XVIII SEMINARIO NAZIONALE di FISICA
NUCLEARE E SUBNUCLEARE
Fisica dello Spin
Mauro Anselmino
Torino University
and INFN
Fisica dello Spin
26 Settembre, 2005 - Otranto
1
Why spin ….?
Spin is one of the most fundamental concepts in physics,
deeply rooted in Poincaré invariance and hence in the
structure of space-time itself. All elementary particles we
know today carry spin, among them the particles that are
subject to the strong interactions, the spin-1/2 quarks and
the spin-1 gluons. Spin, therefore, plays a central role also
in our theory of the strong interactions, Quantum
Chromodynamics (QCD), and to understand spin
phenomena in QCD will help to understand QCD itself.
Research Plan for Spin Physics at RHIC, 2005
Fisica dello Spin
26 Settembre, 2005 - Otranto
2
Polarized Deep Inelastic Scattering: exploring the
proton longitudinal spin structure
 Helicity distributions - Δq, Δg - and their QCD evolution
 Polarized structure functions: g1, g2
 Data and “spin crisis” (not a real crisis)
 The spin carried by the gluons
 Flavour separation
 Weak interactions
 Missing information
Fisica dello Spin
26 Settembre, 2005 - Otranto
3
Surprises: Transverse Single Spin Asymmetries
(unintegrated polarized parton distributions)
 Single Spin Asymmetries (SSA) in elastic processes
 Single Spin Asymmetries in pQCD and in data
 Parton intrinsic motion and spin
 Spin - Transverse Momentum Dependent distribution and
fragmentation functions
 Phenomenology of SSA in inclusive processes
 Mysteries: spin asymmetries in pp → pp processes
Fisica dello Spin
26 Settembre, 2005 - Otranto
4
The last missing piece of the proton
structure: transversity
 The parton transverse spin distribution, h1
 A partner for h1
 Transversity in Drell-Yan processes
 Transversity in SIDIS processes
 Collins function from e+e- data
 Hunting strategies for h1
Fisica dello Spin
26 Settembre, 2005 - Otranto
5
Polarized Deep Inelastic Scattering
What do we know, and how,
about the proton structure?
l,s
L
l’
Main source of information is DIS
q
d
 2 E ' 

L W
4
d dE ' 2Mq E
p,S
W
X
l’,E’
θ
l,E,s
Fisica dello Spin
X
p, S
26 Settembre, 2005 - Otranto
6
parity conserving case (one photon exchange)


L (l , l ' , s)  2 l  l ' l ' l  g  l  l '  2im  s (l  l ' ) 
q q

W ( p, q, S )    g   2
q

 i 
Q2
x
2pq
 S
p  q S   S  q p )
2
2 
q 
g1 ( x, Q ) 
g 2 ( x, Q ) 
2
( p  q)
 pq


Q 2  q 2
Q  4 EE ' sin
2
Fisica dello Spin
pˆ  pˆ

2
 F1 ( x, Q ) 
F2 ( x, Q 2 ) 
pq

2

2
pˆ   p 
pq
q
2
q
q W  qW  0
current conservation
p  q  M ( E  E ' )  M
26 Settembre, 2005 - Otranto
y

E
7
d unp 4 2 E '2

d dE '
q4


F2
 F1
2
2 
2
sin

cos
 M
2 
2 


d
d
4 2 E ' 
g1
g2 



 2
E

E
'
cos


2
x
d dE ' d dE '
Q E 
M
 
measuring dσ one extracts information on
the structure functions F1, F2, g1 and g2
F1,2 related to q(x,Q2), g(x,Q2 )
quark, gluon distributions
g1 related to ∆q(x,Q2), ∆g(x,Q2)
quark, gluon helicity distributions
q  q  q
Fisica dello Spin
q  q  q
g  g  g
26 Settembre, 2005 - Otranto
g  g  g
8
l
QCD parton model
L
l’
q
q

p,S
W
X

Fisica dello Spin
26 Settembre, 2005 - Otranto
9


1
1
2
g1 ( x, Q )   eq Cq  q  q  
C g  g 
2 q 
Nf

2

dy  x
C q  
C  , s  q( y, Q 2 )
x y
y

1
2

(
Q
)
Ci ( x, s )  Ci0 ( x)  s
Ci(1) ( x)  ...
2
q( x, Q 2 )  q ( x, Q 2 )  q ( x, Q 2 )
scheme dependent
coefficient functions
helicity distributions
g ( x, Q 2 )  g  ( x, Q 2 )  g  ( x, Q 2 )
Cq0 ( x)   (1  x)
at LO
Fisica dello Spin
Cg0 ( x)  0
1
g1 ( x, Q )   eq2 q  q 
2 q
2
26 Settembre, 2005 - Otranto
10
QCD evolution
 s (Q 2 ) NS
d
2
qNS ( x, Q ) 
Pqq  qNS
2
dln Q
2
d     s (Q 2 )  Pqq

  
2 
dln Q  g 
2  Pgq
Pqg    
   
Pgg   g 
2

(
Q
) (1)
Pij ( x, s )  Pij0 ( x)  s
Pij ( x)  ...
2
splitting functions
1
1
q NS  (u  u )  (d  d )  (s  s )
2
2
   q  q 
q
Fisica dello Spin
26 Settembre, 2005 - Otranto
11
Fisica dello Spin
26 Settembre, 2005 - Otranto
12
de Florian, Navarro, Sassot
Fisica dello Spin
26 Settembre, 2005 - Otranto
13
Dirk Ryckbosh, DIS 2005
1 1
 S q    ( x, Q 2 ) dx  0.1
2 0
Fisica dello Spin
26 Settembre, 2005 - Otranto
14
Research Plan for Spin Physics at RHIC
February 11, 2005
Figure 11: Left: results for Δg(x,Q2 = 5GeV2) 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
to display the contributions from various x-regions to the integral of Δg. Right: the “net gluon
polarization” Δg(x,Q2)/g(x,Q2) at Q2 = 5 GeV2, using Δg of [2] and its associated band,
and the unpolarized gluon distribution of [82].
Fisica dello Spin
26 Settembre, 2005 - Otranto
15
Spin (Jz) sum rule
1
  S q    S g    Lq    Lg 
2
1 1

