einn 2005 spin dependence-theory september 23rd, milos, greece 1 spin dependence: theory and...
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1 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
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
2 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
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,/, Qkxf Spsa
“Partonic spin cases”
),,( 2,/, QpzD saSh
Polarized fragmentation functions
3 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
What do we know, and how, about the proton structure?
WLE
E
MqE
'
2'd d
d4
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
4 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
parity conserving case (one photon exchange)
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
qppp
2ˆ
qp
Qx
2
2
)'(2'''2),',( llsimllgllllsllL
),()(
) ),(
),(ˆˆ
),(),,(
222
21
22
212
Qxgqp
pqSSqpQxg
qp
Sqi
QxFqp
ppQxF
q
qqgSqpW
qqq qqq ggg ggg
5 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
q
l’lL
Wq
p,S
X
QCD parton model
6 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
gCN
qqCeQxg gf
q
1
2
1),( 22
1
gPP
PPQ
gQ gggq
qgqqs
2
)(
dln
d 2
2
...)(2
)()(),( )1(
20 xC
QxCxC i
sisi
...)(2
)()(),( )1(
20 xP
QxPxP ij
sijsij
coefficient functions
splitting functions
q
),( ,d 21
Qyqy
xC
y
yqC
x s
QCD evolution
7 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
8 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
de Florian, Navarro, Sassot
9 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Research Plan for Spin Physics at RHICFebruary 11, 2005
Figure 11: Left: results for Δg(x,Q2 = 5GeV2) from recent NLO analyses [1, 2, 36] of polarizedDIS. The various bands indicate ranges in Δg that were deemed consistent with the scalingviolations in polarized DIS in these analyses. The rather large differences among these bandspartly result from differing theoretical assumptions in the extraction, for example, regarding theshape of Δg(x) at the initial scale. Note that we show xΔg as a function of log(x), in orderto display the contributions from various x-regions to the integral of Δg. Right: the “net gluonpolarization” 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].
10 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Direct measure of Δg needed
xQxgQSqq gq
d ),()( )(1
0
22
1.0d ),(2
1 1
0
2 xQxSq
large pT di-hadron production in SIDIS,
high pT pions and jets at RHIC,
direct photon production at RHIC,
charm production at RHIC,
Small and large x behaviours, flavour decompositions, ….
qqg , qgqg gggg
qqg ccgg
gqgq LLSS2
1 longitudinal spin sum rule, not the whole story…
F. Tessarotto
R. De Vita
11 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
large pT di-hadron production in SIDIS
12 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
S
p
p'
– pPTθ
θsinPpS T
NA
– p'
5;
4;
3;
2;
1;
M
M
M
M
M
5 independent helicity amplitudes
)(Im 43215NA
pppp
z
y
x
Example:
Transverse single spin asymmetries in elastic scattering
13 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
0NA needs helicity flip + relative phase
–+
++
Im x
+
++
+
sq
N E
mA at quark level
but large SSA observed at hadron level!
QED and QCD interactions conserve helicity, up to corrections )/( EmO q
14 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2
E704 √s = 20 GeV 0.7 < pT < 2.0
STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5
E704 √s = 20 GeV 0.7 < pT < 2.0
SSA, pp → πX
Xpp
Xpp 0
Xpp
15 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
“Sivers moment”
XlNl
dd
ddNA
)dd(d d
)sin()dd(d d2
)sin(2
S
S
)sin(
S
UTSSA
16 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
“Collins moment”
dd
ddNA
XlNl
)dd(d d
)sin()dd(d d2
)sin(2
S
S
)sin(
S
UTSSA
17 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Transverse Λ polarization in unpolarized p-Be scattering at Fermilab
XNp
18 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
pppp pppp
“The largest spin effect ever seen by any human”, S. Brodsky, Como 2005
19 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
)sin(PPpSA STTN
need k┴ dependent quark distribution in p↑
z
y
xΦSΦπ
X
p
S
PT
Transverse single spin asymmetries in SIDIS
Sivers mechanism
or p┴ dependent fragmentation of polarized quark Collins mechanism
(talk by G. Schnell)
20 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
X
p
S
+ –
Brodsky, Hwang, Schmidt model for Sivers function
q q
diquark diquark
21 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
p┴ = PT – z k┴ + O(k┴2/Q2)
Sivers asymmetry in SIDIS
)ˆˆ( ),(2
1
),(),(
/
//
kpSkxf
kxfkxf
pq
N
pqpq
pSk┴
φq
22 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin hep-ph/0501196 (PRD 71, 074006) and hep-ph/0507181
23 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Collins mechanism for SSA
Asymmetry in the fragmentation of a transversely polarized quark
pq
φ Sqp┴
)ˆˆ( ),(2
1
),(),(
/
//
ppSpzD
pzDpzD
qqqh
N
qhqh
initial q spin is transferred to final q', which fragments
'll
Sq
Sq’p┴)sin()ˆˆ( '' Shqq ppS
x
y
ΦSΦh
q
q’
(Fundamental QCD property? D. Sivers)
