Polarization in Heavy Ion
Physics
Sergey Troshin, IHEP, Protvino
Motivation
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Role of polarization measurements in searches of quark‐gluon plasma, studies of the dynamical nature of the deconfined state and identification of the relevant degrees of freedom
Role of orbital angular momentum in peripheral collisions and related observable effects
Bridge between the ideas and methods in spin and heavy ion physics
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Tool – stable pattern of hyperon polarization (lambda, in particular) observed in unpolarized hadron interactions: energy independent, linear rise with xF,
PΛ
P
1 GeV/c
20-30%
Polarization is determined through weak (parity non‐conserving) decay
Λ0 → p + π −
Earlier (mid‐eighties) prediction: isotropic distribution of the parton
momenta in the plasma rest frame. y QGP does not remember the directions of the initial momenta. y Vanishing polarization of hyperons relative to production plane (due to parity conservation there could not be longitudinal polarization).
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Papers: P. Hoyer, Phys. Lett. B, 187, 162, 1987;
A.D. Panagiotou, Phys. Rev. C 33, 1999, 1986;
R. Stock et al., Proc. of the Conference on Quark Matter Formation in Heavy‐Ion Collisions, Singapore 1982. Vanishing hyperon polarization w.r.t. production plane follows
from various models also
b - impact parameter
PΛP (b) → 0, b → 0
Reaction plane (definition)
beam
x
y
reaction plane
y
Peripheral collisions (b is different from 0)
Reaction plane
L
b
s
L ( s , b ) ≅ αb
DC (b)
2
P. Carruthers, 1983: “Enormous orbital angular momentum involved in a high energy nucleus‐nucleus collisions”
_
L( RHIC ) ≅ 105
_
L( LHC ) ≅ 107
0
b
h =1
What are the observable effects of the large angular orbital momentum presented in the peripheral heavy‐ion and hadron collisions?
Burst of polarized vector mesons (P. Carruthers, 1983)?
Strong necessity for the spins of the outgoing particles to line up parallel to each other in the transverse direction to the reaction plane (C.N. Yang and T.T. Chou, 1986)? { Reaction plane is the plane perpendicular to the orbital momentum }
(σ 1T ⋅ σ 2T ) average > 0
due to a net deficiency of orbital angular momentum in the left and right‐moving outgoing systems
Thus, in a process of high energy hadron and nuclear collisions large initial orbital angular momentum can, in principle, be converted into the spin angular momentum of final particles resulting in their polarization relative to the reaction plane. We would try to connect this possibility with the nature of transient strong interaction matter. Asymptotic freedom in QCD formation of QGP ‐ gas of free quarks and gluons [J. C. Collins, M. J. Perry; Phys. Rev. Lett. 34, 1353 ‐ 1356 (1975)]
Experimental facts Discovery of the deconfined state of matter has been announced by the four major experiments at RHIC
Despite the highest values of energy and density have been reached, a genuine quark‐gluon plasma QGP was not found. The deconfined state reveals the properties of the perfect liquid, being strongly interacting collective state and therefore it was labelled as sQGP.
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How can orbital momentum help in detecting nature and properties of transient quark‐gluon matter produced in the non‐central collisions?
Weakly‐coupled matter (parton model with final state interactions) Z.‐T. Liang, X.‐N. Wang, Phys. Rev. Lett, 94, 102301, 2005: no collective rotation of the system, finite transverse gradient of the average longitudinal momentum per produced in the overlap region
parton. It is claimed that relative OAM in collision of partons will lead to global quark polarization due to spin‐orbital coupling.
