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PHENIX Capabilities for Studying the QCD Critical Point. Kensuke Homma / Hiroshima Univ. 9 Jun, 2006 @ RHIC&AGS ANNUAL USERS’ MEETING Outline What is the critical behavior ? Search for critical temperature via correlation length Universality in compressibility Summary Future prospects.

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Phenix capabilities for studying the qcd critical point

PHENIX Capabilities for Studying the QCD Critical Point

Kensuke Homma / Hiroshima Univ.

9 Jun, 2006 @ RHIC&AGS ANNUAL USERS’ MEETING

Outline

What is the critical behavior ?

Search for critical temperature via correlation length

Universality in compressibility

Summary

Future prospects

Kensuke Homma / Hiroshima Univ.


What is the critical behavior

Ordered T<Tc

Critical T=Tc

Disordered T>Tc

What is the critical behavior ?

Spatial pattern of

ordered state

Scale transformation

Black

Black & White

Gray

Various sizes

from small to large

  • Large fluctuations of correlation sizes on order parameters:

  • critical temperature

  • Universality (power law behavior) around Tc caused

    by basic symmetries and dimensions of an underlying system:

  • critical exponent

A simulation based on two dimensional Ising model

from ISBN4-563-02435-X C3342l

Kensuke Homma / Hiroshima Univ.


Search for critical temperature

g-g0

φ

Search for critical temperature

In Ginzburg-Landau theory with Ornstein-Zernike picture,

free energy density g is given as

spatial correlation

disappears

at Tc

external field h causes deviation of free energy

from the equilibrium value g0. Accordingly an order

parameter f fluctuates spatially.

a>0

a=0

a<0

In the vicinity of Tc, f must vanish, hence

1-D spatial multiplicity density fluctuation from the mean density is introduced as an order parameter in the following.

Kensuke Homma / Hiroshima Univ.


Multiplicity density measurements in phenix
Multiplicity density measurements in PHENIX

PHENIX: Au+Au √sNN=200GeV

Zero magnetic field to enhance low pt

Δη<0.7 integrated over Δφ<π/2

PHENIX Preliminary

Negative Binomial Distribution (Bose-Einstein distribution from k emission sources)

Kensuke Homma / Hiroshima Univ.


Number of participants np and centrality

Participant Np

To ZDC

b

To BBC

Spectator

15-20%

10-15%

5-10%

peripheral

central

0-5%

0-5%

Number of participants, Np and Centrality

Multiplicity distribution

Np can be related with initial temperature.


Relations to the observable n b d k
Relations to the observable N.B.D k

Two point correlation function in one dimensional case in a fixed T

Two particle correlation function

Fluctuation caused by

centrality bin width

Relation to N.B.D. k

Kensuke Homma / Hiroshima Univ.


N b d k vs d h
N.B.D. k vs. dh

PHENIX Preliminary

k(dh)

10 % centrality

bin width

Function can fit the data

remarkably well !

dh

PHENIX Preliminary

5% centrality

bin width

Kensuke Homma / Hiroshima Univ.


Correlation length x and static susceptibility c
Correlation length x and static susceptibility c

Divergence of correlation length is the

indication of a critical temperature.

PHENIX Preliminary

Au+Au √sNN=200GeV

Correlation length x(h)

Divergence of susceptibility is the

indication of 2nd order phase transition.

T~Tc?

Np

PHENIX Preliminary

Au+Au √sNN=200GeV

c k=0 * T

Np

Kensuke Homma / Hiroshima Univ.


Stability of the parametrization

PHENIX Preliminary

10% cent. bin width

5% cent. bin width

a

PHENIX Preliminary

Shift to smaller fluctuations

b

PHENIX Preliminary

x

Stability of the parametrization

  • can absorb finite centrality

    bin width effects, namely,

  • finite initial temperature

  • fluctuations, while physically

  • important parameters are

  • stable.

Our parametrization

is well controlled.

Np


What about universality
What about universality?

On going analysis to extract critical exponents are:

  • Compressibility via scaled variance of multiplicity

  • Correlation lengths via multiplicity density fluctuations

  • Heat capacity via pt fluctuations

Kensuke Homma / Hiroshima Univ.


Isothermal compressibility
Isothermal Compressibility

Definition of isothermal compressibility

In grand canonical ensemble, KT can be related to scaled variance

This can be related with N.B.D. k

Given a proper estimate on T and measured Tc,

we can investigate universality among various

collision systems.

Kensuke Homma / Hiroshima Univ.


Np dependence of compressibility
Np dependence of compressibility

All species are scaled to match 200 GeV Au+Au points

1/m+1/k

1/m+1/k

0.2 < pT < 0.75 GeV/c

0.2 < pT < 3.0 GeV/c

Np

Np

  • All systems appear to obey a universal curve

  • by using Glauber T_AB as a volume V.

