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Studies of transverse spin effects at JLab
Harut Avakian
Jefferson Lab
Transversity 2005, Como, September 7-10, 2005
* In collaboration with P.Bosted, V.Burkert and L.Elouadrhiri
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Outline
Physics motivation
SIDIS studies at 6 GeV
Factorization tests
Spin azimuthal asymmetries
Future plans
Summary
2
xF>0 (current fragmentation)
Single pion production in
hard scattering
h
xF<0 (target fragmentation)
xF - momentum
in the CM frame
Target fragmentation
Current fragmentation
h
h
h
h
M
-1
Fracture Functions
PDF
0
kT-dependent PDFs
PDF
GPD
1
xF
Generalized PDFs
Wide kinematic coverage of large acceptance detectors allows studies
of hadronization both in the target and current fragmentation regions
3
Polarized Semi-Inclusive DIS
Cross section is a function of
scale variables x,y,z
n = E-E’
y = n /E
x = Q2 /2Mn
z = Eh /n
Hadron-Parton transition: by
distribution function f1u(x):
probability to find a u-quark with
a momentum fraction x
z
Parton-Hadron transition: by
p+(p-) (z):
fragmentation function D1u
probability for a u-quark to
produce a p+(p-) with momentum
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fraction z
Transverse momentum of quarks
•kT – led to introduction of kT dependent PDFs (TMDs)
•kT – crucial for orbital momentum and spin structure studies
–led to SSA in hard scattering processes
•kT - important for cross section description
-
PT distributions of hadrons in DIS
exclusive photon production (DVCS)
hard exclusive vector meson cross section
pp → p0X (E704,RHIC) cross sections
Spin-Azimuthal Asymmetries: sensitive to kT
To study orbital motion of quarks in semi-inclusive DIS
measurements in a wide range of x,z,PT, f are required.
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SIDIS (g*p→pX) cross section at leading twist (Ji et al.)
e
Unpolarized target
Longitudinally
pol. target
Transversely
e
pol. target
e
p
Boer-Mulders
1998
Kotzinian-Mulders
1996
p
Collins-1993
structure functions = pdf × fragm × hard × soft (all universal)
Off diagonal PDFs related to interference
between L=0 and L=1 light-cone wave functions.
To observe the transverse polarization of quarks in
SIDIS spin dependent fragmentation is required!
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Collins Effect: azimuthal modulation of the fragmentation function
FUT∞h1H1┴
y
ST
fS
sT(q×PT)↔ H1┴
fC
PT f
C sT
D(z,PT)=D1(z,PT)+H1┴(z,PT) sin(fh- fS’)
fh
fS’ = p-fS spin of quark flips wrt y-axis
sin(fh+fS)
x
┴H ┴
FUL∞h1L
1
FUU∞h1 ┴ H1┴
(sTkT)(pSL)↔ h┴1L
sT(p×kT)↔ h1┴
y
PT f
C
fS
fS =
p/2+fh
sinfC=sin(fh- fS’)
sT
y
PT
fh
fh
fS=fh
fS’
x
fS’ = p-fS = p/2-fh
fC
cos(2fh)
sin(2fh)
x
fS’ = p-fS = p-f7h
sT
Schafer-Teryaev sum rule
Precise measurement of Collins asymmetries for different hadrons
(p0 ,p+ +p-) would allow to test the Schafer-Teryaev sum rule
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SIDIS with neutral pions
1)
2)
3)
4)
5)
SIDIS p0 production is not contaminated by diffractive r
p0 SSA sensitive to the unfavored polarized fragmentation
HT effects and exclusive p0 suppressed
Simple PID by p0-mass (no kaon contamination)
Provides information complementary to p+/- information on PDFs
High efficiency reconstruction of p0 r+ ,h
opens a new avenue in SIDIS (HMP)
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HT and Semi-Exclusive Pion Production
E. Berger, S. Brodsky 1979 (DY), E.Berger 1980,
A.Brandenburg, V. Khoze, D. Muller 1995
Fragmentation
p+
A.Afanasev, C.Carlson, C. Wahlquist
Phys.Lett.B398:393-399,1997
p+
p0
HT effects and exclusive
p0 suppressed
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Experimental Setup (CLAS+IC)
Polarized target
solid NH3 polarized target
proton polarization >75%
high lumi ~ 1.51034 s-1cm-2
50o
o
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IC
Inner Calorimeter (424 PbWO4 crystals) for the detection of
high energy photons at forward lab angles (increases p0
acceptance ~3 times at z~0.5).
