Globally polarized QGP in

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• Globally polarized QGP in
• non-central AA collisions at high energies

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• Introduction
• Global polarization of quarks and anti-quarks
• Direct consequences
• Hyperon polarization Vector meson
  spin alignment
• Summary and outlook

Based on Liang Zuo-tang and Wang Xin-Nian,
Phys. Rev. Lett. 94, 102301 (2005) Phys. Lett.
B629, 20 (2005) Gao Jian-hua,
in preparation.
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Introduction
Spin effects usually provide us with useful
information on reaction mechanism and often
surprises. Many examples
RHIC (Relativistic Heavy Ion Collider) (1)
AuAu, 130200AGeV, Heavy Ion Collider at
Highest Energies. (2) p(pol)p(pol), 200500GeV,
first polarized high energy pp collider.

• Do spin physics in AA collisions such as at RHIC
  without beam polarization?!

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Elliptic flow and reaction plane in AA collision
coordinate-space-anisotropy ?
momentum-space-anisotropy
beam direction is z
transverse plan
high density and high temperature system
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Global Orbital Angular Momentum
Huge orbital angular momentum of the colliding
system
reaction plane can be determined by measuring
v2 and v1
Y
impact parameter
normal of the reaction plane
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Global orbital angular momentum

• Gradients in pz-distribution along x-direction

impact parameter
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Transverse Gradient of Shear Velocity
Distribution of number of participant
projectile (P ) or target (T ) nucleons.
P
Collective longitudinal momentum per produced
parton
T
c(s) number of partons produced per
participating nucleon in AA collision,
which is a constant.
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Local Orbital Angular Momentum
for AuAu at 200AGeV
for bRA, ?x1fm
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Quark Scattering with fixed reaction plane
Scattering amplitude in momentum space
a 2-dimensional Fourier transformation to impact
parameter space
reaction plan
Differential cross section w.r.t. the impact
parameter
un-polarized
spin dependence
Quark polarization
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Quark Polarization
talk by Gao Jian-hua
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(No Transcript)
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Consequence I Hyperon polarization

• Recombination mechanism (q1?q2?q3?)?H ?

Assuming
Hyperon ? ? ? ?
PH Ps (4Pq-Ps-3PsPq2 )/ R? (4Ps-Pq-3Ps2 )/ R? 2Ps(5Ps2 )/ R?
RH ? 12 3(1-P q2 ) 3-4PqPsPq2 3-4PqPsPs2 6(1Ps2 )
If
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Consequence I Hyperon polarization

• Fragmentation mechanism q? ? H X.

In analog to

• Theoretical results by assuming
• Only ?s containing the initial quark are
  polarized.
• Polarization of ? is calculated using SU(6)
  wave-function.

Boros, Liang, PRD(98)
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Consequence I Hyperon polarization

• Fragmentation mechanism q? ? H X.

Hyperon ? ? ? ?
PH
PH in the case of Pq Ps
PH in the case of Pq Ps and ns fs
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Consequence I Hyperon polarization

• Some of the expected features

• The same for hyperons and anti-hyperons.
• (Approximately) the same for different hyperons.
• No polarization at b0, increases approximately
  linearly with b.
• Finite for hyperons at small finite pT and y,
  increases with pT, eventually drops to zero at
  very high pT.

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Consequence II Vector meson spin alignment

• No need to determine the direction of the
  reaction plan

Hyperon Spin self-analyzing parity violating
decay H?BM.
B / M1
Vector meson Strong decay V?M1M2.
H/V
rest frame of H/V
Spin density matrix
?00 probability for m0 ?001/3 for
unpolarized V.
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Recombination mechanism
Taking y as the quantization axis
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Fragmentation mechanism
In analog to
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Experiments Hyperon polarization

• Ilya Selyuzhenkov
• from Wayne State Univ.
• for STAR at RHIC

Nucl-ex/0510069
Nucl-ex/0608034
Nucl-ex/0605035
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Experiments Vector meson spin alignment

• China-STAR group

• CHEN Jin-hui (SINAP), DONG Xin (USTC) talks at
  Weihai, July 2006.
• CHEN Jin-hui (SINAP), plenary talk at QM2006.
• TANG Zebo (USTC) talk at XiAn in November.

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Still many open questions

• More realistic calculations taking flow into
  account
• (Gao Jian-huas talk)
• Influence from final state interaction
• Influence of orbital angular momenta in
  hadronization
• Relation to hyperon polarization w.r.t.
  production plan
• Other measurable consequences

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Summary

• A great advantage to study spin effects in
  non-central AA-collisions is the reaction plan
  can be determined experimentally by measuring v1
  and v2.
• There exists a huge orbital angular momentum of
  the colliding system w.r.t. the reaction plan.
• Quarks and anti-quarks are polarized in the
  opposite direction as the reaction plan due to
  spin-orbital interaction in QCD.
• Many consequences, many open questions

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Outlook

• A possible method to study the role of orbital
  angular momentum in high energy spin physics.
• An effective way to study spin-orbital
  interaction in QCD?
• A new window to look at the properties of QGP?

Thank you for your attention!