Heavy ion collisions: Correlations in particle production

1
Heavy ion collisionsCorrelations in particle
production
Sergei A. Voloshin Wayne
State University, Detroit, Michigan
2
Correlations vast world, future of RHIC
measurements
General trend toward many particle
correlation inclusive ? semiinclusive
? 2-particle ? many particle correlations.

• Anisotropic flow
• gt two particle correlations
• gt three particle correlation (mixed
  harmonics)
• gt 4- and more particle correlation.
• Fluctuations in conserved charges gt
  electric charge, strangeness, baryon number
• Transverse momentum correlations (/fluctuations)
• Correlations due to the system evolution
  dynamics/expansion
• particle correlations in the intermediate and
  high pt region.
• gt Many particle correlations and the
  structure of the awayside jet (width
  in phi and eta, multiplicity of particles
  participating in the recoil).
• gt Spatial distribution of partons in
  the transverse plane
• gt High pt particle correlation
  relative to the reaction plane
• Global Polarization
• Parity (and/or CP) violation. Both
  are based on the analysis of correlations
  in particle production relative to the
  orientation of the system orbital
  momentum
• Physics of hadronization gt
  Constituent quark coalescence and correlations

• Anisotropic flow
• gt two particle correlations
• gt three particle correlation (mixed
  harmonics)
• gt 4- and more particle correlation.
• Fluctuations in conserved charges gt
  electric charge, strangeness, baryon number
• Transverse momentum correlations (/fluctuations)
• Correlations due to the system evolution
  dynamics/expansion
• particle correlations in the intermediate and
  high pt region.
• gt Many particle correlations and the
  structure of the awayside jet (width
  in phi and eta, multiplicity of particles
  participating in the recoil).
• gt Spatial distribution of partons in
  the transverse plane
• gt High pt particle correlation
  relative to the reaction plane
• Global Polarization
• Parity (and/or CP) violation. Both
  are based on the analysis of correlations
  in particle production relative to the
  orientation of the system orbital
  momentum
• Physics of hadronization gt
  Constituent quark coalescence and correlations

• Outline
• - Correlation functions, fluctuations.
• Main results from 2 particle transverse momentum
  correlations measurements
• gt centrality and incident energy dependence
• gt widening of the correlations in rapidity.
• Correlations due to transverse radial flow
  gt pt correlations gt Elongation of rapidity
  correlations with centrality narrowing
  of the Charge Balance Function. gt
  Azimuthal correlations Balance function in ??
  gt High pt low pt correlations ( and jet
  tomography)
• Summary

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2-particle correlation functions
Distribution of correlated pairs
Distribution of associated particles (2) per
trigger particle (1)
Probability to find a correlated pair
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Observables and observables.
What are the main requirements for a good
observable? -- be sensitive to the physics under
study -- be defined at the theoretical level,
be detector/experiment independent -- have clear
physical meaning -- not to be limited in scope,
provide new venues for further study
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experimental observations.
All data on ltdpt dptgt are STAR preliminary,
taken from talks of G. Westwall (STAR) at
QM2004 and Nuclear Dynamics WSs 04 and 05
Smooth dependence both on collisionenergy and
centrality
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Short and long range correlations
R(??) 1 - ??? ? ltRgt (Y) 1 - 4/3 ? Y,where
Y (??)max/2
Blue dotted lines assume the same ?. Note
difference in slopes (red vs blue) broadening
of R(??) with centrality
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centrality dependence
In a superposition of two independent
collisions,the ratio of the probability that in
a randomly chosen pair both particles are from
the same collision to the probability that two
particles are from different collisions is about
1.66
At midrapidity, the probability to find a
particle is about 60 larger if one particle has
been already detected.
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centrality dependence
Can it be due to transverse radial flow?

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Elementary NN-collision. Correlation functions.
y
rapidity
x
Correlations are due to local charge(s)
conservation, resonances, due to fluctuations in
number of produced strings, e.g. number of
qq-collisions.
ISR
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Radial flow ? mean pt correlations
All particles produced in the same NN-collision
(qq-string) experience the transverse radial
push that is(a) in the same direction (leads
to correlations in phi) (b) the same in magnitude
(? correlations in pt) ? Position-momentum
correlations caused by transverseexpansion
brings totally new mechanism for momentum
correlations, not present in NN-collisions

• Just a few details
• Long range rapidity correlations (bump- narrow
  in phi and wide in rapidity, charge independent)
• Stronger 2-particle pt correlation in narrow phi
  bins
• Narrowing of the charge balance function(
  -- increase in mt ?
  decreasein rapidity separation) same as in S.
  Pratt et al, in late hadronization scenario
• Charge correlations in phi. Azimuthal Balance
  function
• Everything evolving with centrality (radial flow)

In what follows, radial expansion is treated as
given. Not necessarily as due to pressure in
thermalized matter, could be considered a la
parton wind but numerical calculations are
done in the blast wave model.
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Transverse radial expansion
STAR Collaboration, PRL 92, 112301 (2004)
y
rapidity
x
Blast wave parameterization (Schnedermann,
Sollfrank, Heinz, PRC 48, 2462 (1993), d3n/d3p
e-E/T) of the source at freeze-out
Parameters T-temperature, velocity profile ?t
?r n
Note uniform source densityat r lt R has been
assumed
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Sensitivity to the velocity profile
Results for n0.5 and n2 are shown
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Brief comparison to data