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Factorization studies with pions
g
f
q
1
A1 
( x ) D1q ( z )
q
q
1
q
1
( x)D ( z)
60 days of CLAS+IC
(L=1.5.1034cm-2s-1)
q
A1
LUND-MC
CLAS PRELIMINARY
•Double spin asymmetries consistent with simple partonic picture
•A1p inclusive and p0 (~30 times more data expected) an serve as an important
check of HT effects and applicability of the simple partonic description.
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Azimuthal asymmetries at CLAS
CLAS
Q2=2.23-2.66 GeV2
x=0.28-0.32
z=0.16-0.19
pT=0.41-0.53 GeV
M.Osipenko
Unpolarized Semi-inclusive electroproduction of p+ measured.
Complete 5-dimensional cross sections were extracted.
Direct separation of different structure functions.
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SSA measurements at CLAS
ep→e’pX
W2>4 GeV2
p1sinf+p2sin2f
CLAS PRELIMINARY
Q2>1.1 GeV2
y<0.85
0.4<z<0.7
MX>1.4 GeV
p1= 0.059±0.010
p2=-0.041±0.010
p1=-0.042±0.015
p2=-0.052±0.016
p1=0.082±0.018
p2=0.012±0.019
PT<1 GeV
0.12<x<0.48
• Significant SSA measured for pions with longitudinally polarized target
• Complete azimuthal coverage crucial for separation of sinf, sin2f moments
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Flavor decomposition of T-odd f┴
L
In jet SIDIS with massless quarks contributions from H1┴ vanish
 UU  1 - y + y 2 / 2)  eq2 f1q ( x )D1q ( z )
-
q ,q

sin f
UL
sin f
 UL
M
 SL
y 1 - y - eq2 xf Lq ( x ) D1q ( z )
Q
q ,q
M
 SL
y 1 - y - eq2 xhLq ( x ) H1q ( z )
Q
q ,q
gauge link
contribution
With SSA measurements for p++p- and p0 on neutron and proton
(pp++p-) assuming Hfav=Hu→p+ ≈ -Hu→p-=-Hunfav


A 4d + u) - A u + d / 4)
p
p
4
xfLu ( x)  15
AUL
, p 4u + d ) - AUL ,n d + u / 4)
4
xfLd ( x)  15
p
p
UL ,n
UL , p
With H1┴ (p0)≈0 (or measured) target and beam HT SSAs can be
a valuable source of info on HT T-odd distribution functions
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Longitudinally polarized target SSA using CLAS+IC
sin 2f
AUL
 DUL
h
f
q
1L
( x ) H1q  ( z )
q
q
1
q
q
1
( x) D ( z)
60 days of CLAS+IC
(L=1.5.1034cm-2s-1)
curves, cQSM
from Efremov et al
Hunf=-5Hfav
Hunf=-1.2Hfav
Hunf=0
•Provide measurement of SSA for all 3 pions, extract the Mulders TMD and
study Collins fragmentation with longitudinally polarized target
•Allows also measurements of 2-pion asymmetries
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CLAS12
High luminosity polarized
(~80%) CW beam
Wide physics acceptance
(exclusive, semi-inclusive current
and target fragmentation)
Wide geometric acceptance
12GeV significantly increase the
kinematic acceptance (x10 lumi)
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Collins Effect
Collins
UT ~
•SSA in fragmentation
•Subleading SSA has
opposite sign
•No effect in TFR
Study the Collins fragmentation for all 3 pions with a transversely
polarized target and measure the transversity distribution function.
JLAB12 cover the valence region.
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Sivers effect
UT ~
Sivers
•Asymmetry in distribution
•Subleading SSA has same sign
•Opposite sign effect in TFR
Measure the Sivers effect for all 3 pions with a transversely polarized
target in a wide kinematic range (TFR & CFR).
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CLAS12: Sivers effect projections
In large Nc limit:
f1Tu =
-f1T
d
CLAS12
projected
F1T=∑qeq2f1T┴q
Efremov et al
(large xB behavior of
f1T from GPD E)
CLAS12
projected
Sivers function extraction from AUT (p0) does not require information on
fragmentation function. It is free of HT and diffractive contributions.
AUT (p0) on proton and neutron will allow flavor decomposition w/o info on FF.
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Summary
 Current data are consistent with a partonic picture, and
can be described by a variety of theoretical models.
 Significantly higher statistics of JLab, in a wide
kinematical range will provide a full set of data needed to
constrain relevant distribution
(transversity,Sivers,Collins,…) functions.
 Experimental investigation of properties of 3D PDFs at
JLab, complementary to planed studies at HERMES,
COMPASS, RHIC, BELLE, GSI, would serve as an
important check of our understanding of nucleon
structure in terms of quark and gluon properties.
