systematic studies of global observables by phenix
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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)
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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)
Kensuke Homma / Hiroshima Univ.
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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)
Kensuke Homma / Hiroshima Univ.
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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)
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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Analysis in lower energy: [email protected] in lower energy: [email protected]
Kensuke Homma / Hiroshima Univ.
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Cu+Cu@200GeV
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)
Kensuke Homma / Hiroshima Univ.
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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?
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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.
Kensuke Homma / Hiroshima Univ.
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BackupBackup
Kensuke Homma / Hiroshima Univ.
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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 …
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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.
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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: )()(
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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
Kensuke Homma / Hiroshima Univ.
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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.
Kensuke Homma / Hiroshima Univ.
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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