Systematic studies of global observables by phenix
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Systematic studies of global observables by PHENIX. Longitudinal density fluctuations Meson-meson and baryon-meson correlation Kensuke Homma for the PHENIX collaboration Hiroshima University. Feb 9, 2008 at QM2008 in Jaipur, India. Understanding of QCD phase structure.

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Systematic studies of global observables by PHENIX

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Systematic studies of global observables by phenix

Systematic studies of global observables by PHENIX

Longitudinal density fluctuations

Meson-meson and baryon-meson correlation

Kensuke Homma

for the PHENIX collaboration

Hiroshima University

Feb 9, 2008 at QM2008 in Jaipur, India

Kensuke Homma / Hiroshima Univ.


Understanding of qcd phase structure

Understanding of QCD phase structure

Quark number scaling of elliptic flow

T

What RHIC achieved

  • Dense medium

  • Deconfined phase

    with partonic d.o.f

Tc

Phys. Rev. Lett. 98, 162301 (2007)

CEP ?

Is accessible region by RHIC

really crossover?

Crossover for any kinds

of order parameters?

1st order ?

mB

Kensuke Homma / Hiroshima Univ.


Intuitive observable blob intensity a x blob size x

Intuitive observable: blob intensity a x blob size x

Order parameter

f(h)=r(h)-<r(h)>

f<<1 in T>>Tc,

Ginzburg-Landau(GL)

free energy up to

2nd order term

Two point correlation <f(h1)f(h2)>

in 1-D longitudinal space

At RHIC

Non monotonic increase

ofaxindicates T~Tc

w.r.t. monotonically

decreasing baseline

as mean density <r>

increases.

T=Tc

T<Tc

Many length scales appear

(a typical fk disappears)

GL with higher order terms

Kensuke Homma / Hiroshima Univ.


Density measurement inclusive dn ch d h

Centrality

Density measurement: inclusive dNch/dh

[email protected]

[email protected]

Negative Binomial Distribution

(NBD) perfectly describes

multiplicities in all collision

systems and centralities

at RHIC.

P(Nch)

Nch/< Nch >

[email protected]

[email protected]

[email protected]

[email protected]

Kensuke Homma / Hiroshima Univ.


Two point correlation via nbd

Two point correlation via NBD

Uncorrelated

sources

Correlated

sources

source 1

k=k1

k=k1

k=k1+k2

k=k2

k=k2

k!=k1+k2

source 2

source 1+2

k=1 Bose-Einstein

k=∞ Poisson

NBD

1/k corresponds to integral

of two point correlation

Kensuke Homma / Hiroshima Univ.


Differential multiplicity measurements

Differential multiplicity measurements

dh

Δη<0.7 integrated over Δφ<π/2

PHENIX: Au+Au @√sNN=200GeV

Probability (A.U.)

Phys. Rev. C 76, 034903 (2007)

small dh

large dh

Zero magnetic field to

enhance low pt statistics

per collision event.

n/m

NBD can well describe

differential distribution too.

Kensuke Homma / Hiroshima Univ.


Extraction of ax product

h

h

º

r

h

h

-

r

h

r

h

C

(

,

)

(

,

)

(

)

(

)

2

1

2

2

1

2

1

1

1

2

h

h

C

(

,

)

-

dh

x

=

a

+

b

/

2

1

2

e

r

2

1

1

dh

=

x

<<

dh

k

(

)

(

)

ax

dh

+

b

2

/

Extraction of ax product

Fit with approximated functional form

Parametrization of

two particle correlation

10%

5%

k(dh)

  • absorbs rapidity independent

    bias such as centrality bin width

Exact relation with NBD k

Look at

slopes

Phys. Rev. C 76, 034903 (2007)

dh

Approximated

functional form

Kensuke Homma / Hiroshima Univ.


Vs npart

αξ, β vs. Npart

Dominantly Npart fluctuations

and possibly correlation in azimuth

β is systematically shift to lower values as the centrality bin width becomes smaller from 10% to 5%. This is understood as fluctuations of Npart for given bin widths

αξ product, which is monotonically related with χk=0 indicates the non-monotonic behavior around Npart ~ 90.

Significance with Power + Gaussian:

3.98 σ (5%), 3.21 σ (10%)

Significance with Line + Gaussian:

1.24 σ (5%), 1.69 σ (10%)

●5%

○10%

β

[email protected]

●5%

○10%

αξ

Npart

Phys. Rev. C 76, 034903 (2007)

Kensuke Homma / Hiroshima Univ.


Analysis in smaller system cu cu@200gev

Analysis in smaller system: [email protected]

[email protected]

5% bin width

[email protected]

5% bin width

Kensuke Homma / Hiroshima Univ.


Analysis in lower energy au au@62 4gev

Analysis in lower energy: [email protected]

[email protected]

[email protected]

Kensuke Homma / Hiroshima Univ.


Comparison of three collision systems

Comparison of three collision systems

Npart~90 in

[email protected]

eBJt~2.4GeV/fm2/c

[email protected]

Phys. Rev. C 76, 034903 (2007)

[email protected]

αξ

<mc>/<mc>@AuAu200

Normalized mean

multiplicity to that

of top 5% in

[email protected]

[email protected]

Phys. Rev. C 76, 034903 (2007)

[email protected]

Kensuke Homma / Hiroshima Univ.


Are there symptoms in other observables at around the same npart

Are there symptoms in other observables at around the same Npart?

Kensuke Homma / Hiroshima Univ.


