Spin dependence: theory and phenomenology
Electromagnetic Interactions with Nucleons and Nuclei (EINN 2005)
6th European Research Conference September 21-24, 2005 - Milos, Greece
Mauro Anselmino Torino University
and INFN
Polarized DIS and helicity distributions, spin carried by quarks and gluons?
Spin dependent, k
┴unintegrated parton distributions:
fundamental spin-k
┴correlations?
Transversity distributions, unknown
Transverse single spin asymmetries
) ,
,
(
2, /
,
x k Q
f
a s p S
“Partonic spin cases”
) ,
,
(
2, /
,
z p Q
D
h S a s
Polarized fragmentation functions
What do we know, and how, about the proton structure?
L W
E E Mq E
' 2
' d d
d
4
2
Main source of information is DIS
l, s l’
q
p,S
X
L
W
θ
X
l’, E’
l, E,s p, S
parity conserving case (one photon exchange)
measuring dσ one extracts information on the structure functions F
1, F
2, g
1and g
2F
1,2related to q(x,Q
2), g(x,Q
2) quark, gluon distributions
g
1related to ∆q(x,Q
2), ∆g(x,Q
2) quark, gluon helicity distributions
q
q q p p
p ˆ
2q
p x Q
2
2
( l , l ,' s ) 2 l l ' l ' l g l l ' 2 im s ( l l ' )
L
) ,
) ( (
) ) ,
(
) ,
ˆ ( ) ˆ
, ( )
, , (
2 2 2
2 1
2 2
2 2 1
Q x q g
p
p q S S
q Q p
x q g
p q S
i
Q x q F
p p Q p
x q F
q g q
S q p W
q q
q q q
q
g g
g
g g
g
q
l l’
L
W
q
p,S
X
QCD parton model
e C q q N C g
Q x
g
gf q
q q
1 2
) 1 ,
(
2 21
P g P
P Q P
g
Q
gq ggqg s qq
2
) (
dln
d
22
...
) 2 (
) ) (
( )
,
(
(1)2
0
Q C x
x C x
C
i s i s i
...
) 2 (
) ) (
( )
,
(
(1)2
0
Q P x
x P x
P
ij s ij s ij
coefficient functions
splitting functions
q
q q
) ,
(
d ,
21
q y Q
y C x y q y
C
x
s
QCD evolution
de Florian, Navarro, Sassot
Research Plan for Spin Physics at RHIC February 11, 2005
Figure 11: Left: results for Δg(x,Q
2= 5GeV
2) from recent NLO analyses [1, 2, 36] of polarized
DIS. The various bands indicate ranges in Δg that were deemed consistent with the scaling
violations in polarized DIS in these analyses. The rather large differences among these bands
partly result from differing theoretical assumptions in the extraction, for example, regarding the
shape of Δg(x) at the initial scale. Note that we show xΔg as a function of log(x), in order
Direct measure of Δg needed
q( q q ) S
g ( Q )
1 g ( x , Q ) d x
0
2 2
1 . 0 d
) ,
2 ( 1
10
2
S
q x Q x
large p
Tdi-hadron production in SIDIS,
high p
Tpions and jets at RHIC,
direct photon production at RHIC,
charm production at RHIC,
Small and large x behaviours, flavour decompositions, ….
q q g
, qg qg gg
gg
q qg
c c gg
S
qS
gL
qL
g2
1 longitudinal spin sum rule,
not the whole story…
F. Tessarotto
R. De Vita
large p
Tdi-hadron production in SIDIS
S p
p '
– p
P
Tθ
p P sin θ
S
T
A
N– p '
5
;
4
;
3
;
2
;
1
;
M M M M M
5 independent helicity amplitudes
Im
5(
1 2 3 4)
A
Npp pp
z y
x
Example:
Transverse single spin asymmetries in elastic scattering
0
A N needs helicity flip + relative phase + –
+ +
Im x
+
+ +
+
s q
N
E
A m at quark level but large SSA observed at hadron level!
