Based on works in collaboration with M. Boglione, U. D

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Spin effects and partonic intrinsic k-

• Parton intrinsic motion (k-) in unpolarized
  inclusive processes
• k- and SSA in SIDIS
• k- and SSA in pp interactions
• Spin-k- correlations in distribution (fq/p ) and
  fragmentation (Dh/q ) functions
• Factorization, QCD evolution, universality with
  spin-k- dependent fq/p and Dh/q

Based on works in collaboration with M. Boglione,
U. DAlesio, A. Kotzinian, E. Leader, S. Melis,
F. Murgia and A. Prokudin
Phys. Rev. D71 (2005) 074006 D72 (2005)
094007 D71 (2005) 014002 Phys. Rev. D73 (2006)
014020
Mauro Anselmino, BNL, 21/02/2006
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Partonic intrinsic motion
Plenty of theoretical and experimental evidence
for transverse motion of partons within nucleons
and of hadrons within fragmentation jets
qT distribution of lepton pairs in D-Y processes
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pT distribution of hadrons in SIDIS

Hadron distribution in jets in ee processes
Large pT particle production in
Transverse motion is usually integrated, but
there might be important spin-k- correlations
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Unpolarized SIDIS (LO)
M. Arneodo et al (EMC) Z. Phys. C 34 (1987) 277
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Cahn the observed azimuthal dependence is
related to the intrinsic k- of quarks (at least
for small PT values)
assuming collinear fragmentation, f Fh
These modulations of the cross section with
azimuthal angle are denoted as Cahn effect.
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SIDIS with intrinsic k-
kinematics according to Trento conventions (2004)
factorization holds at large Q2, and
Ji, Ma, Yuan
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The situation is more complicated as the produced
hadron has also intrinsic transverse momentum
with respect to the fragmenting parton.
neglecting terms
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assuming
one finds
with
clear dependence on
(assumed to be constant)
Find best values by fitting data on Fh and PT
dependences
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EMC data, µp and µd, E between 100 and 280 GeV.
Dashed line exact kinematics, red solid line
only terms up to O(k-/Q)
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The closed area shows effects of varying by 20
Data from E665, ELab 490 GeV. s is integrated
from PTcut to PTmax. At low PTcut the non
perturbative k- contributions dominate. At large
PTcut NLO pQCD contributions take over
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EMC data
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EMC data
Fitting the unpolarized data leads to the best
values
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Large PT data explained by NLO QCD corrections
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(collinear configurations)
factorization theorem
X
c
a
b
X
FF
PDF
pQCD elementary interactions
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The cross section
elementary Mandelstam variables
hadronic Mandelstam variables
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RHIC data
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Transverse single spin asymmetries elastic
scattering
S
y
p'
x
PT
?
z
p
p
p'
Example
5 independent helicity amplitudes
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y
FS
F
x
S
p'
PT
?
p
p
z
p'
for a generic configuration
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Single spin asymmetries at partonic level.
Example
needs helicity flip relative phase




x




QED and QCD interactions conserve helicity, up to
corrections
at quark level
but large SSA observed at hadron level!
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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
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STAR-RHIC vs 200 GeV 1.1 lt pT lt 2.5
AN stays at high energies .
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Sivers moment
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Collins moment
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Transverse ? polarization in unpolarized p-Be
scattering at Fermilab
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Transverse single spin asymmetries in SIDIS
y
Fp
FS
x
S
PT
p
z
X
in collinear configurations there cannot be (at
LO) any PT
needs k- dependent quark distribution in p?
(Sivers mechanism) or p- dependent fragmentation
of polarized quark (Collins mechanism)
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Brodsky, Hwang, Schmidt model for Sivers function
S
p
X
q
q


diquark
diquark
needs k- dependent quark distribution in p?
Sivers function
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Sivers mechanism in SIDIS
p- PT z k- O(k-2/Q2)
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M.A., U.DAlesio, M.Boglione, A.Kotzinian, A
Prokudin
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Deuteron target
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M.A, M. Boglione, U. DAlesio, A. Kotzinian, F.
Murgia, A. Prokudin
hep-ph/0511017
First p- moments of extracted Sivers functions,
compared with models
data from HERMES and COMPASS
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Predictions for K production at HERMES
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Q2 gt 1 (GeV/c)2 W2 gt 25 GeV2 PT gt 0.1 GeV/c
Eh gt 4 GeV 0.2 lt zh lt 0.9 0.1 lt y lt
0.9
Predictions for COMPASS, hydrogen target
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predictions for COMPASS, proton target
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Collins mechanism for SSA
Asymmetry in the fragmentation of a transversely
polarized quark
(Fundamental QCD property? D. Sivers)
q
q
y
initial q spin is transferred to final q', which
fragments
Sq
Sq
p-
FS
Fh
x
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neglecting intrinsic motion in partonic
distributions
Collins function
transversity
some data available from HERMES, first extraction
of Collins functions W. Vogelsang and F. Yuan
(assuming Soffer-saturated h1)
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fit to HERMES data on
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spin-k- correlations
Sivers function
Collins function
Amsterdam group notations
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spin-k- correlations
q
f
f
Sq
S?
k-
p-
p
pq
Boer-Mulders function
polarizing f.f.
Amsterdam group notations
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Hadronic processes the cross section with
intrinsic k-
intrinsic k- in distribution and fragmentation
functions and in elementary interactions
factorization is assumed, not proven in general
some progress for Drell-Yan processes, two-jet
production, Higgs production via gluon fusion
(Ji, Ma, Yuan Collins, Metz Bacchetta, Bomhof,
Mulders, Pijlman)
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The polarized cross section with intrinsic k-
helicity density matrix of parton a inside
polarized hadron A
pQCD helicity amplitudes
product of fragmentation amplitudes
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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 amplitudes they
strongly suppress the results of integrations
over k-
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Maximised (i.e., saturating positivity bounds)
contributions to AN
quark Sivers contribution
gluon Sivers contribution
Collins contribution
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SSA in p?p ? p X
E704 data, E 200 GeV
maximized value of AN with Collins effects alone
fit to AN with Sivers effects alone
M.A, M. Boglione, U. DAlesio, E. Leader, F.
Murgia
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Conclusions

• Unintegrated (TMD) distribution functions allow
  a much better description of QCD nucleon
  structure and hadronic interactions (necessary
  for correct differential distribution of final
  state particles, recent paper by Collins, Jung,
  hep-ph/0508280)
• k- is crucial to understand observed SSA in
  SIDIS and pp interactions
• Spin-k- dependent distribution and fragmentation
  functions towards a complete phenomenology of
  spin asymmetries
• Open issues factorization, QCD evolution,
  universality, higher perturbative orders,