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Mauro Anselmino, Torino University and INFN, Vancouver, July 31, 2007

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Generalization of collinear scheme (M. A., M. Boglione, U. D'Alesio, E. Leader, ... 'collinear expansion' at order ki. fits of E704 and STAR data. Kouvaris, Qiu, ... – PowerPoint PPT presentation

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Title: Mauro Anselmino, Torino University and INFN, Vancouver, July 31, 2007


1
The transverse spin structure of the nucleon
Mauro Anselmino, Torino University and INFN,
Vancouver, July 31, 2007
2
The longitudinal structure of nucleons is
simple It has been studied for almost 40 years
Q2
3
essentially x and Q2 degrees of freedom ….
4
Very good or good knowledge of q(x,Q2), g(x,Q2)
and ?q(x,Q2) Poor knowledge of ?g(x,Q2)
(Research Plan for Spin Physics at RHIC)
Talk by L. De Nardo
5
The transverse structure is much more interesting
and less studied
orbiting quarks?
spin-k- correlations?
Space dependent distribution functions
Transverse Momentum Dependent distribution
functions
6
The mother of all functions M. Diehl, Trento
workshop, June 07
Wigner function
(Belitsky, Ji, Yuan)
GPDs
TMDs
7
TMDs in SIDIS
SSA in SIDIS Sivers
functions Collins function from ee- 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)
8
Main source of information on transverse nucleon
structure
SIDIS kinematics according to Trento conventions
(2004)
9
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
10
SIDIS in parton model with intrinsic k-
11
Azimuthal dependence induced by quark intrinsic
motion
EMC data, µp and µd, E between 100 and 280 GeV
M.A., M. Boglione, U. DAlesio, A. Kotzinian, F.
Murgia and A. Prokudin
12
Sivers function
Boer-Mulders function
13
8 leading-twist spin-k- dependent distribution
functions
Courtesy of Aram Kotzinian
14
Collins function
Polarizing fragmentation function
15
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16
Large K asymmetry!
17
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18
Talk by G. Schnell
19
COMPASS measured Collins and Sivers asymmetries
for positive (?) and negative (?) hadrons
small values due to deuteron target cancellation
between u and d contributions
talk by T. Iwata
20
M. Anselmino, M. Boglione, U. DAlesio, A.
Kotzinian, F. Murgia, A. Prokudin
A fit of HERMES COMPASS pion data, information
on u and d Sivers funtions
sea contribution?
no sea contribution
(Kretzer fragmentation functions)
21
Fragmentation functions
DSS de Florian, Sassot, Stratmann KRE
Kretzer HKNS
Hirai, Kumano, Nagai, Sudoh
22
M. Anselmino, M. Boglione, U. DAlesio, A.
Kotzinian, F. Murgia, A. Prokudin
fit of HERMES COMPASS pion and kaon data, with
new set of fragmentation functions (de Florian,
Sassot, Stratmann)
23
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24
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25
Predictions for JLab
26
Present knowledge of Sivers function (u,d)
M. Anselmino, M. Boglione, J.C. Collins, U.
DAlesio, A.V. Efremov, K. Goeke, A. Kotzinian,
S. Menze, A. Metz, F. Murgia, A. Prokudin, P.
Schweitzer, W. Vogelsang, F. Yuan
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-s regions of the
various parameterizations.
27
What do we learn from the Sivers distribution?
number density of partons with longitudinal
momentum fraction x and transverse momentum k-,
inside a proton with spin S
M. Burkardt, PR D69, 091501 (2004)
28
Total amount of intrinsic momentum carried by
partons of flavour a
for a proton moving along the z-axis and
polarization vector
S
29
Numerical estimates from SIDIS data
U. DAlesio
30
Sivers function and orbital angular momentum
D. Sivers
For a proton moving along z and polarized along y
31
Sivers function and proton anomalous magnetic
moment
M. 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
in qualitative agreement with large z data
related result (M. Burkardt)
32
Collins function from ee processes (spin
effects without polarization, D. Boer)
BELLE _at_ KEK
ee- CMS frame
33
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34
Fit of BELLE data
35
Extraction of Collins functions and transversity
distributions from fitting HERMES COMPASS
BELLE data
M. Anselmino, M. Boglione, U.
DAlesio, A. Kotzinian, F.
Murgia, A. Prokudin C. Türk
36
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 …
37
TMDs and SSAs in hadronic collisions
(abandoning safe grounds ….)
(collinear configurations)
factorization theorem (?)
38
excellent agreement with data for unpolarized
cross section, but no SSA
39
BNL-AGS vs 6.6 GeV 0.6 lt pT lt 1.2
E704 vs 20 GeV 0.7 lt pT lt 2.0
observed transverse Single Spin Asymmetries
E704 vs 20 GeV 0.7 lt pT lt 2.0
experimental data on SSA
40
STAR-RHIC vs 200 GeV 1.2 lt pT lt 2.8
and AN stays at high energies ….
talk by L. Bland
41
SSA in hadronic processes intrinsic k-,
factorization?
Two main different (?) approaches
Generalization of collinear scheme
(M. A., M. Boglione, U. DAlesio, E.
Leader, F. Murgia, S. Melis)
42
It generalizes to polarized case
plenty of phases
main remaining contribution to SSA from Sivers
effect
43
U. DAlesio, F. Murgia
E704 data
STAR data
prediction
fit
44
Higher-twist partonic correlations (Efremov,
Teryaev Qiu, Sterman Kouvaris, Vogelsang, Yuan)
hard interactions
twist-3 functions
collinear expansion at order ki-
45
fits of E704 and STAR data
Kouvaris, Qiu, Vogelsang, Yuan
46
Bacchetta, Bomhof, Mulders, Pijlman Vogelsang,
Yuan
factorization ? (Collins)
Sivers contribution to SSA
gluonic pole cross sections take into account
gauge links
Diagram dependent Gauge link Colour factors
(breaking of factorization?)
47
to be compared with the usual cross section
48
Non-universality of Sivers Asymmetries Unique
Prediction of Gauge Theory !
Simple QED example
Drell-Yan repulsive
DIS attractive
Same in QCD
As a result
49
TMDs and SSAs in Drell-Yan processes
(returning to safer grounds and looking at
future ….)
factorization holds, two scales, M2, and
50
Unpolarized cross section already very interesting
Collins-Soper frame
51
(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

! ! !
Talks by R. Kaiser, M. Contalbrigo
52
Conclusions
Increasing 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
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