Significant (order of tens %) polarization of hyperons relative to reaction plane was anticipated. Similar ideas were used for the hyperon polarization in hadron non‐central collisions, S. Voloshin, 2004, nucl‐th/0410089v1. The idea to observe circularly polarized photons as a signal of quark polarization in the QGP was proposed by A. Ipp, A Di Piazza, J. Evers, C.H. Keitel, arXiv: 0710.5700v1. Also: B. Betz, M. Gyulassy, G. Torrieri, Phys. Rev. C 76, 044901, 2007
Typical values of global hyperon polarization relative to reaction plane were predicted to be
R
R
H
q
P = P ≅ 0.3
The measurements of global polarization and were Λ
Λ
performed at RHIC (STAR Collaboration) and upper limit has been obtained R
Λ ,Λ
|P
|≤ 0.02
Au + Au
s NN = 62.4; 200 GeV
P =
R
H
8
πα H
sin(φ p* − ΨRP )
Global polarization measurements in Au+Au collisions, B.I. Abelev et al. Phys. Rev. C 76, 024915 (2007)
Then look the spin alignment of vector mesons (described by spin
density matrix S=1:
⎛ ρ11
⎜
V
ρ = ⎜ ρ 01
⎜⎜
⎝ ρ −11
If
ρ 00 ≠ 1 / 3
ρ10
ρ 00
ρ −10
ρ1−1 ⎞⎟
ρ 0−1 ⎟
⎟
ρ −1−1 ⎟⎠
- the alignment of vector mesons takes place
Global spin alignment for φ, K*0 and global polarization for Λ were not observed for the different centralities.
I. Selyuzhenkov (for the STAR Collaboration), J. Phys. G 34 (2007) S1099
Interesting to measure polarization and spin alignment w.r.t. production plane
Thus, at the moment no experimental evidence exists for conversion of the orbital angular momentum into the spin angular momentum in nuclear collisions and this conclusion is correlated but not necessarily follow from the result on the strongly interacting nature of transient matter observed at RHIC.
The question arise again: what are the experimental manifestations of the large orbital angular momentum could be in
the case of strongly interacting transient matter ?
Ideal liquid low viscosity large interaction cross‐section (about 22 mb)
Large orbital angular momentum rotation of the transient deconfined
matter in the overlap region as a whole, i.e. all parts have the same angular velocity and orbital angular momentum does not convert to spin angular momentum.
Experimental manifestations – directed flow v
1
What is directed flow
S.M. Troshin, N.E. Tyurin, Int. J. Mod. Phys. E, 2008
Several experimental probes of collective dynamics in AA interactions: momentum vn
anisotropies defined by means of the Fourier expansion of
the secondary particle φ
distribution over the momentum azimuthal angle. The azimuthal angle is the angle of the detected particle with respect to the reaction plane, (spanned by the collision axis z and the impact parameter vector b directed along the x axis).
vn = cos nφ
Asimuthal angle of RP is taken to be zero
φ − ΨRP ⇒ φ
∞
⎞
d 3N
1 d 2N ⎛
E 3 =
⎜1 + 2∑ vn cos nφ ⎟
d p 2π pT dpT dy ⎝
n =1
⎠
v1 ( p⊥ ) ≡ ⟨ cos φ ⟩ p⊥ = ⟨bˆ ⋅ p ⊥ / p⊥ ⟩
Provided impact parameter is fixed and known, the directed flow can be studied in nuclear as well as in hadronic collisions.
Centrality and impact parameter
Measurements of the characteristics of multiparticle production processes in hadronic collisions at fixed impact parameter should be performed with selection of the specific events sensitive to the value and direction of impact parameter.
The relationship of the impact parameter with the final state multiplicity. Chou‐
Yang approach: one can restore the values of impact parameter from the charged particle multiplicity.
πb 2 ( N ) W. Broniowski, W. Florkowski,
Phys. Rev. C 65 (2002) 024905
c( N ) ≅
σ inel
c(N) is the centrality of the events with multiplicity larger than N and b(N) is the impact parameter where mean multiplicity is equal to N.
Geometrical picture of hadron collision has an apparent analogy with collisions of nuclei and determination of the reaction plane in the non‐central hadronic collisions could be experimentally feasible with standard procedure.
