fisica dello spin27 settembre 2005, otranto1 surprises: transverse single spin asymmetries...
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Fisica dello Spin 27 Settembre 2005, Otranto 1
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 27 Settembre 2005, Otranto 2
S
p
p'
– pPTθ
θsinPpSdd
ddT
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
Fisica dello Spin 27 Settembre 2005, Otranto 3
S
p
p'
– pPTθ
– p'
z
y
xΦS Φ
for a generic configuration:
)sin(PPpSdd
ddSTT
NA
Fisica dello Spin 27 Settembre 2005, Otranto 4
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
Single spin asymmetries at partonic level. Example: '' qqqq
Fisica dello Spin 27 Settembre 2005, Otranto 5
Helicity conservation in pQCD or QED
qq ,
momenta-four ',qq
qqqqqq E
mOuqu q
','' ... )(
qq ','
helicities ', qq
odd numbers of gamma matrices
Fisica dello Spin 27 Settembre 2005, Otranto 6
BNL-AGS √s = 6.6 GeV 0.6 < pT < 1.2
E704 √s = 20 GeV 0.7 < pT < 2.0
E704 √s = 20 GeV 0.7 < pT < 2.0
experimental data on SSA
Xpp
Xpp
observed transverse Single Spin Asymmetries
dd
ddNA
Fisica dello Spin 27 Settembre 2005, Otranto 7
S
p – pPT z
y
x
X– PT
)(d)(d TT PP
)(d)(d)(d)(d TTTT PPPP
AN= simple left-right asymmetry
Fisica dello Spin 27 Settembre 2005, Otranto 8
STAR-RHIC √s = 200 GeV 1.1 < pT < 2.5
AN stays at high energies ….
Fisica dello Spin 27 Settembre 2005, Otranto 9
“Sivers moment”
XlNl
dd
ddNA
)dd(d d
)sin()dd(d d2
)sin(2
S
S
)sin(
S
UTSSA
Fisica dello Spin 27 Settembre 2005, Otranto 10
“Collins moment”
dd
ddNA
XlNl
)dd(d d
)sin()dd(d d2
)sin(2
S
S
)sin(
S
UTSSA
Fisica dello Spin 27 Settembre 2005, Otranto 11
Transverse Λ polarization in unpolarized p-Be scattering at Fermilab
XNp
Fisica dello Spin 27 Settembre 2005, Otranto 12
pppp pppp
Fisica dello Spin 27 Settembre 2005, Otranto 13
Spin is challenging .......
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
Fisica dello Spin 27 Settembre 2005, Otranto 14
frame c.m. * )sin(PPpSA STTN p
needs k┴ dependent quark distribution in p↑ (Sivers mechanism) or p┴ dependent fragmentation of polarized quark (Collins mechanism)
z
y
xΦSΦπ
X
p
S
PT
Transverse single spin asymmetries in SIDIS
if partons inside p are all collinear there cannot be (at LO) any PT
Fisica dello Spin 27 Settembre 2005, Otranto 15
There must be a primordial intrinsic k┴ due to quark confinement:
GeV/c 0.2 fm 1 px
There is intrinsic k┴ generated by QCD evolution
±1
± ±k┴
k┴ dependent parton distributions (TMD) ),,( 2,/, Qkxf Spsa
),,(ˆd),,(d 22 QpzDQkxf hq
lqlq
lhXlp
The elementary interaction depends on
Azimuthal dependence in unpolarized SIDIS cross section (Cahn effect)
)0,sin,(cos k
Fisica dello Spin 27 Settembre 2005, Otranto 16
EMC data
Fisica dello Spin 27 Settembre 2005, Otranto 17
a b
c
0D
X
X
ffBNL data, PLB 73 (1978)
F. Murgia, U. D’Alesio
Xpp 0 GeV 20soriginal idea from Feynman-Field
GeV 8.0 k k no
non collinear configurations
Fisica dello Spin 27 Settembre 2005, Otranto 18
X
p
S
+ –
Brodsky, Hwang, Schmidt model for Sivers function
q q
diquark, Q
Qqp *
diquark, Q
cannot be forward in order to have a SSA
intrinsic k┴ of quark
Fisica dello Spin 27 Settembre 2005, Otranto 19
p┴ = PT – z k┴ + O(k┴2/Q2)
Sivers mechanism in SIDIS
pSk┴
φq
)ˆˆ( ),(2
1
),(),(
/
//
kpSkxf
kxfkxf
pq
N
pqpq
Fisica dello Spin 27 Settembre 2005, Otranto 20
M.A., U.D’Alesio, M.Boglione, A.Kotzinian, A Prokudin
from Sivers mechanism)sin( S
UTA
Fisica dello Spin 27 Settembre 2005, Otranto 21
Deuteron target hdhupd
N
pu
NUT DDffA Sh
4 //
)sin(
Fisica dello Spin 27 Settembre 2005, Otranto 22
HERMES + E704: Sivers function is not zero
Theory: not quite universal
J. Collins, a “QCD theorem”
Models: few, in fair agreement
Spin-k┴ partonic correlations in nucleons
YD
qTSIDIS
qT ff
11
dT
uT ff 11
chiral models
qqTf
1M. Burkardt
Fisica dello Spin 27 Settembre 2005, Otranto 23
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)
Fisica dello Spin 27 Settembre 2005, Otranto 24
)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
some data available from HERMES, first extraction of Collins functions: W. Vogelsang and F. Yuan (assuming Soffer-saturated h1)
transversity
Fisica dello Spin 27 Settembre 2005, Otranto 25
fit to HERMES data on)sin( Sh
UTA
Fisica dello Spin 27 Settembre 2005, Otranto 26
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
Sivers function Collins function
Fisica dello Spin 27 Settembre 2005, Otranto 27
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/ 2
spin-k┴ correlations
Boer-Mulders function polarizing f.f.
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