Post on 27-Mar-2015
Mauro Anselmino, Torino University and INFN,
Vancouver, July 31, 2007
The transverse spin structure of the
nucleon
xP
P
The longitudinal structure of nucleons is “simple” It has been studied for almost 40
years
Q2
essentially x and Q2 degrees of freedom ….
Very good or good knowledge of q(x,Q2), g(x,Q2) and Δq(x,Q2) Poor knowledge of Δg(x,Q2)
? 2
1 gqgq LLSS
(Research Plan for Spin Physics at RHIC)
Talk by L. De Nardo
spin-k┴ correlations? orbiting quarks?
Transverse Momentum Dependent distribution
functions
Space dependent distribution functions
);,( 2Qxq k ),( 2;Qxq b
k
?
b
The transverse structure is much more interesting and less studied
The mother of all functions M. Diehl, Trento
workshop, June 07
TMD’s
GPD’sWigner function
(Belitsky, Ji, Yuan)
TMDs in SIDIS
SSA in SIDIS: Sivers functions
Collins function from e+e- unpolarized processes (Belle) and first extraction of
transversity
SSA in hadronic processes
Future measurements and transversity
(Trento workshop on “Transverse momentum, spin, and position distributions of partons in hadrons”, June
07)
SIDIS kinematics according to
Trento conventions
(2004)
Main source of information on
transverse nucleon structure
Polarized SIDIS cross section, up to subleading order in 1/Q
Kotzinian, NP B441 (1995) 234
Mulders and Tangermann, NP B461 (1996) 197
Boer and Mulders, PR D57 (1998) 5780
Bacchetta et al., PL B595 (2004) 309
Bacchetta et al., JHEP 0702 (2007) 093
SIDISLAND
SIDIS in parton model with intrinsic k┴
);,();,(ˆd);,(d 222 QzDQyQxf hq
lqlq
q qlhXlp
pkk
factorization holds at large Q2, and
QCDT kP Ji, Ma, Yuan
EMC data, µp and µd, E between 100 and 280 GeV
M.A., M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia and A. Prokudin
Azimuthal dependence induced by quark intrinsic motion
)ˆˆ( ),(),(
)ˆˆ( ),(2
1),(),(
1/
//,/
kpS
kpSkS
kxfM
kkxf
kxfkxfxf
qTpq
pq
Npqpq
Sivers function
Boer-Mulders function
)ˆˆ( ),(2
1),(
2
1
)ˆˆ( ),(2
1),(
2
1),(
1/
///,
kps
kpsks
pq
qpq
Npqpq
kxhM
kkxf
kxfkxfxfq
8 leading-twist spin-k┴ dependent distribution functions
Courtesy of Aram Kotzinian
)ˆˆ( ),(
),(
)ˆˆ( ),(2
1 ),(),(
1/
//,/
pps
ppsps
qqq
hqh
qqqh
Nqhqh
pzHMz
ppzD
pzDpzDzDq
Collins function
)ˆˆ( ),(
),(2
1
)ˆˆ( ),(2
1 ),(
2
1),(
1/
///,
ppS
ppSpS
Tqh
Nqhq
pzDMz
ppzD
pzDpzDzD
Polarizing fragmentation function
),(),(
)dd(d d
)sin()dd(d d2
)sin(2
//
2
)sin(
pzDkxfe
ΦΦ
ΦΦΦΦ
AΦΦ
qpq
N
q q
S
SS
ΦΦUTS
S
Large K+ asymmetr
y!
),(),(
)dd(d d
)sin()dd(d d2
)sin(2
/12
)sin(
pzDkxhe
ΦΦ
ΦΦΦΦ
AΦΦ
qh
N
q qq
S
SS
ΦΦUTS
S
Talk by G.
Schnell
COMPASS measured Collins and Sivers asymmetries for positive (●) and negative (○) hadrons
dhuhpd
N
pu
NUT DDffA Sh
////
)sin( 4
small values due to
deuteron target:
cancellation between u and d contributions
dh
N
uh
NduUT DDhhA Sh
//11)sin( 4
talk by T. Iwata
M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. ProkudinA fit of HERMES + COMPASS pion
data, information on u and d Sivers funtions
no sea contribution
sea contribution?
