons J. P. Chen, Z. -E.
Meziani, P. Souder, PhD Student X. Zheng

• 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)

50
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

51

• BigBite (8.8 GeV)
• HMSSHMS (11 GeV)
• 1800 hours (X. Zheng)
• Solenoid, 200 hours

52
Semi-inclusive Deep Inelastic Scattering
Transversity and TMDs
53
Leading-Twist Quark Distributions


( A total of eight distributions)

No K- dependence

K- - dependent, T-even
K- - dependent, T-odd
54
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 integrating 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)

55
AUTsin(?) from transv. pol. H target
Simultaneous fit to sin(? ?s) and sin(? - ?s)
Collins moments
Sivers moments

• Sivers function nonzero (p)?
• orbital angular momentum of quarks
• Regular flagmentation functions

• Non-zero Collins asymmetry
• Assume dq(x) from model, then
• H1_unfav -H1_fav
• Need independent H1 (BELLE)

56
Current Status

• Collins Asymmetries
• - sizable for proton (HERMES)
• large at high x, large for p-
• p- and p has opposite sign
• unfavored Collins fragmentation as large
  as favored (opposite sign)?
• - consistent with 0 for deuteron (COMPASS)
• Sivers Asymmetries
• - non-zero for p from proton
• - consistent with zero for p- from proton and
  for all channels from deuteron
• - large for K
• Very active theoretical and experimental study
• RHIC-spin (PHENIX, STAR, BRAHMS), JLab
  (Hall A 6 GeV, CLAS12, ),
• KEK (Belle), GSI FAIR (PAX)
• Fits/models by Anselmino et al., Yuan et al. and
  other groups
• Solenoid with polarized 3He at JLab 12 GeV

57
E06-010/06-011 Single Target-Spin Asymmetry in
Semi-Inclusive n?(e,e'p/-) Reaction on a
Transversely Polarized 3He Target
Spokespersons Xiaodong Jiang,Jian-ping Chen,
Evaristo Cisbani, Haiyan Gao, Jen-Chieh
PengStudents K. Allada,C. Dutta, X. Qian,
M. Shabestari, One from UIUC.
Collins
Sivers
See K. Allada and C. Dutta talks
58
Collins and Sivers Asymmetries at 12 GeV

• Projections with MADII (1200 hours) for neutron
  by L. Zhu
• Summed over two other variables (z, PT)
• Similar precision with SHMS/HMS
• Hall B 12GeV (p), better precision, still summed
  over
• Need much higher precision data to study 3-d (x,
  z and PT) dependence
• High luminosity AND large acceptance
• 12 GeV baseline equipment
• will have either high luminosity (Hall C/A)
  or large acceptance (Hall B)

p- p
Collins
Sivers
59
Solenoid detector for SIDIS
GEMs

Gas Cerenkov
3He target
GEMs
Calorimeter
60
Spin Structure with the Solenoid at JLab 12 GeV

• DIS-PV needs Solenoid (luminosity 5x1038 ,
  acceptance 300 msr)
• Test SM, study hadronic physics Charge Symmetry,
  Higher-Twist, d/u at high-x
• Neutron spin structure with polarized 3He and
  solenoid
• highest polarized luminosity 1036
• A solenoid with detector package (GEM, Shower
  counter gas Cherenkov)
• large acceptance 700 msr for
  polarized
• ? high luminosity and large acceptance
• Inclusive DIS improve by a factor of 10-100
• A1 at high-x 200 hours, high
  precision
• d2 at high Q2 100 hours, very high
  precision
• parity violating spin structure g3/g5
  first significant measurement
• SIDIS improve by a factor of 100-1000
• transversity and TMDs,
• spin-flavor decomposition (2 orders
  improvement)

61
Solenoid Projection vs PT and x for p (60 days)

• For one z bin
• (0.5-0.6)
• Will obtain 4
• z bins (0.3-0.7)
• Also p- at same
• time
• With upgraded
• PID for K and K-

62
Summary

• Spin structure study full of surprises and
  puzzles
• A generation of experiments from JLab exciting
  results
• Spin sum rules and polarizabilities test cPT
  calculations
• Reasonable to 0.05 for HBcPT and to 0.1 for
  RBcPT/D?
• ? dLT puzzle
• New data and experiments help solve the puzzle
• g2, d2 higher-twist effects and q-g
  correlations, LQCD
• Spin-duality transition and link between hadrons
  and quark-gluons
• A1 at high-x valence structure, flavor
  decomposition
• Bright future
• Complete a chapter in inclusive spin structure
  study (A1, d2 ,)
• Transversity and TMDs new dimensions
• New tools (12 GeV, Solenoid) greatly enhance our
  capability

63
3-D Projections for Collins and Sivers Asymmetry
(p)
64
14.3 degree
65
SIDIS Kinematical with the Solenoid (10o-17o)
W vs x

• Q2 vs x

DIS cuts W gt 2.3 GeV W gt 1.6 GeV Q2 gt 1.0
GeV2 0.3 lt z lt 0.7
z vs x
PT vs x
66
Hep-ex/0610068
COMPASS leading hadron results
67
A1n and Du/u, Dd/d results in the news

• Physics News Update, 12/18/2003
• Bringing the Nucleon into Sharper Focus
• Science Now , 12/23/2003
• Quarks in a Surprising Spin
• Science News, 1/3/2004
• Topsy Turvy
• Physics Today Update, 2/2004
• Spinning the Nucleon into Sharper
  Focus
• APS-DNP current research topic, 5/5/2004
• The Spin Structure of the Nucleon in the
  Valence Quark Region

68
Preliminary CLAS (Hall B) A1p results Wgt2from
S. Kuhn

69
Projection with MAD 2000 hours (X.
Jiang)comparison with HERMES
Flavor Decomposition with SIDIS

• Solenoid improves precision by 2 orders of
  magnitude.