• Possible reasons for discrepancy
• diffusion, thermalization time
• spatial source profile (not uniform density
  in transverse plane, e.g. cylinder shell)

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Initial and freeze-out configurations
Uncertainty particles are at the same
positionat the moment of production, but the
blastwave parameterization is done at freeze-out

• Smearing would depend on the
• thermalization time (which is supposedly small)
• diffusion during the system evolution before
  freeze-out
• non-zero expansion velocity in pp

Should we take it as a possibility to study all
the above effects?
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Rapidity correlations

• How to disentangle initial correlations at the
  parton production stage and obtaineddue to the
  transverse expansion? - Charge dependent and
  charge independent correlations.
• Correlation of conserved charges (Balance
  Functions). In this case the correlationsexisted
  already at the production moment would be
  modified by radial flow.
• Charge independent correlations particles at
  large rapidities, initially uncorrelated, become
  correlated, as all of them are pushed by radial
  flow in the same direction.

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?? x ?? correlations

• Charge independent correlations particles at
  large rapidities, initially uncorrelated, become
  correlated, as all of them are pushed by radial
  flow in the same direction. For those, one needs
  2d correlations (rapidity X azimuth) Shown
  below hand drawn sketch.

Peripheral
Central
??
??
??
??
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?? x ?? correlations, II
Talk by André Mischke (STAR)
In central Au-Au - jet-like correlation (short
range) sits on top of a wide, nearly flat
correlation in eta.
Q How one could distinguish between two
scenarios? A Correlations. Check for charge
dependent and charge independent correlations.
In longitudinal flow scenarioeverything would
widen, in transverse flow widening is charge
independent, but charge balance function would
shrink (similarto lower pts)
3 lt pT(trig.) lt 6 GeV/c2 lt pT(asso.) lt pT(trig.)
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Azimuthal correlations
Figures are shown for particles from the same NN
collision. Dilution factor to be applied!
First and second harmonics of the distribution
on the left
n1, T110 MeV
! - the large values of transverseflow, gt 0.25,
would contradict non-flow estimates in
elliptic flow measurements
No momentum conservation effects has been
included. Those would be important for the
charge independent first harmonic correlations.
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AA collision. Single jet tomography.
In this picture, the transverse momentum of the
(same side, large ??) associated particles would
be a measure of the space position the hard
scattering occurred
The plot on the right shows particle
azimuthaldistribution (integrated over all pts)
with respect to the boost direction. In order to
compare with data it should be also convoluted
with jet azimuthal distribution relativeto
radial direction.
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summary

• 2-particle transverse momentum correlation
• similar from SPS to full RHIC collision energies
• smooth centrality dependence, qualitatively
  consistent as due totransverse radial expansion

• Transverse radial flow leads to strong
  space-momentum correlation. In combination with
  space correlations between particles created in
  the same NN collision, it leads to
  characteristic two (and many) particlerapidity,
  transverse momentum, and azimuthal correlations.
• This phenomenon provides a natural (at present,
  qualitative) explanation of the centrality
  dependence of mean pt pseudorapidity/azimuthal
  anglecorrelations. It can be further used to
  study the details of the systemequilibration/ther
  malization and evolution (e.g. thermalization
  time, velocityprofile, etc.)
• Transverse radial flow push of particles
  created in the same NN collisionwhere hard
  scattering occurred jet quenching leads to
  azimuthal correlations of high pt trigger
  particle with soft particles at
  ratherdifferent rapidity. The mean transverse
  momentum of the associated particles would be
  a measure of how deep in the system the hard
  collisionoccurred.

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EXTRA SLIDES
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Ebye and inclusive approaches
Most of the present measurementsare done this way
Would be better, easier to analyze
theoretically. (! Numerically both are very
close)
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Comparison to Fpt
200 GeV AuAuSTAR Cuts ? lt 1.0?? 360?0.1 lt
pt lt 2 GeV
200 GeV AuAuSTAR withPHENIX Cuts ? lt 0.35??
2x90?0.2 lt pt lt 2 GeV
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Parity violation study via 3-particle correlations
hep-ph/0406311
a gt 0 ? preferential emission along the angular
momentum The sign can vary event by event,
aQ/N?, where Q is the topological charge,
Q1,2, ?at dN/dy100, a1.
Looking for the effect ofD. Kharzeev,
hep-ph/0406125
Projections on the direction of angular momentum
All effects non sensitive to the RP cancel
out! Possible systematics clusters that flow
projections onto reaction plane
And using only one particle instead of the event
flow vector
note that for a rapidity region symmetric with
respect to the midrapidity v10
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Same charge /all in AuAu_at_200
G. Westfall
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Short and long range correlations II
2-particle correlation functions
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Short range correlations and PSD
Long range 1/N HBT (dpt)(dpt)(dpt)1/(RsRoRl
) HBT/Long range N/(RsRoRl) PSD
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?? near-side correlations (contd)
STAR preliminary

• Significant broadening at low pT(trig.),
• disappears with increasing pT(trig.)
• Nch(asso.) invariant with collision system
• Understanding - Recombination effects ?
• - Interplay of medium-induced
• gluon radiation and collective
• longitudinal flow ?

Armesto et al., PRL93, 242301 (2004) S.A.
Voloshin, nucl-th/0312065
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Relation to the mean pt fluctuations
Statistical fluctuations those in the case of
independent particle production with the same
single-particle inclusive distributions.