Post on 30-Dec-2015
description
June 1, 2005 Jianwei Qiu, ISU 1
Single Transverse Spin Asymmetries
Jianwei QiuIowa State University
RBRC Workshop onSingle Spin Asymmetries
June 1 – 3, 2005Brookhaven National Lab, Upton, NY
June 1, 2005 Jianwei Qiu, ISU 2
Single spin asymmetry – definition
Single spin asymmetry before QCD
Single spin asymmetry within the collinear
factorization – high twist matrix elements
KT- factorization – Sivers and Collins effects
Connection between high twist matrix elements
and Sivers and Collins functions
Open questions
Outline
June 1, 2005 Jianwei Qiu, ISU 3
Single Spin Asymmetry – definition
Spin-avg X-section:
Spin-dep X-section:
Single spin asymmetry:
single longitudinal spin asymmetry:
single transverse spin asymmetry:
June 1, 2005 Jianwei Qiu, ISU 4
Symmetry and Single Spin Asymmetry
Even though cross section is finite,
single
spin asymmetries can vanish if the
polarized cross
sections are independent of spin directions
due to
the fundamental symmetries of the
interactions
AL vanishes for Parity conserved interactions:
AL ≠ 0 for W+ production
good for parton flavor separation
June 1, 2005 Jianwei Qiu, ISU 5
Single transverse spin asymmetry before QCD
Almost 40 years ago, AN in inclusive DIS was proposed by Christ and Lee to test the Time-Reversal invariance:
In the approximation of one-photon exchange,
AN of inclusive DIS vanishes if Time-Reversal
is invariant for EM and Strong interactions
N. Christ and T.D. Lee, Phys. Rev. 143, 1310 (1966)
June 1, 2005 Jianwei Qiu, ISU 6
AN = 0 for inclusive DIS
DIS cross section:
Leptionic tensor is symmetric: Lμν = Lνμ
Hadronic tensor:
Polarized cross section:
P and T invariance:
June 1, 2005 Jianwei Qiu, ISU 7
Large AN in hadronic collisionsprocess: only one hadron is transversely polarized:
Large asymmetries AN
observed in hadron
collisions: decay of production of ’s
FNAL - E704
PT=0.5~2 GeV/cs=23.5 GeV
June 1, 2005 Jianwei Qiu, ISU 8
Single spin asymmetry corresponds
to a T-odd triple product
June 1, 2005 Jianwei Qiu, ISU 9
Single transverse spin asymmetry – AN
in the parton model
the operator for δq has even γ’s quark mass term
the phase requires an imaginary part loop diagram
transverse spin information at leading twist – transversity:
q x = Chiral-odd helicity-flip density
PQCD calculable partonic parts should not depend on light current quark mass – singals a high twist effect in pQCD
June 1, 2005 Jianwei Qiu, ISU 10
Single transverse spin asymmetry – AN
in collinear factorization approach Leading twist PDF with transverse hadron spin:
5
( , )q x s
need an even number ’s:
Twist-3 matrix elements
An extra transverse index extra gluon (its polarization) extra vector direction
June 1, 2005 Jianwei Qiu, ISU 11
Spin flip from interference between a quark state and a quark-gluon composite state Observed hadron momentum provides the 3rd vector
( )NA i s p
Unpinched pole to give the phase:
Q: pQCD factorization beyond leading twist?
High twist contribution to AN
x
June 1, 2005 Jianwei Qiu, ISU 12
Multiple scales in hadronic collisions
(3) (2) (1)
(1) Hard collision: Q >> ΛQCD
(2) Gluon shower: <kT>dynamic ~ F[Q2,log(s/Q2)]
(3) Hadron wave function: <kT>intrinsic ~ 1/fm ~ ΛQCD
PQCD factorization:
(1) Perturbative IR safe single hard
partonic “cross section”
(2) Leading log DGLAP evolution of PDFs
(3) Nonperturbative PDFs
June 1, 2005 Jianwei Qiu, ISU 13
Perturbative QCD factorization – (I)
42 2
0
1 1 perturbati
1T( , vely( , ) ) H
rQd k k k
k i k i
Perturbative pinch poles:
Perturbative factorization:
22 2
0
2 2H( , 0) 1 1
( 1
T , )T dkdxd k k
i ikQ
rk
kx
2 2
2T
T
k kk x
xp n k
p n
Short-distance
Nonperturbative matrix element
T
H(Q)k k
p p
Parton state of momentum, k, lives much longer than the time of hard collision: |k2|<<|Q2|
Remove soft interactions between different time scales
June 1, 2005 Jianwei Qiu, ISU 14
Perturbative QCD factorization (II)
2 ~ TQ n k kxp
Collinear factorization:
Provides systematic ways to quantify high order corrections
KT –factorization 2 Tp nQ x k k /
2 2ˆ ( ,) ), (h iphy
iTs
hTx k T x k
No all-order proof of kT – factorization for an arbitrary kT
Factorization fails beyond the next-to-leading powers in hadronic collisions
Leading Twist
Power corrections
perturbative
Long lived parton state
/2 2
/33
/4
2
22 4
2
ˆ [1 ...] ( )
ˆ + [1 ...] ( )
ˆ + [1 ...] ( )
+ ...
