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Directed flow as an effect of
the transient state rotation in
hadron and nucleus collisions
S.M. Troshin, N.E. Tyurin
IHEP, Protvino
Motivation
Directed flow introduced for
description of nucleus collisions
can be extended to hadronic
reactions. Role of rotation
of the transient matter.
Directed flow
Several experimental probes of collective dynamics in AA
interactions: momentum anisotropies
defined by means of
n
the Fourier expansion of the secondary particle 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).
v

v1 ( p )  cos   p  bˆ  p  / p 
Recent experimental results
(RHIC)
Incidend-energy scaling: in the projectile frame directed flow does not
depend on the incident energy.
Directed flow is vanishing in central collisions and increases with
centrality.
It has the same values for Cu-Cu and Au-Au collisions.
Our goal is to treat hadron-hadron collisions and confront
predictions for hh collisions with experimental results for AAcollisions keeping in mind similarity of hh and AA
The 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 realizable with the utilization of the standard
procedure.
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.
b 2 ( N )
c( N ) 
 inel
W. Broniowski, W. Florkowski,
Phys. Rev. C 65 (2002) 024905
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.
Inclusive cross-section
Inclusive cross-section integrated over impact does not depend on
azimuthal angle (for unpolarized particles)


d
I ( s, b,  )
 8  bdb
2
d
|
1

iU
(
s
,
b
)
|
0
unitarity
S-matrix representation
1  iU ( s, b)
S ( s , b) 
1  iU ( s, b)
One-to-one transform
S U 
ImU ( s, b)
 ( s , b) 
| 1  iU ( s, b) |2
-1
1
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 n ]
2
n 1
vn ( s, b, y, p )  vn ( s, b, y, p ) | 1  iU ( s, b) |2
Transient state
LQCD  Leff
Leff  L   L I  LC
Transient state generation time
Quark-Pion Liquid
ttsg  tint
RQ   / mQ
Overlap region
~ ( s , b) 
N
(1   kQ  ) s
mQ
D h1 c  D h2 c
x
y
Rotation of transient matter
(quark-pion liquid)
s
L  b
DC (b)
2
Coherent rotation with the same angular velocity (minimal value
of kinetic energy for the given value of the orbital angular
momentum L)
Such coherent rotation is absent in the parton picture. The
parton interaction was assumed to be a driving force of the
orbital angular momentum conversion to the global system
polarization (due to spin-orbital coupling),
which, however, has not been detected experimentally.
Z.-T. Liang, X.-N. Wang,
B.I. Abelev et al, (STAR
Phys. Rev. Lett. 94 (2005) 102301, Collaboration), arXiv:0705.1691.
ibid. 96 (2006) 039901.
Rotation as an 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
Incident-energy independence
 Effect of rotation is most significant in
the peripheral part of the rotating quarkpion liquid and weaker in less peripheral
regions, i.e. the directed flow depends
on the depth where the excitation of the
quark-pion liquid takes place
Depth should be proportional to the energy loss of
constituent valence quark in the medium prior an excitation
occurs, i.e. should be proportional to the rapidity
difference between the rapidity of the final particle and the
rapidity of the projectile particle.
Experimental data (STAR Collaboration:
nucl-ex/0701045v2)
Transverse momentum
dependence of directed flow
Size of the region where the virtual massive quarkcomes from
the quark-pion liquid is determined by its transverse
momentum, i.e. R  1/ p It is evident that R should not be
larger than the interaction radius of the valence constituent
quark (interacting with the quarks and pions from the transient
liquid state). The production processes with high transverse
momentum such that R is much less than the geometrical size
of the valence constituent quark resolve its internal structure as
a cluster of the non-interacting partons.
Transverse momentum
dependence (STAR)
Conclusion
 Qualitative features of the transient state in hh and AA
collsions and role of rotating quark-pion liquid in the
directed flow formation.
 Effect of rotation is maximal for peripheral collisions.
 Vanishing directed flow can serve as a signal of a
genuine QGP formation.
 If QGP is formed, OAM can be converted to the global
polarization of the secondary particles.
 LHC studies of anisotropic flows.
As it was predicted by Z.-T. Liang and X.-N. Wang