Transverse Spin and DrellYan Process

1
Transverse Spin and Drell-Yan Process
Jen-Chieh Peng
University of Illinois at Urbana-Champaign
PKU-RBRC Workshop on Transverse Spin Physics,
Beijing, June 30 July 4, 2008
Outline

• Brief overview of TMDs and Drell-Yan
• Recent Drell-Yan results from Fermilab E866
  (Boer-Mulders functions)
• Future prospects for Drell-Yan experiments

2
Complimentality between DIS and Drell-Yan
Drell-Yan
DIS
Both DIS and Drell-Yan cross sections are well
described by NLO calculations
3
Three parton distributions describing quarks
transverse momentum and/or transverse spin
1) Transversity
2) Sivers function
3) Boer-Mulders function
4
Transversity and TMD PDFs are probed in
Semi-Inclusive DIS


Unpolarized
Boer-Mulders
Transversity
Polarized target

Sivers
Polarzied beam and target
SL and ST Target Polarizations ?e Beam
Polarization
5
Transversity and TMD PDFs are also probed in
Drell-Yan
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A Brief History
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Meson East Spectrometer
(E605/772/789/866)
Open-aperture
Closed-aperture
Beam-dump (Cu)
J/?
J/?
?
s(J/?) 15 MeV
s(J/?) 150 MeV
s(J/?) 300 MeV
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Independent confirmation of GSR measurement in DIS
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Gluon distributions in proton versus neutron?
Lingyan Zhu et al., PRL, 100 (2008) 062301
(arXiv 0710.2344)
Gluon distributions in proton and neutron are
very similar
10
Decay angular distributions from E866 Drell-Yan
200,000 high-mass Drell-Yan events
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Drell-Yan decay angular distributions
T and F are the decay polar and azimuthal angles
of the µ in the dilepton rest-frame
Collins-Soper frame
A general expression for Drell-Yan decay angular
distributions
In general
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Drell-Yan decay angular distributions
T and F are the decay polar and azimuthal angles
of the µ in the dilepton rest-frame
Collins-Soper frame
A general expression for Drell-Yan decay angular
distributions
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Decay angular distributions in pion-induced
Drell-Yan
NA10 p- W
Z. Phys. 37 (1988) 545
Dashed curves are from pQCD calculations
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Nuclear Effect?
NA10 Z. Phys. C37, 545 (1988)
Open Deuterium Solid Tungsten
Nuclear effect seems not to be the dominant
contribution.
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Decay angular distributions in pion-induced
Drell-Yan
E615 Data 252 GeV p- W
Phys. Rev. D 39 (1989) 92
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Decay angular distributions in pion-induced
Drell-Yan
Is the Lam-Tung relation violated?
140 GeV/c
194 GeV/c
286 GeV/c
Data from NA10 (Z. Phys. 37 (1988) 545)
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Boer-Mulders function h1-
?10.47, MC2.3 GeV
Boer, PRD 60 (1999) 014012
?gt0 implies valence BM functions for pion and
nucleon have same signs
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Motivation for measuring decay angular
distributions in pp and pd Drell-Yan

• No proton-induced Drell-Yan azimuthal decay
  angular distribution data
• Provide constraints on models explaining the
  pion-induced Drell-Yan data. (h1- is expected to
  be small for sea quarks. Some other models
  predict similar effects for pN and pN)
• Test of the Lam-Tung relation in proton-induced
  Drell-Yan
• Compare the decay angular distribution of pp
  versus pd (information on flavor dependence)

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Azimuthal cos2F Distribution in pd Drell-Yan
Lingyan Zhu et al., PRL 99 (2007) 082301
With Boer-Mulders function h1- ?(p-W?µµ-X)
valence h1-(p) valence h1-(p) ?(pd?µµ-X)
valence h1-(p) sea h1-(p)
?gt0 suggests same sign for the valence and sea BM
functions
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What does this mean?

• These results suggest that the Boer-Mulders
  functions h1- for sea quarks are significantly
  smaller than for valence quarks and have the same
  sign as valence quarks.
• A combined analysis of pp and pd, together with
  the pp and pd Drell-Yan cos(2?) data can lead
  to extraction of valence and sea Boer-Mulders
  functions.