physh
s s
s s
s
i i h
ii
is
h
ih
T
TQ
TQ
x
x
x
June 1, 2005 Jianwei Qiu, ISU 15
Factorization:
1 2
1 2
,
,
F
D
T x x F
T x x D
Normal twist-2 distributions
Twist-3 correlation functions:
have different properties under the P and T transformation
1 2 1 2an, ,dF DT x x T x x
1 2,DT x x does not contribute to the AN
1 2,FT x x is universal, x1=x2 for AN due to the pole
AN from polarized twist-3 correlations
June 1, 2005 Jianwei Qiu, ISU 16
Single spin asymmetry within the
collinear factorization Generic twist-3 factorized contributions
Even ’s !
Even ’s !
Provides hadron spin dependence
transversity
(1) Calculated by Qiu and Sterman, Phys. Rev. D, 1999
(2) Calculated by Kanazawa and Koike, Phys. Lett. B, 2000
June 1, 2005 Jianwei Qiu, ISU 17
Leading twist-3 contribution to AN
Minimal approach (within the collinear factorization):
if ( , ) ( ) (1 )1N F
nA T x x q x xxu
n
June 1, 2005 Jianwei Qiu, ISU 18
Predictive power of the factorization approach
June 1, 2005 Jianwei Qiu, ISU 19
What is the T(3)(x)?
Represents a fundamental quantum correlationbetween quark and gluon inside a hadron
June 1, 2005 Jianwei Qiu, ISU 20
What the T(3) (x) tries to tells us?
Consider a classical (Abelian) situation:
June 1, 2005 Jianwei Qiu, ISU 21
Model for TF(x,x)
TF (x,x) tells us something about quark’s transverse motion in a transversely polarized hadron
One parameter and one sign!
It is non-perturbative, has unknown x-dependence
1
if ( , ) ( ) (1 )
N
nF
Axu
T
n
x x q x x
June 1, 2005 Jianwei Qiu, ISU 22
Numerical results – (I)(compare apples with oranges)
Qiu and StermanPhy. Rev. D, 1999
June 1, 2005 Jianwei Qiu, ISU 23
Numerical results – (II)(compare apples with oranges)
Qiu and StermanPhy. Rev. D, 1999
June 1, 2005 Jianwei Qiu, ISU 24
Numerical results – (III)(comparison with RHIC data)
Comparison with
STAR data
Too small PT value
to be comfortable
for initial state
twist-3
See Koike’s talk on
final state twist-3
New data from
STAR,
BRAHMS, PHENIX
June 1, 2005 Jianwei Qiu, ISU 25
Twist-3 vs KT approachTwist-3 contribution in collinear factorization – leading corrections from parton correlation (a minimal approach)
Effect of non-vanish parton kT (when kT ~ pT):
(3)
(3)
(
)1
(
( )
1
1
)T TA Bs p
T
p pN
x T xxAxS
x Tp x
T
x
MNon-perturbative scale, e.g., di-quark mass, …
1 1T TA Bs p
Np p TA
MS Mf
px
June 1, 2005 Jianwei Qiu, ISU 26
Sivers’ functions
Sivers’ functions: 1 ( )Tf x
1( , , ) ( , , ) ( ) T
n k sq x k s q x k s f x
M
Sivers’ functions are connected to a polarized hadron beam
Sivers’ functions are T- odd, but do not need another T- oddfunction to produce nonvanish asymmetries – the extractedproportional factor is T- odd, proportional to AN
Polarized SIDIS cross section:
1
( , , ) [ ( , , ) ( , , )] ( )
( ( ))T
x Q p q x k s q x k s D z
P n k s x zf D
June 1, 2005 Jianwei Qiu, ISU 27
Collins’ functions
Collins’ functions: 1 ( )H x
1( , , ) ( , , ) ( ) k n
D z k s D x k s H zM
Collins’ functions are connected to the unpolarized Fragmentation contributions to a hadron
Collins’ functions are T- odd, need another T- odd function to produce nonvanish asymmetries
Polarized SIDIS cross section:
1
( , , ) ( , ) [ ( , , ) ( , , )]
( (z), )
x Q p q x s D z k s D z k s
k n q x Hs
June 1, 2005 Jianwei Qiu, ISU 28