(Kretzer fragmentation functions)
DSS = de Florian, Sassot, Stratmann KRE = Kretzer HKNS = Hirai, Kumano, Nagai, Sudoh
Fragmentation functions
M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia, A. Prokudin
fit of HERMES + COMPASS pion and kaon data, with new set of fragmentation functions (de Florian, Sassot,
Stratmann)
Predictions for JLab
The first and 1/2-transverse moments of the Sivers quark distribution functions. The fits were constrained mainly (or solely) by the preliminary HERMES data in the indicated x-range. The
curves indicate the 1-σ regions of the various parameterizations.
),( )( 12)2/1(
1
kxf
M
kdxf q
Tq
T k
M. Anselmino, M. Boglione, J.C. Collins, U. D’Alesio, A.V. Efremov, K. Goeke, A. Kotzinian, S. Menze, A. Metz, F. Murgia, A. Prokudin, P. Schweitzer, W. Vogelsang, F. Yuan
),( 2
12
22)1(
1
kxf
M
kdf q
Tq
T k
Present knowledge of Sivers function (u,d)
S
kp
k
number density of partons with longitudinal
momentum fraction x and transverse momentum k┴, inside a proton with spin S
0),( /
2 a paxfddx kkk
M. Burkardt, PR D69, 091501 (2004)
What do we learn from the Sivers distribution?
),(ˆ 2
ˆ cosˆ sin
)ˆˆ( ),(ˆ2
1),(ˆ
/
2
//2
kxfkdkdx
kxfkxfddx
pa
NSS
pa
Npa
a
ji
kpSkkk
Total amount of intrinsic momentum carried by partons of flavour a
for a proton moving along the +z-axis and polarization vector
jiS ˆ sinˆ cos SS
S
ak
)sin()ˆˆ( SkpS
GeV/c ˆ cosˆ sin 13.0
GeV/c ˆ cosˆ sin 14.003.002.0
0.050.06-
jik
jik
SSd
SSu
uk
dk? 0
du kk
Sivers functions extracted from AN data in Xpp give also opposite results,
with
036.0 032.0 du kk
Numerical estimates from SIDIS dataU. D’Alesio
Sivers function and orbital angular momentum
Sivers mechanism originates from
qLS then it is related to the quark orbital angular momentum
D. Sivers
For a proton moving along z and polarized along y
? 2
),( 1
0 /
qy
pq
NL
kxfdx
Sivers function and proton anomalous magnetic momentM. Burkardt, S. Brodsky, Z. Lu, I. Schmidt
Both the Sivers function and the proton anomalous magnetic moment are related to correlations of proton wave functions with opposite helicities
? ),( 1
0 /
2qpq
N Ckxfddx k
in qualitative agreement with large z data:
d
uΦΦ
UT
ΦΦ
UT
S
S
A
A
) sin(
) sin(
related result (M. Burkardt)
Collins function from e+e–
processes (spin effects without polarization, D. Boer)
e+e- CMS frame: GeV 52.10 ,2
ss
Ez h
Xhhqqee
BELLE @ KEK
e+
1hP
2hP e-
e+
thrust-axis
z
y
x
1p
2p
)()( 2/1/12 zDzDAq
N
q
N
Fit of BELLE data
Extraction of Collins functions and transversity distributions from fitting HERMES +
COMPASS + BELLE data
M. Anselmino, M. Boglione, U. D’Alesio, A. Kotzinian, F. Murgia,
A. Prokudin C.
Türk
What do we learn (if anything yet) from the transversity distributions and the Collins
functions ? h1u and h1d have opposite signs
They are both smaller than Soffer bound
Still large uncertainties
Tensor charges appear to be smaller than results from lattice QCD calculations M. Wakamatsu, hep-ph/0705.2917
Collins functions well below the positivity bound. Favoured and unfavoured ones have opposite signs, comparable magnitudes
Only the very beginning …
)(ˆd)()( d //,,,,,
/ zDxfxf ccdab
bpbagqqdcba
pa
PDF FF pQCD elementary
interactions
(collinear configurations)Xpp 0factorization theorem
(?)
ab
c
0DX
X
f
fp
p
TMDs and SSAs in hadronic collisions (abandoning safe
grounds ….)
