systematic studies of global observables by phenix

Kensuke Homma / Hiroshima Univ.

1

Systematic studies of global Systematic studies of global observables by PHENIXobservables by PHENIX

1.1. Longitudinal density fluctuationsLongitudinal density fluctuations2.2. Meson-meson and baryon-meson Meson-meson and baryon-meson

correlationcorrelation

Kensuke Homma Kensuke Homma for the PHENIX collaborationfor the PHENIX collaboration

Hiroshima UniversityHiroshima University

Feb 9, 2008 at QM2008 in Jaipur, IndiaFeb 9, 2008 at QM2008 in Jaipur, India


2

Understanding of QCD phase structureUnderstanding of QCD phase structure

1st order ?

CEP ?

T

B

What RHIC achievedDense mediumDeconfined phase with partonic d.o.f

Quark number scaling of elliptic flow

Tc

Is accessible region by RHICreally crossover?

Crossover for any kindsof order parameters?

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

http://link.aps.org/abstract/PRL/v98/e162301





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Intuitive observable: blob intensity Intuitive observable: blob intensity x blob size x blob size

GL with higher order terms

Many length scales appear(a typical k disappears)

T=Tc

T<Tc

Order parameter

<<1 in T>>Tc,Ginzburg-Landau(GL)free energy up to2nd order term TT

T

C

ck /1

1

)/||exp(

220

212

Two point correlation <)>in 1-D longitudinal space

Non monotonic increaseof indicates T~Tcw.r.t. monotonicallydecreasing baselineas mean density <>increases.

At RHIC


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Density measurement: inclusive dNDensity measurement: inclusive dNchch/d/d

[email protected] Au+Au@200GeV

Cu+Cu@[email protected]

Nch/< Nch >p+p@[email protected]

Negative Binomial Distribution(NBD) perfectly describesmultiplicities in all collisionsystems and centralitiesat RHIC.

P(N

ch)

Cen

tral

ity


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Two point correlation via NBDTwo point correlation via NBD

nk

kk

k

kn

knP k

n

kn

11

/1

1

/1

/

)()1(

)(

2

2

)( k=1 Bose-Einsteink=∞ Poisson

source 1

source 2source 1+2

NBD

Uncorrelatedsources

Correlatedsources

k=k1+k2

k=k1

k=k2

k=k1

k=k2k!=k1+k2

1/k corresponds to integralof two point correlation


6

Differential multiplicity measurementsDifferential multiplicity measurements

Δη<0.7 integrated over Δφ<π/2PHENIX: Au+Au @√sNN=200GeV

NBD can well describedifferential distribution too.

n/

small

large

Pro

babi

lity

(A.U

.)

Zero magnetic field to enhance low pt statisticsper collision event.

Phys. Rev. C 76, 034903 (2007)

http://link.aps.org/abstract/PRC/v76/e034903


7

Extraction of Extraction of product product

/2

1212

2111212212

/),(

)()(),(),(

eC

C

2

/2

21

20 0 21212

21

)1/(2

),(

1)1(

)(

e

ddC

n

nnk

)(/2

1)(

k

Parametrization of two particle correlation

Exact relation with NBD k

Fit with approximated functional form

/ 2

1

2 12

2 1 1 1 2 12 2 12

),(

)()(),(),(

eC

C

absorbs rapidity independentbias such as centrality bin width

Look atslopes

10% 5%

Approximatedfunctional form

k

Phys. Rev. C 76, 034903 (2007)



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αξαξ, , ββ vs. Npart vs. Npart

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%)

||/ 2

12

10C

k TT

TT

βαξ

●5% ○10%

●5% ○10%

Npart

Au+Au@200GeV

Dominantly Npart fluctuationsand possibly correlation in azimuth

Phys. Rev. C 76, 034903 (2007)



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Cu+Cu@200GeV

5% bin width

Analysis in smaller system: Cu+Cu@200GeVAnalysis in smaller system: Cu+Cu@200GeV

Cu+Cu@200GeV

5% bin width


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[email protected]

Analysis in lower energy: [email protected] in lower energy: [email protected]

[email protected]


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Cu+Cu@200GeV

[email protected]

Comparison of three collision systemsComparison of three collision systems

Au+Au@200GeV

Au+Au@200GeV

<c>/<c>@AuAu200

Normalized meanmultiplicity to thatof top 5% inAu+Au@200GeV

Npart~90 in AuAu@200GeVBJ~2.4GeV/fm2/c Phys. Rev. C 76, 034903 (2007)

Phys. Rev. C 76, 034903 (2007)




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Are there symptoms in othAre there symptoms in other observables at around ter observables at around t

he same Npart?he same Npart?