  • This behavior is dominated by low pt charged particles !!!

Kensuke Homma / Hiroshima Univ.


Comparison of scaled variance to na49 17 gev pb pb
Comparison of scaled variance to NA49 (17 GeV Pb+Pb)

The NA49 scaled variance was corrected for impact parameter fluctuations from their 10% wide centrality bins and scaled up by 15% to lie on the 200 GeV Au+Au curve.

0.2 < pT < 3.0 GeV/c

Np

Given a reasonable temperature estimate with collision energies

as well as Np, we would be able to study the universality by determining

the critical exponent around Tc.

Kensuke Homma / Hiroshima Univ.


Summary
Summary

  • Two point correlation lengths have been extracted based on the function form by relating pseudo rapidity density fluctuations and the GL theory up to the second order term in the free energy. The lengths as a function of Np indicates non monotonic increase at Np~100.

  • The product of the static susceptibility and the corresponding temperature shows no obvious discontinuity within the large systematic errors at the same Np where the correlation length is increased.

  • Isothermal compressibility via scaled variance of multiplicity shows a universal curve in various collision systems as a function of Np.

Kensuke Homma / Hiroshima Univ.


Future prospects
Future prospects

  • If non monotonic increase of x is a good measure to define Tc and one can discuss critical exponents on thermodynamic quantities around Tc …

  • Preferable conditions to investigate critical

  • points along a phase boundary are:

  • High multiplicity per collision event

  • reasonably high initial temperature

  • capability to enhance lower pt particles

  • larger acceptance

  • Scan higher baryon density region

  • lower colliding energies

  • asymmetric colliding energy helps?

  • device with high position resolution

    in the forward region.

T

QGP

Tricritical point

Hadronic

mB

K. Rajagopal and F. Wilczek, hep-ph/0011333

Kensuke Homma / Hiroshima Univ.


Back up slides
Back up slides

Kensuke Homma / Hiroshima Univ.


Average of wave number dependent density fluctuations from free energy

Fourier expression of order parameter

Statistical weight can be obtained from free energy

coefficient of

spatial fluctuation

Average of wave number dependentdensity fluctuations from free energy

Kensuke Homma / Hiroshima Univ.


Fourier transformation of two point correlation function
Fourier transformation oftwo point correlation function

Kensuke Homma / Hiroshima Univ.


Function form of correlation function

A function form of correlation function is obtained by inverse Fourier transformation.

Function form of correlation function

Kensuke Homma / Hiroshima Univ.


From field picture to particle picture

σ inverse Fourier transformation.inel is total inelastic cross section

From field picture to particle picture

Kensuke Homma / Hiroshima Univ.


Normalized factorial moment

Total rapidity interval inverse Fourier transformation.ΔY is divided into M equal bins

Normalized factorial moment

Kensuke Homma / Hiroshima Univ.


Second order nfm and correlation function
Second order NFM inverse Fourier transformation.and correlation function

Kensuke Homma / Hiroshima Univ.


Nbd and nfm

Bose-Einstein distribution inverse Fourier transformation.

Negative binomial distribution

σ: standard deviation

μ: average multiplicity

NBD (k→∞) = Poisson distribution

NBD (k<0) = Binomial distribution

NBD and NFM

Kensuke Homma / Hiroshima Univ.


Nbd k and integrated correlation function
NBD inverse Fourier transformation.k and integrated correlation function

Kensuke Homma / Hiroshima Univ.


Susceptibility

Susceptibility is defined by the response of phase for the external field.

In the static limit of k = 0,

χ cannot be extracted separately without temperature control, but χT value can be obtained by the mean multiplicity μ and α and ξ.

Susceptibility

Kensuke Homma / Hiroshima Univ.


Multiplicity measurement at phenix

Geometrical acceptance external field.

(Δη<0.7, Δφ<π/2)

Multiplicity measurement at PHENIX

  • Data was collected at the no magnetic filed condition to enhance charged particles with low momenta.

  • Charged tracks were reconstructed based on drift chamber by requiring association with two wire chamber (PC1, PC3) and EM calorimeter and collision vertex position measured by BBC.

  • All detector stability is carefully confirmed.

  • Dead areas of detectors are corrected by the MC simulation.

Kensuke Homma / Hiroshima Univ.


Charged particle multiplicity distributions and negative binomial distribution nbd

DELPHI: Z external field. 0 hadronic Decay at LEP

2,3,4-jets events

E802: 16O+Cu 16.4AGeV/c at AGS

most central events

[DELPHI collaboration] Z. Phys. C56 (1992) 63

[E802 collaboration] Phys. Rev. C52 (1995) 2663

Universally, hadron multiplicity distributions agree with NBD in high energy collisions.

Charged particle multiplicity distributions and negative binomial distribution (NBD)

Kensuke Homma / Hiroshima Univ.


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