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Extraction of Boer-Mulders functions from pd
Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt,
arXiv0803.1692)
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Quark-diquark Models for Boer-Mulders Function
h1-

• Initial-state gluon interaction can produce
  nonzero h1- for the proton in the quark-scalar
  diquark model. In this model,
• h1- f1T-.
• Boer,BrodskyHwang, PRD67,054003(2003).
• Recent quark-diquark model including
  axial-diquarks Gamberg, Goldstein Schlegel,
  arXiv 0708.0324.

B-M u-quark
B-M d-quark
Sivers d-quark
Sivers u-quark
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A simple explanation for the signs of the up- and
down-quark Boer-Mulders functions
1) Transversity
2) Sivers function
3) Boer-Mulders function
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Sea-quark Boer-Mulders Functions
1) Use quark-spectator-antiquark model to
calculate pion B-M functions. Pion-induced
Drell-Yan data are well reproduced.
(Lu and Ma, hep-ph/0504184)
2) Use pion-cloud model convoluted with the pion
B-M function to calculate sea-quark B-M for
proton.
(Lu, Ma, Schmidt, hep-ph/0701255)
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Extraction of Boer-Mulders functions from pd
Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt,
arXiv0803.1692)
Fit to the pd Drell-Yan data
Satisfy the positivity bound
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Extraction of Boer-Mulders functions from pd
Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt,
arXiv0803.1692)

• It seems unlikely that pd data alone can
  determine the flavor structure of BM functions!

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Extraction of Boer-Mulders functions from pd
Drell-Yan
(B. Zhang, Z. Lu, B-Q. Ma and I. Schmidt, Private
communication)
Predict larger values of ? for pp than for pd
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New results on the Azimuthal cos2F Distribution
in pp Drell-Yan

• pp is similar to pd
• A global fit to all pion and proton data is
  needed

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Angular Distribution in E866 pp/pd Drell-Yan
PT (GeV/c)
pp and pd Drell-Yan show similar angular
distributions. Should be analysed togther for
better constraints on BM.
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QCD correction
(Talk by Werner Vogelsang)
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Future prospect for Drell-Yan experiments

• Fermilab pp, pd, pA
• Unpolarized beam and target
• RHIC
• Polarized pp collision
• COMPASS
• p-p and p-d with polarized targets
• FAIR
• Polarized antiproton-proton collision
• J-PARC
• Possibly polarizied proton beam and target

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Outstanding questions to be addressed by future
Drell-Yan experiments

• Does Sivers function change sign between DIS and
  Drell-Yan?
• Does Boer-Mulders function change sign between
  DIS and Drell-Yan?
• Are all Boer-Mulders functions alike (proton
  versus pion Boer-Mulders functions)
• Flavor dependence of TMD functions
• Independent measurement of transversity with
  Drell-Yan

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Fermilab E906 dimuon experiment (Geesaman, Reimer
et al., expected to run 2010-2011)

• BM functions can be measured at larger x
• Azimuthal angular distributions of J/?

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Nuclear modification of spin-dependent PDF?
EMC effect for g1(x)
Bentz, Cloet et al., arXiv0711.0392
Very difficult to measure !
Easier to measure the nuclear modification of
Boer-Mulders functions (only unpolarized targets
are required)?
(suggested by Gary Goldstein)
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Summary

• The Drell-Yan process compliments the SIDIS as a
  powerful independent tool for measuring
  transversity and TMD PDFs.
• First results on azimuthal decay angular
  distributions on unpolarized p-p or p-d Drell-Yan
  are now available.
• Pronounced cos2F azimuthal dependence previously
  observed in pion-induced Drell-Yan is not
  observed in p-p or p-d Drell-Yan
• These results suggest that the Boer-Mulders
  functions h1- for sea quarks are smaller than for
  valence quarks.
• Future Drell-Yan experiments at Fermilab, J-PARC
  and other facilities can provide new information
  (flavor dependence of valence and sea, opposite
  sign for SIDIS and D-Y) on Boer-Mulders and other
  TMDs.

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Decay angular distributions for pd Drell-Yan at
800 GeV/c
pd at 800 GeV/c
No significant azimuthal asymmetry in pd
Drell-Yan!