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Meson-meson and baryon-meson fluctuationsMeson-meson and baryon-meson fluctuations

K

K

K

KKKdyn

2

)1()1(),( 22

p

p

p

pppdyn

2

)1()1(),( 22

Npart ~90

Au+Au@200GeV

Au+Au@200GeV


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

Deviation from scaling at low KEDeviation from scaling at low KETT region ? region ?

Npart ~90


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ConclusionConclusion1. Correlation function derived from GL free energy density up to 2nd or

der term in the high temperature limit is consistent with what was observed in NBD k vs in three collision systems. This provides a way to directly determine transition points without tunable model parameters with relatively fewer event statistics.

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

3. The trends of 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.

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


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BackupBackup


17

How about <cc> suppression?How about <cc> suppression?

Npart~90 in AuAu@200GeVBJ~2.4GeV/fm2/c

Cu+Cu@200GeV

Au+Au@200GeV

NpartarXiv:0801.0220v1 [nucl-ex]

102

If we put a biased line …


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Other symptoms?: baryon-meson correlationOther symptoms?: baryon-meson correlation

K

K

K

KKKdyn

2

)1()1(),( 22

p

p

p

pppdyn

2

)1()1(),( 22

Npart ~90

KET/nq

Npart ~90


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KEKET T + Number of constituent Quarks (NCQ) scaling+ Number of constituent Quarks (NCQ) scaling

Scaling holds well for different centralities Deviations at low KET may be due to radial flow


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Future prospectFuture prospect

1. It would be important to see coherent behaviors on other observables like; J/ 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 measurementif is really the indication of a phase transition.

2. 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.


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What is the energy density at Npart~90?What is the energy density at Npart~90?

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

Measurement of transverse energy ET

Preliminary


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Density correlation in longitudinal spaceDensity correlation in longitudinal space

dyydz

yt

yz

)cosh(

)cosh(

)sinh(

)()(2

1)cosh(

)cosh(2

1

),,(

2

2

2

20

Uyyy

xddyghTgSy

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

Longitudinal space coordinate z can be transformed into rapiditycoordinate in each proper frame of sub element characterized by a formation time where dominant density fluctuations are embedded.

Due to relatively rapid expansion in y, analysis in y wouldhave an advantage to extract initial fluctuationscompared to analysis in transverse plane.

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


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Direct observable for Tc determinationDirect observable for Tc determination

)0()(

1

)1)((

1)(

20

0

220

1

20

2

GTTTa

kTTa

gg

h

ck

ck

kk

hcbTaTAghTg 64220 6

1

4

1)(

2

1))((

2

1),,(

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

spatial correlation disappears at Tc → )()( 0 cTTaTa

)(

)()(

)()(2

)(

)()(

1||

)(||

0

2

)(/||22

22

)(2

2

c

Ty

k

yikk

TTa

TAT

eTTAY

NTyG

kTATaY

NT

dyeyGY

Susceptibility in long wavelength limit

Correlation length

1-D two point correlation function

Fourier analysis

Product between correlation length and amplitude can alsobe a good indicator for T~Tc

Susceptibility


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NBD fitsNBD fitsin in

CuCu@200CuCu@200

16 fit examples in most left edge in top 10% eventsout of 28/2*(1+28) times NBD fits

Level (window size)L=28(1-PHENIX)

L=0

L=240


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Hit and dead map of East armHit and dead map of East arm

3-sigma cut as the central cutto define dead map.

Today only 3-sigma result will be shown.

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

bins

256

bins

Hit map Dead map

Num

ber

of b

ins


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Position Position dependent NBD dependent NBD

correctionscorrections• Require geometrical

correction factor on NBD k below 2.0

• -window size is defined as:

L=28(1-/PHENIX)

Correction factor on NBD kC

orr

ecte

d N

BD

k

L=0L=72

L=152 L=224

L=79L=7

L=159>0.06

=0.7

Example of 5% most central sample

L=231


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Cu+Cu@200GeV with only statistical errorsCu+Cu@200GeV with only statistical errors

10% bin width5% bin widthwith 2.5% shift

Confirmation of absorptionof bin width bias

Fit with only statistical errorsin k vs.


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Corrected mean multiplicity <Corrected mean multiplicity <cc>>Cu+Cu@200GeV5% bin width

Cu+Cu@200GeV10% bin width

[email protected]% bin width

systematic studies of global observables by phenix

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