2
  S q   0 ( x, Q ) dx  0.1
2


 S g  (Q )   g ( x, Q 2 ) dx   0.6
0

2
1
de Florian, Navarro, Sassot
Direct measure of Δg needed
 large pT di-hadron production in SIDIS,
  g  qq
gg  gg , qg  qg
 direct photon production at RHIC, qg  q
 charm production at RHIC, gg  cc
 high pT pions and jets at RHIC,
 role of orbital angular momentum
Fisica dello Spin
26 Settembre, 2005 - Otranto
16
large pT di-hadron production in SIDIS
h1
h2
Fisica dello Spin
26 Settembre, 2005 - Otranto
17
pp   0 X
(collinear configurations)
factorization theorem

0
D
X
c
p
f
a
ˆ
b
f
p
X
d 

a ,b , c , d  q , q , g
f a / p  f b / p  dˆ abcd  D / c
FF
PDF
pQCD elementary
interactions
Fisica dello Spin
26 Settembre, 2005 - Otranto
18
p p  0 X
RHIC
s  200 GeV
Fisica dello Spin
26 Settembre, 2005 - Otranto
19
ALL 
polarized case: measure
d 
d ()  d () d

d ()  d () d
1
dˆ ()  dˆ ()
2

0
D
X
c
f
p, S
ˆ
a
b
f
p, S
X
d 

a ,b , c  q , q , g
 f a  f b  dˆ abcd  D / c
Δq, Δg
pQCD elementary
asymmetries
Fisica dello Spin
26 Settembre, 2005 - Otranto
FF
20
RHIC proposal
2005
Fisica dello Spin
26 Settembre, 2005 - Otranto
21
prompt photon production at RHIC
pp  X
Fisica dello Spin
26 Settembre, 2005 - Otranto
22
Flavour separation - W production at RHIC
X
f
p,
l
ab  cd :
W
L
A

ˆ
a

AL 
b
f
d ()  d ()
d ()  d ()
parity violating longitudinal
single spin asymmetry
p
s  500 GeV
X
u d   W   l 
d  u  W   l 
d  u  W   l 
u d   W   l 
u ( x1 )d ( x2 )  d ( x1 )u ( x2 )

u ( x1 )d ( x2 )  d ( x1 )u ( x2 )
Fisica dello Spin
for W  change u  d
26 Settembre, 2005 - Otranto
23
Flavour decomposition in SIDIS,
g1
A1 ( x, Q ) 

F1
2
A1h ( x, z, Q 2 ) 
lN  lhX
2
2
e

q
(
x
,
Q
)
q q
e
2
q q
DIS
2
q ( x, Q )
2
2
h
2
e

q
(
x
,
Q
)
D
(
z
,
Q
)
q q
q
e
Unknowns:
2
q q
2
h
q
2
q ( x, Q ) D ( z , Q )
(q  q )
SIDIS
q Dqh
uV , u s , u , dV , d s , d , s, s ,...
qs  q ? s  s ? u  d ? ...
Fisica dello Spin
26 Settembre, 2005 - Otranto
24
large x behaviour
g1
A1 
F1

2
2
e

q
(
x
,
Q
)
q q
2
2
e
q
(
x
,
Q
)
q q
u

( x  1)
u
Fisica dello Spin
26 Settembre, 2005 - Otranto
25

l
Charged–Current Deep-Inelastic
Scattering (neutrino factory)
S. Forte, M. Mangano, G. Ridolfi
W
p,S
X
sˆ  s 
sq
q
2
q
q q 
pˆ  pˆ

q p 
2
2
W ( p, q, S )    g   2  F1 ( x, Q ) 
F2 ( x, Q )  i 
F3 ( x, Q 2 )
q 
pq
2pq


p  q S   S  q p )
 S
2
2 
 i  q 
g1 ( x, Q ) 
g 2 ( x, Q ) 
2
p

q
(
p

q
)




1 1
sq
2
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ


p
s

s
p

p
p
g
(
x
,
Q
)
 
 
  3

p q 2
pq

q q

s  q  pˆ  pˆ
2

g 4 ( x, Q )    g   2

pq  pq
q

Fisica dello Spin


2
 g 5 ( x, Q )


26 Settembre, 2005 - Otranto
26
LO QCD parton model results
W
1
( x, Q 2 )  u ( x, Q 2 )  d ( x, Q 2 )  c ( x, Q 2 )  s ( x, Q 2 )
W
1
( x, Q 2 )  u ( x, Q 2 )  d ( x, Q 2 )  c( x, Q 2 )  s ( x, Q 2 )
g
W
5
( x, Q 2 )  u ( x, Q 2 )  d ( x, Q 2 )  c ( x, Q 2 )  s ( x, Q 2 )
g
W
5
( x, Q 2 )  u ( x, Q 2 )  d ( x, Q 2 )  c( x, Q 2 )  s ( x, Q 2 )
g
g
g 2  g3  0
g 4  2xg 5
Some combinations of the polarized structure functions are of
particular interest. For example:
W  W 
1
g
 u  u  d  d  s  s  c  c  
Fisica dello Spin
26 Settembre, 2005 - Otranto
27