Experimental Study of Transversity
Lattice QCD and Experiment:
Revealing the Structure of Hadrons
Jefferson Laboratory, November 21 & 22, 2008
M. Grosse Perdekamp, University of Illinois
Content
• A brief history and first transversity extraction from data
• Connection with lattice: tensor charge
• Transversity in transverse momentum dependent (TMD) processes
• Transversity in transverse moment independent processes
November 22 nd
Experimental Study of Transversity
2
Transverse Spin Phenomena in
Hard Scattering QCD
QCD: Asymmetries for transverse spin are small at
high energies (Kane, Pumplin, Repko, PRL 41, 1689–1692 (1978) )
Experiment
AN 
mq
4
example, mq  3MeV , s  20GeV
,
A

10
N
+
(E704, Fermi National Laboratory):
s
π
QCD
pp  
 Test
X !
π0
s  20 GeV
1  R  L
Observable : AN 
P R L
November 22 nd
Experimental Study of Transversity
π-
3
Single Transverse Spin Asymmetries AN
persist at √=62.4 GeV and 200 GeV
√s=200 GeV STAR
√s=62.4 PHENIX and BRAHMS
AN
AN
STAR
xF
Large single spin asymmetries persist
at higher √s=62.4 and 200 GeV
November 22 nd
Experimental Study of Transversity
xF
4
Inspect Factorized Expression for Cross Section

s p1
qi ( x1 )
Proton
Structure
G( x2 )
P2


fragmentation
process
x1P1
ij
a LL
x2 P2
hard scattering
reaction

Jet
Proton Structure
Can initial and/or final state effects
generate large transverse spin
asymmetries? (ALL ~10-1)
pQCD
3 
d
ˆ (qi q j  qk ql )
d 3  pp     X

 qi ( x1 , kq ,T )  G( x2 ) 
 FFqk .l ( z, ph,T )
dx1dx2 dz
dx1dx2
small spin
dependence
(aLL~10-4)
November 22 nd
Experimental Study of Transversity
fragmentation
function
5
Transverse Spin in QCD: Two Solutions
(I) “Transversity” quark-distributions
and Collins fragmentation
Correlation between proton- und quark-spin
and spin dependent fragmentation
AN
π+
 q( x)  H1 ( z2 , k 2 )
Quark transverse
spin distribution
π0
Collins FF
π-
(II) Sivers quark-distribution
Correlation between proton-spin and
transverse quark momentum
q
1T
f
( x, k )  D ( z)
2

h
q
xF
Sivers distribution
November 22 nd
Experimental Study of Transversity
6
(I)-a Quark Transversity Distributions
proton
spin
gluon probe
Transversity
quark distributions
quark with transverse
spin in the final state!
q
quark
spin
qi ( x, Q )  q ( x, Q )  q ( x, Q )
2

i
2

i
2
For a proton with spin direction transverse to the
probe momentum:
minus
probability to find a quark with spin parallel to the proton spin
“
“
“ spin anti-parallel “
“
November 22 nd
Experimental Study of Transversity
7
(I)-b Collins Effect in the Quarkfragmentation in the Final State

ss
q
π
q
Collins q
Effect
sq

p 
h, p h
q

k
π
NL : pions to the left
q
Collins Effect:
Fragmentation of a
transversely polarized NL
AN =
quark q into spin-less
hadron h carries an NL
azimuthal dependence:


NR : pions to the right
- NR
+ NR

p 

ph 
=0

 

 k  ph   s q
 sin 
November 22 nd
Experimental Study of Transversity
8
The Collins Effect Must be Present
In Semi-Inclusive Deep Inelastic Lepton Proton!
proton
spin
photon probe
November 22 nd
q
quark
spin
quark with transverse
spin in the final state
followed by Collins
effect in the quark
fragmentation
Experimental Study of Transversity
9
First Observation of the Collins Effect
in Polarized Deep Inelastic Electron-Proton Scattering
HERMES
Collins Asymmetries in semiinclusive deep inelastic scattering
e+p  e + π + X
~ Transversity (x) x Collins(z)
AUT sin(s)
November 22 nd
Experimental Study of Transversity
10
The Collins Effect Must be Present
In e+e- Annihilation into Quarks!
electron


q1
q2
quark-2
spin
quark-1
spin
positron
November 22 nd


Collins effect in e+eQuark fragmentation
will lead to effects
in di-hadron correlation
measurements!
Experimental Study of Transversity
11
Observation of the Collins Effect in e+eAnnihilation with Belle
Belle (UIUC/RBRC) group
PRELIMINARY
Collins Asymmetries in e+eannihilation into hadrons
e++e-  π+ + π- + X
~ Collins(z1) x Collins (z2)
j2
Q

