Transversity
(transverse spin and transverse motion)
(unravelling the spin-orbital motion of partons?)
Towards transversity distributions:
theory and experiments
Collins mechanism
Transverse Single Spin Asymmetries
Sivers mechanism
Spin and k┴ dependent parton
distributions (TMD)
Mauro Anselmino, Como, September 7, 2005

2
f a ,s / p ,S ( x, k , Q )
Transversity 2005
1
Parton distributions
q , q
and
h1
q  q  q
q  q  q
T q  q  q
g  g  g
(or
q, T q)
are fundamental leading-twist
quark distributions
quark distribution – well known
quark helicity distribution – known
all equally
important
transversity distribution – unknown
gluon helicity distribution – poorly known
q
related to
q   5q
chiral-even
T q
related to
q   5q
chiral-odd
2 | T q |  q  q
Mauro Anselmino, Como, September 7, 2005
positivity bound
Transversity 2005
2
+
+
+
+
–
+
–
–
+
+
+
–

in helicity basis
+
h1 ( x, Q 2 ) 
+
Mauro Anselmino, Como, September 7, 2005
=
q( x, Q 2 )
q( x, Q 2 )
=
q( x, Q 2 )
T q( x, Q 2 )
1
 |   i |  
2
–
–
decouples from DIS
(no quark helicity flip)
Transversity 2005
3
h1 must couple to another chiral-odd function. For example:
D-Y, pp → l+l– X, and SIDIS, l p → l π X, processes
–
+
–
+
+
–
+
+
+
Mauro Anselmino, Como, September 7, 2005
–
–
+
–
h1 x h1
J. Ralston and D.Soper, 1979
J. Cortes, B. Pire, J. Ralston,
1992
h1 x Collins
function
–
J. Collins, 1993
Transversity 2005
4
No gluon contribution to h1
simple Q2 evolution
 g  2
+1
+
–1
  1
–
Q2 = 25 GeV2
Q02 = 0.23 GeV2
V. Barone, T. Calarco, A. Drago
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
5
h1 in Drell-Yan
processes
l+
γ*
p
l–
qT
qL
d 2
4 2
1

dM 2 dxF 9M 2 s x1  x2
p
qq   *  l l 
Elementary LO interaction:
xF  x1  x2
Q2 = M 2
 ea qa ( x1 ) qa ( x2 )  qa ( x1 ) qa ( x2 )
2
a
x1 x2  M 2 / s  
3 planes: plane ┴ polarization vectors,
p-γ* plane, l+l– γ* plane
Mauro Anselmino, Como, September 7, 2005
x F  2q L / s
plenty of spin effects
Transversity 2005
6


 
h1 from p p  l l X at RHIC
d  d
ATT 
 aˆTT


d  d


aˆTT
 e h ( x )h ( x )  h ( x )h ( x )
 e q( x )q ( x )  q ( x )q( x )
2
q q
1q
1
1q
2
1q
1
1q
2
2
q q
1
2
1
2
dˆ   dˆ 
sin 2


cos(2 )
2


1  cos 
dˆ  dˆ
RHIC energies:
  2  10 3
s  200 GeV M 2  100 GeV 2
small x1 and/or x2
h1q (x, Q2) evolution much slower than
Δq(x, Q2) and q(x, Q2) at small x
Barone, Calarco, Drago
ATT at RHIC is very small
smaller s would help
Mauro Anselmino, Como, September 7, 2005
Martin, Schäfer, Stratmann, Vogelsang
talk by A. Mukherjee
Transversity 2005
7


 
h1 from p p  l l X at GSI
2
ATT  aˆTT

q eq h1q ( x1 )h1q ( x2 )  h1q ( x1 )h1q ( x2 )
 e q( x )q( x )  q ( x )q ( x )
2
q q
1
2
1
GSI energies: s  30  210 GeV
2