21
support slides…
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Higher Twist SSAs
Discussed as main sources of SSA
due to the Collins fragmentation
Target sinf SSA (Bacchetta et al. 0405154)
In jet SIDIS only contributions ~ D1 survive
Beam sinf SSA
With H1┴ (p0)≈0 (or measured) Target and Beam SSA can be a
valuable source of info on HT T-odd distribution functions
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SIDIS: factorization studies
P.Bosted
JLab data at 6GeV are consistent with factorization and
partonic description for variety of ratio observables
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p
Collinear Fragmentation
quark
The only fragmentation function at leading twist
for pions in eN→e’pX is D1(z)
ALL  PT DLL
q
q
g
(
x
)
D
 1
1 ( z)
q
f
q
1
( x ) D1q ( z )
q
Ee =5.7 GeV
No significant variation observed in z distributions of p+ for different
x ranges (0.4<z<0.7, MX>1.5) and for A1p as a function of PT
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CLAS12: Transversity projections
Collins
AUT ~
10-3
Simultaneous measurement of, exclusive r,r+,w with a transversely polarized target
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SSA: x-dependence
 ULsin f  S L
M
- eq2 xhL ( x) H1q ( z )
Q q ,q
PRELIMINARY
HT–SSA significant for
p + and p 0 (non-Collins?)
5.7 GeV
AUL (p 0) ~ H1favore+H1unfavored
•Study the Collins fragmentation mechanism with long. polarized target
• For p - and p 0 SSA is sensitive to unfavored fragmentation
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SSA: kinematical dependence
sin 2f
AUL
 DUL
h
f
q
1L
( x ) H1q  ( z )
q
q
1
( x ) D1q ( z )
q
• Indicate a negative sin2f moment measured for p +.
• Some indication of negative p- SSA (more data required for p - and p 0)
• More data required to correct for exclusive 2p contribution.
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PT-dependence of beam SSA
sinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3)
In the perturbative limit
1/PT behavior expected
(F.Yuan SIR-2005)
2.0
Non-perturbative TMD
Perturbative region
Asymmetries from kT-odd and kT-even (g1) distribution functions are
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expected to have a very different behavior (flat A1p(PT) observed at 5.7 GeV).
Exclusive production background from PYTHIA
Pions from string (direct) present the lower
limit for current fragmentation events
Filled (open) symbols represent pions from
exclusive (all) vector mesons.
electron
p0 sample “clean” at large z (non-string
pions are mainly from semi-inclusive r+,
30 w)
First glimpse of Twist-2 TMD h1L┴
For Collins fragmentation use chirally invariant Manohar-Georgi model (Bacchetta et al)
PRELIMINARY
Distribution functions from
cQSM from Efremov et al
CLAS-5.7GeV
Systematic error only from
unknown ratio of favored and
unfavored Collins functions
(R= H1d→p+/H1u→p+), band
correspond to -2.5<R<0
p- and p0 SSA will also give access to h1Ld
•More data required with p- & p0
•Exclusive 2 pion background may
be important
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CLAS+Inner Calorimeter (IC)
IC E/E=0.0034/E+0.038/√E+0.022
CLAS+IC
p0
CLAS
Reconstruction efficiency of high energy p0 with IC increases ~ 3 times at
large z due to small angle coverage (target in ~60cm from IC)
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Transversity
Sub-leading pion
opposite to leading
(into page)
Simple string fragmentation
(Artru model)
L=1
r production may produce
an opposite sign AUT
Leading r opposite to
leading p(into page)
r
SIDIS @11 GeV: 2 pions
r+
Understanding of 2 pion
asymmetries will help to
understand transversity
measurements
r0
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SIDIS: factorization studies
GRVS
HERMES
• A1 inclusive, from p+p- sum and p0 are consistent (in range 0.4<z<0.7 )
•There is an indication that A1p of p+ + p- is lower than inclusive at large z.
•More data required for 2 pion (r) final state studies
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GEANT simulation
Maximum angle ~50o
50o
13
o
Minimum angle ~14o
Angular acceptance for charged tracks for eg1+IC configuration
(polarized target at -67 cm from IC)
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exclusive production background
Pions from string present the lower limit for current fragmentation events
Fraction of pions from non-diffractive vector mesons adds up to SIDIS sample
Fraction of pions from exclusive rho-0(black squares) should have a
special treatment
36
exclusive production background
Fraction of charged pions from rho-0 especially high for neutron target
37
production background from exclusive events
Non string pions are mainly from semi-inclusive rho+
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SSA: PT-dependence of sinf moment
sinfLU(UL) ~FLU(UL)~ 1/Q (Twist-3)
AUL (CLAS @5.7 GeV)
ALU CLAS @4.3 GeV
AUT HERMES @27.5 GeV
PRELIMINARY
TMD
pQCD
Beam and target SSA for p+ are consistent with increase with PT
In the perturbative limit is expected to behave as 1/PT
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