Transversity

1
Transversity Hall-B at JLab
H. Avakian, L. Elouadrhiri
Jefferson Lab
International Workshop on Transversity
Trento June 2004

• Introduction
• Factorization and spin-azimuthal asymmetries at
  CLAS
• Transition from exclusive to semi-inclusive
  processes
• Summary Outlook

2
Polarized Semi-Inclusive DIS
Cross section defined by scale variables x,y,z
Hadron-Parton transition by distribution
function f1u(x) probability to find a u-quark
with a momentum fraction x
Parton-Hadron transition by fragmentation
function Dp (z) probability for a u-quark to
produce a p with a momentum fraction z.
1u
3
SIDIS studies require

• Factorization in SIDIS into a distribution
  function f fragmentation function D and hard
  scattering part.

• Applicability of partonic description at JLab
  energies
• Low W and Q2
• Low MX in ep-gtehX
• Control over background processes
• Resonances in the t-channel
• Exclusive vector mesons

4
SIDIS factorization
SIDIS (gp-gtpX) x-section at leading twist
Ji et al.
Structure functions FUU,FLL factorize into TMD
distributions (hep-ph 0405085)
P- has contributions from distribution,
fragmentation and soft gluon radiation
5
Contributions to s in Polarized SIDIS
Twist-2 TMDs from Mulders et al
sUU
sLL
Sivers
sUT
sUT
Collins
sUL
KM
Kinematic factors depend on the beam energy
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Quantum Phase-Space Distributions of Quarks
Wpu(k,r) Mother Wigner distributions
Same PDFs in exclusive and semi-inclusive
analysis
d2kT
d3r
IPDs Wpu(x,r)
GPDs Hpu(x,x,t), GDAs Fudp(x,x)
dr
FT
TMD PDFs fpu(x,kT), TMD FFs Dup(kT,z)
IPDs Wpu(x,rT),
GPD
x0,t0
d2r
dx
d2kT
Measure momentum transfer to target Direct info
about spatial distributions
Measure momentum transfer to quark Direct info
about momentum distributions
PDFs fpu(x), FFs Dup(z)
Form Factors F1pu(t),F2pu(t )..
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The CLAS Detector
Scattering of 5.7 GeV polarized electrons off
polarized NH3 and unpolarized hydrogen

• 8M p in DIS kinematics,SIDIS
  Q2gt1.5GeV2,W2gt4,ylt0.85,
• beam polarization 73
• target polarization 72 (f0.2)

8
Missing mass of pions in ep?epX
p0
p-
p
n
D
D0
MXgt1.4 (Q2gt1.5,W2gt4) applied to exclude the
kinematics where t-channel resonances may have
significant contribution
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Multiplicities and Factorization
DIS Q2gt1 W2gt4 MXgt1.1 (1.4) ylt0.85
Dup KKP (LO)
The fraction of p from struck quark in a range
0.5ltzlt0.8 is not changing significantly with beam
energy (LUND studies).
No significant variation observed in z
distributions of p for different x ranges
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A1p shows no significant Q2 and z dependence
ep ? e p X ( Ee 5.7 GeV, MX gt 1.1)
A1p
x dependence of CLAS A1p (A20) consistent with
HERMES data and factorization.
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Longitudinally Pol Target Twist-2 SSA for p
SSA x-dependence CLAS (5.7 GeV) is consistent
with predictions for Collins effect from
Efremov et al. hep-ph/0208124

• First indication of a non-zero sin2f moment
• (Kotzinian-Mulders asymmetry)
• AULsin2f is a clean source of Collins SSA

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Target SSA sinf moment (HERMES effect)
Target SSA measured at different E,W consistent
At least 3 possible sources!
13
Beam SSA sinf moment (CLAS _at_4.3 GeV)
ssinfLU FLUHLT 1/Q (Twist-3)
Beam SSA shows no significant dependence on W,E
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ALU from CLAS 4.3 and 5.7GeV data
DIS-cuts Q2gt1 GeV2 Wgt2 GeV y lt 0.85 0.5 lt z lt 0.8
5.7GeV
No significant dependence on beam energy
4.3 GeV
No significant ALU dependence on Mx beyond the
neutron.
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ALU x-dependence CLAS _at_ 4.3 and 5.7 GeV
0.5ltzlt0.8
Beam SSA analyzed in terms of the Collins effect
by Schweitzer et al. using e(x) from cQSM
4.3 GeV and 5.7 GeV data consistent
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ALU z-dependence CLAS 4.3 vs. 5.7 GeV
Data also consistent with z-dependence of the
Collins function from Efremov et al.
Sivers effect by F.Yuan using h1- from MIT bag
model
z-dependence of ALU at 4.3 GeV and 5.7 GeV
consistent with increase at low z
17
2 pion electroproduction Kinematics
z-pion related to cosq
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Exclusive pp- and pp0
e p e p ?
p p-
n
r
r0
r0 PID by Mpp and missing p-
r PID by Mpp and missing neutron
Fit Mpp with a BW polinomial background.
19
Beam SSA for exclusive pp0
Missing mass
Invariant mass
Significant positive beam asymmetry for exclusive
r
20
p SSA from r(pp-)
Modulation exist even for vanishing helicity
change amplitudes
r0
(CLAS _at_5.7GeV)
p SSA at large z may have a significant
contribution from r
21
SSA for p0 from ep-gtern