Ph 2
e-

Ph1
e+
A12 cos(12)
November 22 nd
Experimental Study of Transversity
12
j1
Extraction of Quark Transversity Distributions
and Collins Fragmentation Functions SIDIS + e+e√s=10 GeV e++ e π+ + π- +X
Program:
QCD analysis of Collins asymmetries
in SIDIS (HERMES & COMPASS) +
Collins asymmetries in e+e- (Belle)
 extract quark transversity distributions
and Collins fragmentation functions
27.5 GeV e+p  π + X
November 22 nd
160 GeV μ+d  π + X
Experimental Study of Transversity
13
Extraction of Quark Transversity Distributions
and Collins Fragmentation Functions SIDIS + e+eFit includes:
Soffer
Bound
HERMES SIDIS
New fit
+ COMPASS SIDIS
Old fit
Old fit
+ Belle e+e-
New fit
 transversity dist.
+ Collins FF
Anselmino, Boglione, D’Alesio,
Kotzinian, Murgia, Prokudin, Turk
and Melis at Transversity 2008,
Ferrara. Previously:
Phys. Rev. D75:05032,2007
November 22 nd
Experimental Study of Transversity
14
Prokudin et al. at Ferrara
November 22 nd
Experimental Study of Transversity
15
Prokudin et al. at Ferrara
Prokudin et al. at Ferrara
November 22 nd
Experimental Study of Transversity
16
Prokudin et al. at Ferrara
November 22 nd
Experimental Study of Transversity
17
Transversity Extraction + Tensor Charge with Collins FF
SIDIS 
trans versity  Collins
HERMES, COMPASS
e  e -  Collins FF
Theory
Transversity
& Tensor Charge
Done: We solved the (transversity)
proton spin problem!
Lattice QCD: Tensor Charge
November 22 nd
Experimental Study of Transversity
?
18
Cross Checks with Different Targets:
(I) proton-target at COMPASS
Preliminary COMPASS Collins Asymmetries for
Proton Target vs predictions from Anselmino et al.
Stefan Levorato
at Transversity
2008, Ferrara
20% of collected data
have been used. Futher
analysis in progress!
Good agreement of
COMPASS proton data
with preditions from
fit to HERMES, Belle
and COMPASS-d!
November 22 nd
Experimental Study of Transversity
19
Cross Checks with Different Targets:
(II) 3He-target at JLab, E06-010/06-011
Spokespersons:
Projected Collins Asymmetries for 3He Target
vs predictions from Vogelsang & Yuan
X. Jiang (Los Alamos)
J.P. Chen (JLab)
E. Cisbani (INFN)
H. Gao (Duke)
J.-C. Peng (UIUC)
First 6 GeV JLab
neutron (3He)
measurement
presently taking
data!
November 22 nd
Experimental Study of Transversity
20
Can we gain a consistent description of
the original AN asysmmetries?
Work in progress: complete analysis of
SIDIS (Collins & Sivers) +
e+e- (Collins) +
pp AN (Collins & Sivers)
Anselmino et al.
Note: impact of unpolarized FFs
thick line DSS
thin line Kretzer
November 22 nd
Experimental Study of Transversity
21
Collins Extraction of Transversity: model dependence
from Transverse Momentum Dependences!
Collins
AUT