Meson meson and baryon meson fluctuations

Meson-meson and baryon-meson fluctuations

[email protected]

[email protected]

Npart ~90

Kensuke Homma / Hiroshima Univ.


Deviation from scaling at low ke t region

Deviation from scaling at low KET region ?

Npart ~90

In lower KET, there seems to be different behaviors between baryon and mesons. The transition is at Npart~90.

Kensuke Homma / Hiroshima Univ.


Conclusion

Conclusion

  • Correlation function derived from GL free energy density up to 2nd order term in the high temperature limit is consistent with what was observed in NBD k vs dh in three collision systems. This provides a way to directly determine transition points without tunable model parameters with relatively fewer event statistics.

  • The product of susceptibility and temperature, ax as a function of Npart indicates a possible non monotonic increase at Npart~90. The corresponding Bjorken energy density is 2.4GeV/fm3 with t=1.0 fm/c and the transverse area=60fm2

  • The trends of ax in smaller system in the same collision energy (Cu+Cu 200GeV) and in the same system size in lower collision energy (Au+Au 62.4) as a function of mean multiplicity are similar to that of Au+Au at 200GeV except the region where the possible non monotonicity is seen. We need careful error estimates and increase of statistics for smaller size and lower energy systems to obtain the conclusive result.

  • Combining other symptoms in the same multiplicity region, we hope to understand possibly interesting behaviors.

Kensuke Homma / Hiroshima Univ.


Backup

Backup

Kensuke Homma / Hiroshima Univ.


How about cc suppression

102

Npart

arXiv:0801.0220v1 [nucl-ex]

How about <cc> suppression?

[email protected]

Npart~90 in

[email protected]

eBJt~2.4GeV/fm2/c

[email protected]

If we put a biased line …

Kensuke Homma / Hiroshima Univ.


Other symptoms baryon meson correlation

Other symptoms?: baryon-meson correlation

Npart ~90

KET/nq

Npart ~90

Kensuke Homma / Hiroshima Univ.


Ke t number of constituent quarks ncq scaling

KET + Number of constituent Quarks (NCQ) scaling

  • Scaling holds well for different centralities

  • Deviations at low KET may be due to radial flow

Kensuke Homma / Hiroshima Univ.


Future prospect

Future prospect

  • It would be important to see coherent behaviors on other observables like; J/y suppression pattern, breaking point of quark number scaling of V2, fluctuation on baryon-meson production, low pt photon yield and so on to investigate what kind of phase transition is associated with ax measurement, if ax is really the indication of a phase transition.

  • Quick finer energy and species scan with 100M events for each system would provide enough information on the structure of the possible non monotonicity. This would reveal the relation between initial temperature and speed of blob evolution and speed of medium expansion.

Kensuke Homma / Hiroshima Univ.


What is the energy density at npart 90

What is the energy density at Npart~90?

Measurement of transverse energy ET

Preliminary

Npart~90 corresponds to etBJ~2.4GeV/fm2/c

Kensuke Homma / Hiroshima Univ.


Density correlation in longitudinal space

Density correlation in longitudinal space

Longitudinal space coordinate z can be transformed into rapidity

coordinate in each proper frame of sub element characterized by

a formation time t where dominant density fluctuations are embedded.

Due to relatively rapid expansion in y, analysis in y would

have an advantage to extract initial fluctuations

compared to analysis in transverse plane.

In narrow midrapidity region like PHENIX, cosh(y)~1 and y~h.

Longitudinal multiplicity density fluctuation from the mean density can be an order parameter:

Kensuke Homma / Hiroshima Univ.


Direct observable for tc determination

Direct observable for Tc determination

GL free energy density g with f ~ 0 from high temperature side is insensitive to transition order, but it can be sensitive to Tc

spatial correlation

f disappears at Tc →

Fourier analysis

Susceptibility

Susceptibility in long wavelength limit

1-D two point correlation function

Product between correlation

length and amplitude can also

be a good indicator for T~Tc

Correlation length

Kensuke Homma / Hiroshima Univ.


Nbd fits in cucu@200

NBD fitsin [email protected]

L=0

16 fit examples in most left edge in top 10% events

out of 28/2*(1+28) times NBD fits

Level (window size)

L=28(1-dh/DhPHENIX)

L=240

Kensuke Homma / Hiroshima Univ.


Hit and dead map of east arm

Hit and dead map of East arm

Hit map

Dead map

256 f bins

256 h bins

3-sigma cut as the central cut

to define dead map.

Today only 3-sigma result will be shown.

Number of bins

Number of hits (counts*events per minimum bin size)

Kensuke Homma / Hiroshima Univ.


Position dependent nbd corrections

Example of 5% most central sample

Position dependent NBD corrections

L=72

L=0

dh=0.7

  • Require geometrical correction factor on NBD k below 2.0

  • h-window size dh is defined as:

    L=28(1-dh/DhPHENIX)

Corrected NBD k

L=79

L=7

Correction factor on NBD k

L=152

L=224

L=159

L=231

dh>0.06

Kensuke Homma / Hiroshima Univ.


Cu cu@200gev with only statistical errors

[email protected] with only statistical errors

Confirmation of absorption

of bin width bias

5% bin width

with 2.5% shift

10% bin width

Fit with only statistical errors

in k vs. dh

Kensuke Homma / Hiroshima Univ.


Corrected mean multiplicity m c

Corrected mean multiplicity <mc>

[email protected]

10% bin width

[email protected]

5% bin width

[email protected]

10% bin width

Kensuke Homma / Hiroshima Univ.


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