• Different contributions from r for different
  pions
• SSA from rn may affect SSA for SIDIS p0 at
  large z

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SSA in ep-gtepX
PYTHIA at 5.7 GeV
Larger fraction of p from r at low x and large z
r contribution to SSA (20) may be responsible
for the difference in p and p0 beam SSA at large
z
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SSA in ep-gtepX
HERMES 27.5 GeV
CLAS 5.7 GeV
Strange pattern p0 SSA bigger at very low and
very large z
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Target SSA in exclusive p0 production
CLAS _at_5.7GeV
HERMES 27.5 GeV
ep-gtep0p
Large positive p0 target SSA in the exclusive
limit confirmed by CLAS at 5.7 GeV
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LUND MC with Long. Pol. Target SSA for p
f distributions from MC vs 5.7 CLAS
data. Fiducial cuts on e,p and smearing applied.
sinf and sin2f moments arising from the Collins
effect added in MC using predictions from
Efremov et al. Phys.Rev.D67063511,2003
Simulated and reconstructed SSA moments consistent
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Long. Pol. Target SSA for p at 12GeV
large x high luminosity
6 GeV

• The sin 2f asymmetry for 2000 h of
  projected CLAS data.

x,PT dependence of AULsin2f may provide access
to h1L(x,PT)
Efremov et al.
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Transverse Target SSA at CLAS and CLAS
CLAS _at_ 5.7GeV
Collins
AUT
Expected precision of the AUT and extracted
du/u from transverse spin asymmetry
0.5ltzlt0.8
Sivers
AUT
Separate the Sivers effect using different
kinematic dependences
CLAS _at_ 11GeV
Simultaneous measurement of SIDIS, exclusive
r,r,w and DVCS asymmetries with a transversely
polarized target.
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Exclusive vector meson production at CLAS and
CLAS
Provide access to different combinations of
orbital momentum contributions Ju,Jd r0 -gt 2Ju
Jd r -gt Ju - Jd w -gt 2Ju - Jd

• Significant transverse target SSA predicted for
  exclusive r0, r
• (Goeke et al hep-ph/0106012)

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Summary

• Current CLAS data are consistent with a partonic
  picture
• The data consistent with factorization (no
  x/z-dependence observed in single and double spin
  asymmetry measurements).
• Spin and azimuthal asymmetries extracted for
  SIDIS p are in agreement with theory predictions
  and measurements at higher energies.
• Measured asymmetries (ltsin2fgt, ltsinfgt, ),
  provide a unique access to new transverse
  momentum dependent distribution and fragmentation
  functions

• Global analysis of SSA for exclusive and
  semi-inclusive final states with polarized beam
  and target needed for separation of contributions
  from different mechanisms and precision
  measurements of underlying distribution functions.

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CLAS Transverse target at 5.7 GeV
Chicane magnets needed to re-steer the primary
electron beam
With the B field (5T) pointing perpendicular to
the beam direction Mollers being focused into the
torus coils between the sectors
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The CLAS
Detector
Forward Cerenkov
Forward EC
Forward DC
Inner Cerenkov
Central Detector
Preshower EC
Forward TOF
Torus Cold Ring
Coil Calorimeter
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Pion SSA (sinusoid evolution)
HERMES _at_27.5 GeV
CLAS at _at_5.7 GeV
no sign of significant sin2f term in the beam SSA
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DIS Cuts
z
Rapidity (hgt1) and xF cuts related to z cut
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Photon Sivers Effect
Target SSA (Brodsky et al.)
Essential constituents
Light-cone spin wave function of a nucleon
Beam SSA (Afanasev Carlson)
Final state interaction from gluon exchange
Beam SSA has the same source and provides access
to essential parameters with less ambiguities
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Kinematic factors for different targets
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CLAS - Performance
Forward Detector Central Detector Angular
coverage Tracks (inbending) 10o - 40o 42o
- 135o Tracks (outbending) 5o -
40o 42o - 135o Photons 3o - 40o 42o -
135o Track resolution dp (GeV/c)
0.003p 0.001p2 0.02pT dq (mr) 1 5
df (mr) 2 - 5 2 Photon detection Energy
range gt 100 MeV gt 50 MeV dE/E 0.09 (1
GeV) 0.06 (1 GeV) dq (mr) 6 (1 GeV)
15 (1 GeV) Neutron
detection heff 0.5 (p gt 1.5 GeV/c)
Particle id e/p gtgt1000 ( lt 5 GeV/c)
gt100 ( gt 5 GeV/c) p/K (4s) lt 3
GeV/c 0.6 GeV/c K/p (4s) lt 5 GeV/c 1.1 GeV/c
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Q2
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Sivers and Boer (T-odd ) distribution functions
T-odd functions change sign from DIS to DY
(Collins-02)

• Boer et al. scalar diquark
• f1T-uh1-u f1T-d0
• F. Yuan MIT bag model
• Bacchetta et al scalarvector diquarks
• (non-0 f1T-d)
• Anselmino et al (pp scattering)
• 0 in large class of chiral soliton models (cQSM)

d-quark
u-quark
d-quark contribution suppressed
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Rho-MC ALU for gp-gtpX
E27.5 GeV
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Beam SSA for exclusive events
Beam SSA for p0,p,r are consistent