24 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
)sin( ),()/(]y)-(1[1 )(
),( )/()1( )( dd
dd
/22
/2
/
21
2
Sh
q pqpqq
q qh
Nqq
hN
pzDxyxfe
pzDxyyxhe
A
neglecting intrinsic motion in partonic distributions:
]d[ddd
)sin( ]d[ddd 2)sin(
Sh
ShSh
UTShA
Collins function
First extraction of Collins functions from HERMES data: W. Vogelsang and F. Yuan (assuming Soffer-saturated h1)
transversity
25 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
fit to HERMES data on)sin( Sh
UTA
26 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Extraction of Collins functions from HERMES + BELLE data
P1 depends on
)( )(
)( )(
21
2)1(
1)1(
zDzD
zDzD NN
jets theinside pions of onsdistributi azimuthal twothe
between is that , and ofspin thebetween event,by event n,correlatio
27 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Fits to HERMES Collins data, preliminary results
28 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Fits to BELLE Collins data, preliminary results M.A, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin, in preparation
29 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
qTpq
N fM
kf
1/
2
pSk┴
φq
pq
φ Sqp┴
)ˆˆ( ),(2
1
),(),(
/
//
ppSpzD
pzDpzD
qqqh
N
qhqh
)ˆˆ( ),(2
1
),(),(
/
//
kpSkxf
kxfkxf
pq
N
pqpq
Amsterdam group notations
q
hqh
N HMz
pD 1/
2
spin-k┴ correlations – Trento conventions
Sivers function Collins function
YD
qTSIDIS
qT ff
11
30 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
q
pq
N hM
kf 1/
p
Sqk┴
φq
pq
φSΛp┴
)ˆˆ( ),(2
1
),(2
1),(
/
//
ppSpzD
pzDpzD
N
qhq
)ˆˆ( ),(2
1
),(2
1),(
/
//
kpSkxf
kxfkxf
qpq
N
pqpq
Amsterdam group notations
qTq
N DMz
pD
1/
spin-k┴ correlations
Boer-Mulders function polarizing f.f.
31 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
SSA in p↑p → π X
fit to AN with Sivers effects alone
maximized value of AN
with Collins effects alone
E704 data, E = 200 GeV
U. D’Alesio, F. Murgia M.A, M. Boglione, U. D’Alesio, E. Leader, F. Murgia
32 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
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
qq , and 1h (or ) , qq T
qqq
qqq
qqqT
q qq 5chiral-even
qT qq 5 related to chiral-odd
qqqT ||2
ggg gluon helicity distribution – poorly known
ggg gluon distribution ~ known
33 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
+–– –
++ +
+ +
+ =),( 2Qxq),( 2Qxq
+– =),( 2Qxq
),( 2QxqT
|| 2
1 iin helicity basis
–+
+ – ),( 2
1 Qxh decouples from DIS (no quark helicity flip)
34 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
h1 must couple to another chiral-odd function. For example: D-Y, pp → l+l– X, and SIDIS, l p → l π X, processes
++ –
++
–
+ –
–– +
–
+ –
h1 x h1
h1 x Collins function
J. Ralston and D.Soper, 1979 J. Cortes, B. Pire, J. Ralston, 1992
J. Collins, 1993
35 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
–+
+1 –1
2 g
1
No gluon contribution to h1
simple Q2 evolution
Q2 = 25 GeV2 Q02
= 0.23 GeV2
V. Barone, T. Calarco, A. Drago
36 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Elementary LO interaction:
3 planes: plane ┴ polarization vectors,p-γ* plane, l+l– γ* plane
)( )()( )(1
9
42121
2
212
2
2
2
xqxqxqxqexxsMdxdM
daaaa
aa
F
sqxsMxxxxx LFF /2 / 22121
llqq *
plenty of spin effects
h1 in Drell-Yan processes
p p
Q2 = M2
qT
qL
l+
l–γ*
37 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
h1 from
)()(
)()(ˆ
)()()()(
)()()()(ˆ
21
2111
21212
211121112
xuxu
xhxha
xqxqxqxqe
xhxhxhxheaA uu
TT
q q
q qqqqq
TTTT
22 GeV 2 GeV 21030 MsGSI energies: large x1,x2
one measures h1 in the quark valence region: ATT
is estimated to be large, between 0.2 and 0.4
at GSIXllpp
PAX proposal: hep-ex/0505054
s = 210 GeV2 is best energy (talk by P. Reimer at workshop)
38 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Energy for Drell-Yan processes
"safe region": /JMM
s
M J /2
QCD corrections might be very large at smaller values of M:
yes, for cross-sections, not for ATT K-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
39 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
s=30 GeV2 s=45 GeV2
s=210 GeV2s=900 GeV2
40 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
Alternative accesses to transversity
Inclusive Λ production and measure of Λ polarization
)()(1 zDxhP T (transverse fragmentation function)
Two pion production: l p↑ → π π X
),()(dd 1 pzqxh I (interference
fragmentation function)
Vector meson production: l p↑ → ρ X
),()()( ,0,1110 pzDxhV
(generalized fragmentation function)
Inclusive hadronic production: p p↑ → π X
),()(dd/1
pzDxh
q
N
Single Spin Asymmetry in D-Y processes
),()(dd 11 pzhxh (Boer-Mulders function)
(problematic)
41 EINN 2005 Spin dependence-theory September 23rd, Milos, Greece
The spin story goes on .......
Polarization data has often been the graveyard of fashionable theories. If theorists had their way, they might just ban such measurements altogether out of self-protection.
J.D. BjorkenSt. Croix, 1987
Spin is one of the most fundamental concepts in physics, deeply rooted in Poincare 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.
RHIC proposal 2005