KT - Factorization
Factorization requires a separation of perturbative hard scale from nonperturbative hadronic scale a physical hard scale, Q, much larger than the kT
Q ~ pT >> kT
kT-factorization measures parton kT directly, while
twist-expansion gives integrated kT information No formal proof of kT-factorization for hadronic
collisions at kT ~ pT
kT-factorization works for semi-inclusive DIS and
Drell-Yan, or others with a large scale Q
June 1, 2005 Jianwei Qiu, ISU 29
Semi-inclusive deeply inelastic scattering
ℓℓ’
q
P
k
pk’
sT
Breit frame:
Two scale problem: Q2=-q2, pT
Fixed order pQCD:
Sudakov resummation:
q
k
k’P
QCDTQ p
TQ p
Single spin asym:
low pT data sensitive to parton kT
( ) 0 N TA s P p
If P is anti-parallel to p
June 1, 2005 Jianwei Qiu, ISU 30
ℓℓ’
q
P
k
pk’
sT
In q-P frame, if
2
2Tkk xP k nk n
T Tk p Q 2k we can neglect
in partonic part But, we cannot neglect
in partonic rt paTk
One can define kT-dependent and gauge invariant parton distributions Soft interaction between the hadrons can spoil factorization
S
Sudakov resummation (done in b- or kT-space) resums dynamical kT from gluon shower Parton orbital motion is more relevant to the intrinsic kT
Intrinsic vs dynamical kT
June 1, 2005 Jianwei Qiu, ISU 31
Open questions – (I)
kT approach Twist-3
1 ( )Tf x ( , )FT x x
1 ( )H z (3) ( , )D z z
Sivers:
Collins:
How much overlap between kT-approach at low pT
and twist expansion at high pT?
What these nonperturbative functions try to tell us?
“direct kT” vs “kT – moments”
June 1, 2005 Jianwei Qiu, ISU 32
Although there is kT-factorization in SIDIS, Drell-Yan
and the others, how to separate dynamical kT from
intrinsic kT ?
How Sivers and Collins functions are affected by
the process dependent gluon shower (resummation)?
…
Open questions – (II)
If there is no KT – factorization, how universal are
Sivers and Collins functions?
June 1, 2005 Jianwei Qiu, ISU 33
Backup transparencies
June 1, 2005 Jianwei Qiu, ISU 34
Collinear approximation is important
With collinear approximation:
Cuts
Cuts =
In general, matrix elements with different cuts are not equal:
≠
IR safe
June 1, 2005 Jianwei Qiu, ISU 35
When does the factorization lose its predictive power?
At the time when the nonperturbative functions lose their universalityFor final-state fragmentation:
Factorization breaks if the fragmentationtook place inside the hadronic medium
If the lifetime of the parton state of momentun k is shorter than the medium size
Lifetime: 02
1 22 2 fmmedium
jet
y t L rE m
2
25 GeV
GeVjetm
June 1, 2005 Jianwei Qiu, ISU 36
Asymmetries
Double longitudinal spin asymmetries:
Reduce under parity to:
Double transverse spin asymmetries:
Single longitudinal spin asymmetries:
Single transverse spin asymmetries:
June 1, 2005 Jianwei Qiu, ISU 37
Measure Sivers’ and Collins’ functions
12
Sin2
((
( ) ( )
) )qUT
q q
HeA
e q
x zq
x D z
SIDIS:
Collins functions:
June 1, 2005 Jianwei Qiu, ISU 38
Seperate Sivers’ and Collins’ functions
June 1, 2005 Jianwei Qiu, ISU 39
Initial success of RHIC pp runs
cross section measured
over 8 order of magnitude
[PRL 91, 241803 (2003)]
Good agreement with NLO
pQCD calculation at low pT
Can be used in interpretation
of spin-dependent results
9.6% normalization error not shown