 aˆTT
2
M  2 GeV
h1u ( x1 )h1u ( x2 )
u ( x1 )u ( x2 )
2
large x1,x2
one measures h1 in the
quark valence region: ATT
is estimated to be large,
between 0.2 and 0.4
PAX proposal: hep-ex/0505054
Talks by M. Contalbrigo,
N. Nikolaev, M. Maggiora
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
8
Energy for Drell-Yan processes
"safe region": M  M J / 
M 2J / 

s
Fermilab E866
800 GeV/c
QCD corrections might be very
large at smaller values of M:
yes, for cross-sections, not for ATT
K-factor almost spin-independent
H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270
V. Barone et al., in preparation
talks by M. Guzzi, A. Bianconi
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
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s=30 GeV2
s=210 GeV2
Mauro Anselmino, Como, September 7, 2005
s=45 GeV2
s=900 GeV2
Transversity 2005
10
s=30 GeV2
s=210 GeV2
Mauro Anselmino, Como, September 7, 2005
s=45 GeV2
s=900 GeV2
Transversity 2005
11
data from CERN WA39, π N processes, s = 80 GeV2
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
12
h1 x Collins from SIDIS processes

Asymmetry in the fragmentation of a
transversely polarized quark
φ S
q
p┴
pq
(Fundamental QCD property? D. Sivers)
q’

Dh / q  ( z , p )  Dh / q ( z , p ) 
q

1 N
 Dh / q  ( z , p ) S q  ( pˆ q  pˆ  )
2
y
initial q spin is transferred to
final q', which fragments

S q '  ( pˆ q '  pˆ  )  sin(  h   S )
“Trento conventions”
 Dh / q 
N
p
2
H1 q
z Mh
Sq
Sq’
p┴
Φh
ΦS
x
l  l'
Amsterdam notations
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
13
neglecting intrinsic motion in partonic distributions:
d   d 
Collins function
A 



d  d
2
2
N
e
h
(
x
)
(
1

y
)
/(
xy
)

Dh / q  ( z , p )
q  q 1q
sin(  h   S )
2
2
2
q  eq f q / p ( x) [1  (1 - y) ] /( xy ) Dq / p ( z, p )
h
N
sin( h   S )
AUT
2


[d


d

] sin(  h   S )



[d


d

]

some data available from HERMES, first extraction of Collins functions:
W. Vogelsang and F. Yuan (assuming Soffer-saturated h1)
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
14
fit to HERMES data on
sin( h   S )
AUT
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
15
Extraction of Collins functions from HERMES + BELLE data
P1 depends on
 N D (1) ( z1 )  N D (1) ( z2 )
D( z1 ) D( z2 )
(talk by R. Seidl)
M.A, M. Boglione, U. D’Alesio, A.
Kotzinian, F. Murgia, A. Prokudin,
in preparation
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
16
Fits to HERMES Collins data, preliminary results
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
17
Fits to BELLE Collins data, preliminary results
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
18
HERMES + BELLE: Collins function is not zero
Theory: probably universal
Collins, Metz
Models: few, in disagreement
Amrath, Bacchetta, Metz,
Kundu, Mulders, …
pion-quark vertex ?
loop?
assumes h1 = ∆q
disfavoured Collins
functions = 0
Talk by. A. Bacchetta
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
19
Alternative accesses to transversity
Inclusive Λ production and measure of Λ polarization
transverse fragmentation function
P  h1 ( x)  T D( z)


T D  Dq  Dq



p
X
COMPASS analysis in progress
Talk by A. Ferrero
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
20

l
p
  X
Two pion production:
d  d  h1 ( x)  qI ( z , p )


interference
fragmentation function
AUT ~ sin( R   S ) h1 qI
qI  H1
Talks by P. van der Nat, M. Radici
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
21
Vector meson production: l p   X

10 (V )  h1 ( x)  D1,0,  ( z, p )
(generalized fragmentation
function)
Inclusive hadronic production: p p   X

