Mauro Anselmino: The transverse spin structure of the nucleon III

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Mauro Anselmino The transverse spin structure of
the nucleon - III
About SSA in hadronic interactions
TMDs and SSA in inclusive hadronic
interactions TMDs and SSA in Drell-Yan
processes Drell-Yan processes, the transversity
golden channel Alternative ways to
transversity A fundamental QCD test
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TMDs and SSAs in hadronic collisions

(collinear configurations)
factorization theorem
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Latest PHENIX data on unpolarized cross section
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STAR-RHIC vs 200 GeV 1.2 lt pT lt 2.8
and AN stays at high energies .
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SSA in hadronic processes intrinsic k-,
factorization?
Two main different (?) approaches (W. Vogelsang)
Generalization of collinear scheme (assuming
factorization)
first proposed by Field-Feynman
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Possible sources of SSA, simple approach (one k-
at a time)
suppressed by phases
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General formalism with helicity amplitudes
non planar process, plenty of phases
main remaining contribution to SSA from Sivers
effect
M.A., M. Boglione, U. DAlesio, E. Leader, S.
Melis, F. Murgia, PR D71, 014002 (2005), PR D73,
014020 (2006)
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Computation of helicity amplitudes
Dirac-Pauli helicity spinors
if scattering is not planar all Fi are different
and many phases remain in the amplitudes they
strongly suppress the results of integrations
over k-
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8 leading-twist spin-k- dependent distribution
functions
Courtesy of Aram Kotzinian
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U. DAlesio, F. Murgia
E704 data
STAR data
prediction
fit
For a somewhat different approach see lectures by
W. Vogelsang, great progresses in the last months
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TMDs and SSAs in Drell-Yan processes

factorization holds, two scales, M2, and
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Unpolarized cross section already very interesting
Collins-Soper frame
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For example, the cos 2f term can be originated by
the Boer-Mulders effect
Polarized D-Y processes with intrinsic k- have a
rich structure, similar to SIDIS
SSA in D-Y has a contribution from the coupling
of the transversity distribution to B-M function
B-M
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Sivers effect in D-Y processes
By looking at the cross section one can single
out the Sivers effect in D-Y processes
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M. A., M. Boglione, U. DAlesio, A. Kotzinian, F.
Murgia, A. Prokudin
See later for crucial issue concerning Sivers
function in D-Y
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Simple partonic cross section at collinear level
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Direct access to transversity from double
transverse spin asymmetry
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Possible access transversity Drell-Yan processes
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RHIC energies
small x1 and/or x2
h1q (x, Q2) evolution much slower than ?q(x, Q2)
and q(x, Q2) at small x
Barone, Calarco, Drago
ATT at RHIC is very small smaller s would help
Martin, Schäfer, Stratmann, Vogelsang
ATT for Drell-Yan processes at RHIC
upgrades in luminosity expected
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h1 from
at GSI
large x1,x2
GSI energies
one measures h1 in the quark valence region ATT
is estimated to be large, between 0.2 and 0.4
PAX proposal hep-ex/0505054
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Energy for Drell-Yan processes
"safe region"
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
M. Guzzi,V. Barone, A. Cafarella,C. Corianò and
P.G. Ratcliffe
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s30 GeV2
s45 GeV2
s210 GeV2
s900 GeV2
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s30 GeV2
s45 GeV2
s210 GeV2
s900 GeV2
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data from CERN WA39, pN processes, s 80 GeV2
H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya
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Some alternative accesses to transversity
Inclusive ? production and measure of ?
polarization
COMPASS analysis in progress
the ? polarization vector can be measured by
looking at the proton angular distribution as
resulting from ? ? pp decay in the ? helicity
rest frame
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collinear configuration, no need for intrinsic k-
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Two hadron production in SIDIS
Di-hadron Fragmentation Function (DiFF)
Chiral odd fragmentation function of a
transversely polarized quark into two hadrons
(interference between s and p wave)
Bacchetta, Boer, Jaffe, Jakob, Radici
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TMDs measurements at BELLE (spin physics without
polarization)
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(M. Boglione seminar)
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A fundamental QCD test
The Sivers function, being related to gauge
links, is not universal, but it changes from
process to process
or, rather, it enters different processes with
different numerical factors
J. Collins
Following example taken from a talk prepared by
M. Grosse-Perdekamp and delivered by L. Bland,
Trento 2007
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Non-universality of Sivers Asymmetries Unique
Prediction of Gauge Theory !
Simple QED example
Drell-Yan repulsive
DIS attractive
Same in QCD
As a result
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Not all spin problems have been solved, but
enormous progresses have been made The
spin-orbiting structure of quarks in nucleons
begins to emerge Theory. Unintegrated PDF and FF
play a crucial role their Q2 evolution is
needed. Factorization and universality issues
must be clarified, Experiment. New data from
COMPASS (proton target), JLab, RHIC, and GSI. D-Y
processes very promising
Thanks and see you again!