d ( ) 
H1,q ( z, p ) sin( S    qh ) sin( S  h )
dy
d ( ) h
2
2
e
d

d

d
k
q
(
x
,
k
)
Dq ( z, p )
q q  S h 

dy
 eq2  dS dh d 2 kq( x, k )
q
k┴ transverse quark momentum in nucleon
p┴ transverse hadron momentum in fragmentation
Anselmino, Boglione, D’Alesio,
Kotzinian, Murgia, Prokudin, Turk
Phys. Rev. D75:05032,2007
The transversse momentum dependencies are unknown and
difficult to obtain experimentally!
November 22 nd
Experimental Study of Transversity
22
Future measurement of kT- (PDFs) and
pT- (FFs) dependencies
(I) pT dependence of Collins and the unpolarized fragmentation functions
can be measured with present data sample at Belle (1.5 Billion hadronic
events). Super KEK-B will have 50 x more luminosity!
(II) pT dependence of Collins
effect can be also measured
with high precision at JLab
12 GeV, later at EIC.
12 GeV - solenoid
Need ideas to get at the
kT dependence of pdfs using
The pT dependence from
e + e -!
November 22 nd
Experimental Study of Transversity
23
Sudakov Suppression of TMDs
Convolution integral sensitive to soft factor that leads to (Sudakov)_
suppression of Collins asymmetries
~ 1/√Q in SIDIS
~ 1/Q in e+e-
D. Boer Nucl. Phys. B603 192 (2001)
Convolution in SIDIS can be avoided by weighted
integration in SIDIS. However, not possible in in e+e- !
November 22 nd
Experimental Study of Transversity
24
Measurements of transversity with transverse
momentum independent functions !!
p p 
 l  l  X
(PAX, FAIR)
p p 
 jet  X
(RHIC) need to improve systematics on rel. luminosity
ep  
 e  X
(SIDIS at JLab - 12 GeV, EIC) need Lambda-FF  e+e-
pp  
   X
(RHIC, JPARC) need Lambda-FF  e+e-
ep  
       X
(SIDIS at JLab - 12 GeV, EIC ) need IFF  e+e-
pp  
       X
(RHIC, JPARC) need IFF  e+e-
November 22 nd
Drell Yan  req. polarized anti-protons
Experimental Study of Transversity
25
First IFF Asymmetries in Hermes and COMPASS
2002-2004 data
all +/- pairs
proton target
A. Bacchetta, M. Radici hep-ph/0608037 model calculations
proton
HERMES kin
November 22 nd
deuteron COMPASS kin
Experimental Study of Transversity
26
Transversity Quark Distributions at RHIC:
Di-Hadron “Interference Fragmentation Functions
IFF Asymmetries in proton-proton
collisions
p+p  π+ + π- + X
~ Transversity (x) x IFF(z)
N
: Pion Pair Yiel d
q( x ) : Transversi ty quark DFs
qˆ ( z ) : IFF Fragmenta tion Func.
 k┴, p┴ integrate out
Ongoing work:
N  ( )  N  ( )
AT 
Pbeam N  ( )  N  ( )
 q( x1 )G( x2 ) cos( ) IFF ( z )
1
November 22 nd
AT in PHENIX
IFF in Belle
Experimental Study of Transversity
27
First PHENIX Results on IFF
Asymmetries for Pion Pairs
Ruizhe Yang, Transverse Spin Workhop in Beijing, July 2008
Expect small asymmetries at mid-rapidity (Bachetta et al.)
More statistics is
on tape. Need to
move measurement forward!
Systematic errors
Polarization 5%
Relative lumi. 5x10-4
No systematic
effects detected
from bunch shuffling
Consistent with 0, despite the second bin of 0h- pairs and the last bin of
h+h- pairs are 2 from 0
November 22 nd
Experimental Study of Transversity
28
Projections for IFF measurement at BELLE
j2
IFF sensitivity projection from data
e-

Ph1

Ph 2
e+


Ph1  Ph 2
j1
thrust
axis
e  e   (   ) jet1 (   ) jet 2 X
A  H1 ( z1 , m1 ) H1 ( z2 , m2 ) cos(1  2 )
Artru and Collins, Z. Phys. C69, 277 (1996)
Boer, Jakob, and Radici, PRD67, 094003 (2003)
November 22 nd
Experimental Study of Transversity
29
Measurements of quark transversity
1991
2002-2008
Underway
p+p
E704, 1991
Large forward
SSA
SIDIS
November 22 nd
Future
RHIC
Collins in jets
STAR, PHENIX,
BRAHMS
RHIC
Inclusive AN
IFF asym.
HERMES
COMPASS
AUT
e++e-
Courtesy
Ruizhe Yang
JParc, FAIR
Drell-Yan
COMPASS
JLab 12 GeV
p target
Collins, IFF
JLab 3He
EIC Collins in jets
BELLE
BELLE
BELLE
Collins FF
IFF
pT dependence
Experimental Study of Transversity
30
Summary
• First measurements of transversity quark distributrions
are available.
• TMD dependence of Collins function makes theoretical
interpretation difficult. Knowledge of pT and (?) kT
dependence may come from future measurements in
e+e- and SIDIS.
• Non-TMD processes are available. Within the next few
years measurements using di-hadron interference fragmentation
functions will be available.
• We can aim to extract the tensor charge in a theoretically clean
way and compare to lattice QCD!
November 22 nd
Experimental Study of Transversity
31