Talk by F.
Murgia
d  d  h1 ( x)   D / q ( z, p )


N
Single Spin Asymmetry in D-Y processes
d  d  h1 ( x)  h ( z, p )



1
(Boer-Mulders distribution)
 f q / p
N
k q

h1
M
Talks by D. Boer, G. Goldstein, M. Radici
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
22
Transverse
SSA
S
y
p'
θ
p
x
PT
z
–p
– p'
Single Spin Asymmetry in elastic scattering. Example:


      
AN  
 S  p  PT  sin θ

 
6 independent helicity amplitudes

AN  2 Im  5 (1   3 )   6 ( 2   4 )
Mauro Anselmino, Como, September 7, 2005

qq '  qq '
M  ; 
M  ;  
M  ;  
M  ; 
M  ; 
M  ; 
Transversity 2005
 1
 2
 3
 4
 5
 6
23
y
ΦS
S
Φ
x
p'
θ
p
PT
–p
z
– p'
for a generic configuration:


      
AN  
 S  p  PT  PT sin( S  )

 
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
24
AN  0
needs helicity flip + relative phase
–
+
Im
+
+
+
+

x
+
+
AN 
mq
E
s
at quark level
large SSA observed at hadron level
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
25
BNL-AGS √s = 6.6 GeV
0.6 < pT < 1.2
p p   X
E704 √s = 20 GeV
0.7 < pT < 2.0
STAR-RHIC √s = 200 GeV
1.1 < pT < 2.5
p p   0 X
E704 √s = 20 GeV
0.7 < pT < 2.0
p p   X
SSA, pp → πX
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
26
Unweighted Collins moment:
Mauro Anselmino, Como, September 7, 2005
Unweighted Sivers moment:
Transversity 2005
27
Transverse Λ polarization in unpolarized p-Be scattering at Fermilab
p N   X
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
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p p  p p
Mauro Anselmino, Como, September 7, 2005
p p  p p
Transversity 2005
29
Brodsky, Hwang, Schmidt model for Sivers function


S
p
X
q
+
diquark


q
–
  
S  p  PT  PT sin(   S )
diquark
needs k┴ dependent quark distribution in p↑: Sivers function
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
30

f q / p  ( x, k  )  f q / p ( x, k  ) 

1 N
 f q / p  ( x, k ) S  ( pˆ  kˆ )
2
 fq/ p
N
2k   q

f1T
M
Amsterdam notations
Sivers asymmetry in SIDIS
talk by A. Prokudin
p┴ = PT – z k┴ + O(k┴2/Q2)
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
31
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
32
Deuteron target


sin( h   S )
AUT
 N f u / p   N f d / p  4 Duh  Ddh
Mauro Anselmino, Como, September 7, 2005
Transversity 2005

33
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
First p┴ moments of
extracted Sivers
functions, compared
with models
data from HERMES and
COMPASS
N f q(1)   f1T(1) q
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
34
SSA in p↑p → π X
E704 data, E = 200 GeV
fit to AN with Sivers
effects alone
maximized value of AN
with Collins effects alone
U. D’Alesio, F. Murgia
M.A, M. Boglione, U. D’Alesio,
E. Leader, F. Murgia
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
35
HERMES + E704: Sivers function is not zero
Spin-k┴ partonic correlations in nucleons
Talks by M. Burkardt
D. Sivers, X. Artru
Theory: not quite universal
f1Tq
SIDIS
  f1Tq
D Y
J. Collins, a “QCD theorem”
Models: few, in fair agreement
u
1T
f
d
1T
f
f1Tq   q
Talk by A. Baccheta
chiral models, A. Drago, P. Pobilytsa
M. Burkardt
Sum rules: talk by O. Teryaev
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
36
Looking forward to an interesting
workshop, thanks!
Mauro Anselmino, Como, September 7, 2005
Transversity 2005
37