RHIC data GeV 200s
Xpp
excellent agreement with data for unpolarized cross section, but no
SSA
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
and AN stays at high energies ….
STAR-RHIC √s = 200 GeV 1.2 < pT < 2.8
talk by L. Bland
SSA in hadronic processes: intrinsic k┴, factorization?
Two main different (?) approachesGeneralization of collinear scheme (M. A., M. Boglione, U. D’Alesio, E. Leader, F. Murgia, S. Melis)
ab
c
0DX
X
ffp p
),()(ˆd)()( d //,,,,,
/
pkkkk zD,,xf,xf cbacdab
bbpbaagqqdcba
pa
It generalizes to polarized case
),()(ˆˆ
)()(d
,
,,;,,;,
,/,/
,/,/ ,,
''''
''
pkk
kk
zD,MM
,xf,xf
CC
cc
cdab
badc
cdab
badc
B
B
bbA
A
aa
BA
ba
bbSBbSBb
aaSAaSAaXCSBSA
plenty of phases
main remaining contribution to SSA from Sivers effect
),()(ˆd
)()( d
/
//
,
pkk
kk
zD,
,xf,xf
cbacdab
bbpbaaq
pq
NXpSp
E704 data
STAR data
U. D’Alesio, F. Murgia
fit prediction
Higher-twist partonic correlations (Efremov, Teryaev; Qiu, Sterman; Kouvaris, Vogelsang, Yuan)
)(),()(),,( d /21/21,,
zDkkHxfkkT chcab
bBbcba
a S
twist-3 functions
hard interactions
contribution to SSA
) ( XhBA
“collinear expansion” at order ki┴
)()1( / xfxxNT Aaaaaa
fits of E704 and STAR data
Kouvaris, Qiu, Vogelsang, Yuan
Gluonic pole cross sections and SSA in
XhhHH 2121
Bacchetta, Bomhof, Mulders, Pijlman; Vogelsang, Yuan
)()(ˆ)()( d 2/1/][2/1,,
)1(1 211
zDzDdxfxf dhchcdbaHbcba
T
gluonic pole cross sections take into account gauge links
Sivers contribution to SSA
D
Dcdab
DGcdba dCd ˆˆ ][
][][D
GC Diagram dependent Gauge link Colour factors
factorization ? (Collins)
)( )1(1 Ta fT
(breaking of factorization?)
Gluonic pole cross sections and SSA in
XhhHH 2121
to be compared with the usual cross section
llqqllqqlqlqlqql dddd ˆˆ ˆˆ
][][
Simple QEDexample:
DIS: attractive Drell-Yan: repulsiveSame in QCD:
As a result:
Non-universality of Sivers Asymmetries:Unique Prediction of Gauge Theory !
TMDs and SSAs in Drell-Yan processes (returning to safer
grounds and looking at future ….)
p p
Q2 = M2
qT
qL
l+
l–γ*
llqqqq q
YD QxfQxf ˆd );,();,(d 22
21 kk
factorization holds, two scales, M2, and
Tq
2cossin
2cossincos1
3
1
4
31 222
d
d
Unpolarized cross section already very interesting
Collins-Soper frame
(Polarized) Drell-Yan cross sections allow to
access many TMDs (Boer-Mulders, …) D-YLAND
verify whether
and offer the golden channel to measure the transversity distribution
q
qqTT xhxhA )()( 2111
YD
qTSIDIS
qT ff
11 ! ! !
Talks by R. Kaiser, M. Contalbrigo
ConclusionsIncreasing knowledge about quark transverse motion, and spin-k┴ correlations (Sivers function)
First experimental information on h1
Work in progress on GPDs and quark space distribution (Lq)
Towards resolving the orbital motion of quarks in a proton …
More data from HERMES, COMPASS, JLab and RHIC Thanks