Spin and k dependent parton distributions

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Spin and k- dependent parton distributions
- a closer look at the nucleon structure -
(with the help of antiprotons)

• integrated partonic distributions
• the missing piece, transversity
• partonic intrinsic motion (TMD)
• spin and k- transverse Single Spin
  Asymmetries
• SSA in SIDIS and p-p, p-pbar inclusive
  processes
• conclusions

Mauro Anselmino, ECT Trento, 04/07/2006
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K- integrated parton distributions
quark distribution well known
all equally important
quark helicity distribution known
transversity distribution unknown
gluon helicity distribution poorly known
related to
chiral-even
chiral-odd
related to
positivity bound
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de Florian, Navarro, Sassot
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Research Plan for Spin Physics at RHIC
February 11, 2005
Figure 11 Left results for ?g(x,Q2 5GeV2)
from recent NLO analyses 1, 2, 36 of
polarized DIS. The various bands indicate ranges
in ?g that were deemed consistent with the
scaling violations in polarized DIS in these
analyses. The rather large differences among
these bands partly result from differing
theoretical assumptions in the extraction, for
example, regarding the shape of ?g(x) at the
initial scale. Note that we show x?g as a
function of log(x), in order to display the
contributions from various x-regions to the
integral of ?g. Right the net
gluon polarization ?g(x,Q2)/g(x,Q2) at Q2 5
GeV2, using ?g of 2 and its associated
band, and the unpolarized gluon distribution of
82.
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The missing piece, transversity














in helicity basis


decouples from DIS (no quark helicity flip)


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h1 must couple to another chiral-odd function.
For example


h1 x h1


J. Ralston and D.Soper, 1979 J. Cortes, B. Pire,
J. Ralston, 1992




h1 x Collins function






J. Collins, 1993
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No gluon contribution to h1
simple Q2 evolution
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1


Q2 25 GeV2 Q02 0.23 GeV2
V. Barone, T. Calarco, A. Drago
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First ever transversity, according to Gary
Goldstein, QCD-N06, Villa Mondragone, June 15,
2006
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Elementary LO interaction
3 planes
plenty of spin effects
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h1 from
at RHIC
RHIC energies
small x1 and/or x2
h1q (x, Q2) evolution much slower than ?q(x, Q2)
and q(x, Q2) at small x
ATT at RHIC is very small smaller s would help
Barone, Calarco, Drago
Martin, Schäfer, Stratmann, Vogelsang
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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, p N processes, s 80 GeV2
H. Shimizu, G. Sterman, W. Vogelsang and H. Yokoya
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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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orbiting quarks?
spin-k- correlations?
Transverse Momentum Dependent distribution
functions
Space dependent distribution functions (GPD)
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in collinear parton model
thus, no dependence on azimuthal angle ?h at
zero-th order in pQCD
the experimental data reveal that
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
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assuming
one finds
with
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
M.A., M. Boglione, U. DAlesio, A. Kotzinian, F.
Murgia and A. Prokudin
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Large PT data explained by NLO QCD corrections
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dashed line parton model with unintegrated
distribution and fragmentation functions solid
line pQCD contributions at LO and a K factor (K
1.5) to account for NLO effects
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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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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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Transverse ? polarization in unpolarized p-Be
scattering at Fermilab
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Sivers moment
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Collins moment
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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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8 leading-twist spin-k- dependent distribution
functions
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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. 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.
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fit to HERMES data on
W. Vogelsang and F. Yuan
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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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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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Special channels available with antiprotons
Results from U. DAlesio
Maximised (i.e., saturating positivity bounds)
contributions to AN
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Predictions for AN in D-Y processes
Sivers function from SIDIS data, large asymmetry
and cross section expected
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SSA in p?p ? D X
only Sivers effect no transverse spin transfer
in
dominance of gluonic channel, access to gluon
Sivers function
assuming saturated Sivers function
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predictions based on Sivers functions extracted
from fitting E704 data
maximised contributions from h1 times B-M, not
suppressed by phases
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predictions based on Sivers functions from E704
data
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Conclusions

• Polarized antiprotons are the only way to
  access directly the transversity distribution
  optimum energy at s 200 GeV2
• 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, (Collins, Jung, hep-ph/0508280)
  
• k- is crucial to understand observed SSA in
  SIDIS and pp interactions antiprotons
  will add new information and allow further test
  of our understanding
• Spin-k- dependent distribution and fragmentation
  functions towards a complete phenomenology of
  spin asymmetries
• Open issues factorization, QCD evolution,
  universality, higher perturbative orders,