QED and QCD interactions conserve helicity, up to corrections O ( m
q/ E )
BNL-AGS √s = 6.6 GeV 0.6 < p
T< 1.2
E704 √s = 20 GeV 0.7 < p
T< 2.0
STAR-RHIC √s = 200 GeV 1.1 < p
T< 2.5
E704 √s = 20 GeV 0.7 < p
T< 2.0
SSA, pp → πX
X p
p
X p
p
0X p
p
“Sivers moment”
X l
N
l
d d
d d
A
N
) d d
( d d
) sin(
) d d
( d 2 d
) sin(
2
S S
) sin(
SUT
S
A
S“Collins moment”
d d
d d
A
NX l
N
l
) d d
( d d
) sin(
) d d
( d 2 d
) sin(
2
S S
) sin(
SUT
S
A
STransverse Λ polarization in unpolarized p-Be scattering at Fermilab
p p p
p p p p p
“The largest spin effect ever seen by any human”, S. Brodsky, Como 2005
p P P sin( )
S
A N T T S
need k
┴dependent quark distribution in p
↑z y
Φ
SΦ
πx
X
p
S
P
TTransverse single spin asymmetries in SIDIS
Sivers mechanism
X
p
S
+ –
Brodsky, Hwang, Schmidt model for Sivers function
q q
diquark diquark
p
┴= P
T– z k
┴+ O(k
┴2/Q
2)
Sivers asymmetry in SIDIS
ˆ ) ( ˆ
) ,
2 ( 1
) , ( )
, (
/ / /
k p S
k x f
k x f
k x f
p q N
p p q
q
p
k
┴φ S
q
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181
Collins mechanism for SSA
Asymmetry in the fragmentation of a transversely polarized quark
p
q φ S p
┴ qˆ ) ( ˆ
) ,
2 ( 1
) ,
( )
, (
/ / /
p p
S p
z D
p z D
p z D
q q q
h N
q q h
h
initial q spin is transferred to
final q', which fragments S
qS
q’p
┴) sin(
ˆ ) ( p ˆ p
S
y
q q’
(Fundamental QCD property? D. Sivers)
) sin(
) ,
( )
/(
] y) - (1 [1
) (
) ,
( )
/(
) 1
( ) (
d d
d d
/ 2
2 /
2
/ 2
1 2
S h
q q q p q p
q h q
N q
q h
N
p z D
xy x
f e
p z D
xy y
x h
e A
neglecting intrinsic motion in partonic distributions:
] d
[d d
d
) sin(
] d
[d d
2 d
) sin(
S h
S h
S h
UT h S
A
Collins function
First extraction of Collins functions from HERMES data:
W. Vogelsang and F. Yuan (assuming Soffer-saturated h
1)
trans vers ity
fit to HERMES data on A
UTsin(h S )Extraction of Collins functions from HERMES + BELLE data
P
1depends on ) ( ) (
) ( )
(
2 1
2 ) 1 ( 1
) 1 (
z D z D
z D
z
D
NN
jets the inside
pions two azimuthal distributi ons of the spin of and , that is between the n, event by event, between correlatio
q
q
Fits to HERMES Collins data, preliminary results
Fits to BELLE Collins data, preliminary results
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation
q
N
k f
f
2
p
k
┴φ S q
p
q φ S p
┴ qˆ ) ( ˆ
) ,
2 ( 1
) ,
( )
, (
/ / /
p p
S p
z D
p z D
p z D
q q q
h N
q q h
h
ˆ )
( ˆ ) ,
2 ( 1
) , ( )
, (
/ / /
k p S
k x f
k x f
k x f
p q N
p p q
q
Amsterdam group notations
q
N
p H
D
2
1spin-k
┴correlations – Trento conventions
Sivers function Collins function
q p
q
N
h
M f k
1/
p
S
qk
┴φ
q
p
q φ S p
┴ Λˆ ) ( ˆ
) ,
2 ( 1
) ,
2 ( ) 1 ,
(
/ / /
p p
S p
z D
p z D
p z D
q q N
q q h
ˆ )
( ˆ )
, 2 (
1
) , 2 (
) 1 ,
(
/ / /
k p S
k x f
k x f
k x f
p q q N
p p q
q
Amsterdam group notations
q q T
N
D
M z
D p
1/
spin-k
┴correlations
Boer-Mulders function polarizing f.f.
SSA in p
↑p → π X
fit to A with Sivers maximized value of A
E704 data, E = 200 GeV
Parton distributions
are fundamental leading-twist quark distributions
quark distribution – well known quark helicity distribution – known
transversity distribution – unknown
all equally important
related to
positivity bound
q
q , and h
1(or q , q
T)
q q q
q q q
Tq q q
q q
5q chiral-even
T
q
related to q
5q chiral-odd q
q
T
q
|
| 2
g g g gluon helicity distribution – poorly known
g g
g gluon distribution ~ known
+ –
– –
+
+ +
+ +
+ = q q ( ( x x , Q , Q 2 2 ) )
+ – = q T ( q x ( , x Q , Q 2 ) 2 )
| |
2
1 i
in helicity basis
+ –
decouples from DIS
h
1must couple to another chiral-odd function. For example:
D-Y, pp → l
+l
–X, and SIDIS, l p → l π X, processes
+
+ –
+
+ –
+ –
– – +
–
+ –
h
1x h
1h
1x Collins function
J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992
J. Collins, 1993
+ –
+1 –1
2
g 1
No gluon contribution to h
1simple Q
2evolution
Q
2= 25 GeV
2Q
02= 0.23 GeV
2V. Barone, T. Calarco, A. Drago
Elementary LO interaction:
3 planes: plane ┴ polarization vectors, p-γ* plane, l
+l
–γ* plane
( ) ( ) ( ) ( )
1 9
4
2 1
2 1
2 2
1 2
2 2
2
x q x q x
q x q x e
x s M dx
dM d
a a
a a
a a F
s q
x s
M x
x x
x
x
F
1
21 2
2/
F 2
L/
l l
q
q *
plenty of spin effects
h
1in Drell-Yan processes
p p
Q
2= M
2q
Tq
Ll
+l
–γ*
h
1from
( ) ( ) ( ) ( ) ˆ ( ( ) ) ( ( ) )
) ( )
( )
( )
ˆ (
2 1
2 1
1 1
2 1
2 1
2
2 1
1 1
2 1
1 1
2
x u x u
x h
x a h
x q x q x
q x q e
x h
x h
x h
x h
a e
A
TT u uq q
q q q q q q
TT
TT
2 2
2 GeV GeV
210
30
M
s
GSI energies: large x
1,x
2one measures h
1in the quark valence region: A
TTis estimated to be large, between 0.2 and 0.4
at GSI
X l l p
p
PAX proposal: hep-ex/0505054
Energy for Drell-Yan processes
"safe region": M M
J /s M
J
2 /
QCD corrections might be very large at smaller values of M:
yes, for cross-sections, not for A
TTK-factor almost spin-independent
Fermilab E866 800 GeV/c
H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya, hep-ph/0503270
V. Barone et al., in preparation
s=30 GeV
2s=45 GeV
2s=210 GeV
2s=900 GeV
2Alternative accesses to transversity
Inclusive Λ production and measure of Λ polarization
) ( )
1