Transient state in nuclei and
hadron collisions
LQCD ⇒ Leff
Leff = L χ + L I + LC
Transient state generation time
Quark-Meson Liquid
Δttsg << Δtint
RQ = κ / mQ
Overlap region
(1 − ⟨ kQ ⟩ ) s h1
~
N ( s, b) ∝
D c ⊗ D h2 c
mQ
x
y
1 + iU ( s, b)
S ( s, b) =
1 − iU ( s, b)
unitarity
Inclusive cross‐section:
∞
I ( s , b, ξ )
dσ
= 8π ∫ bdb
2
dξ
| 1 − iU ( s, b) |
0
Fixed impact parameter b
I = ∑n ≥3 I n
∞
1
I ( s , b, y , p ⊥ ) =
I 0 ( s, b, y, p⊥ )[1 + ∑ 2vn ( s, b, y, p⊥ ) cos nφ ]
2π
n =1
vn ( s, b, y, p⊥ ) = vn ( s, b, y, p⊥ ) | 1 − iU ( s, b) |−2
Rotation as origin of directed
flow
Assumed particle production mechanism at moderate transverse
momenta is an excitation of a part of the rotating transient state of massive constituent quarks (interacting by pion exchanges) by the one of the valence constituent quarks with subsequent hadronization of the quark‐pion liquid droplets .
Q
1
| v1 |∝
Δl
Δl ∝ Δy
1
| v1 |∝
| y − ybeam |
Weakly increasing energy dependence of the directed flow (due to increase of elastic scattering cross section
Δy =| y − ybeam |
v1 ∝ σn
P dependence of directed flow
T
R ≈ 1 / pT
At high transverse momentum an internal structure of constituent quark is resolved – vanishing directed flow is expected
Directed flow in nuclear collisions
Au+Au and Cu+Cu at 62.4 and 200 GeV at RHIC (STAR
preliminary data)
Other effects related to OAM
Contribution to elliptic flow
v2 ( p⊥ ) ≡ ⟨ cos 2φ ⟩ p⊥ = ⟨ ( p x2 − p y2 ) / p⊥2 ⟩
S.M. Troshin, N.E. Tyurin, hep‐ph/0609248
F. Becattini, F. Piccinini, J. Rizzo, Phys. Rev. C77: 024906, 2008. [arXiv: 0711.1253] Conclusion: expectations for the
LHC
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What kind of the deconfined matter would be produced at the LHC energies?
Vanishing directed flow – weakly‐coupled system, QGP.
What about global polarization? Is this a signal of QGP formation? Not necessarily, the reason is the reflective (antishadowing) scattering.
Spin correlations
due to antishadowing
. S.M. Troshin, Phys.Lett.B597:391,2004
The generic geometric picture at fixed energy beyond the black
disc limit can be described as a scattering off the partially
reflective and partially absorptive disk surrounded by the black
ring which becomes grey at larger values of the impact
parameter.
The evolution with energy is characterized by increasing
albedo due to the interrelated increase of reflection and
decrease of absorption at small impact parameters.
1 dσ inel
ImU ( s, b)
η ( s, b) ≡
=
2
4π db
| 1 − iU ( s, b) |2
LHC
Black disk
1/ 4
1/ 4
1/ 4
b
b
Evolution with energy
R(s )
b
∞
Mean multiplicity
n ( s) =
∫ n ( s, b)η (s, b)bdb
0
∞
∫η (s, b)bdb
0
Negative imbalance of the orbital
momentum at the LHC energies
s R ( s ) n ( s ) xL ( s )
ΔL ≈ −
2 2
2
This imbalance should be compensated by the
total spin of final particles
S = − ΔL
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Qualitative features of the transient state in hh and AA collsions and role of rotating quark‐meson liquid in the directed flow formation.
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Effect of rotation is maximal for peripheral collisions – centrality dependence.
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Vanishing directed flow can serve as a signal of a genuine QGP formation.
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If genuine QGP is formed, OAM can be converted to the global polarization of the secondary particles.
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LHC studies of anisotropic flows: global polarization at such high energies can exists even when sQGP is formed, it is then results from reflective scattering.
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Further studies (theoretical and experimental) are necessary in this field combining experiences of spin studies with multiparticle production.