Systematic studies of global observables by PHENIX. Longitudinal density fluctuations Mesonmeson and baryonmeson 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
Longitudinal density fluctuations
Mesonmeson and baryonmeson correlation
Kensuke Homma
for the PHENIX collaboration
Hiroshima University
Feb 9, 2008 at QM2008 in Jaipur, India
Kensuke Homma / Hiroshima Univ.
Quark number scaling of elliptic flow
T
What RHIC achieved
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.
Order parameter
f(h)=r(h)<r(h)>
f<<1 in T>>Tc,
GinzburgLandau(GL)
free energy up to
2nd order term
Two point correlation <f(h1)f(h2)>
in 1D 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.
Centrality
Negative Binomial Distribution
(NBD) perfectly describes
multiplicities in all collision
systems and centralities
at RHIC.
P(Nch)
Nch/< Nch >
Kensuke Homma / Hiroshima Univ.
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 BoseEinstein
k=∞ Poisson
NBD
1/k corresponds to integral
of two point correlation
Kensuke Homma / Hiroshima Univ.
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.
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
/
Fit with approximated functional form
Parametrization of
two particle correlation
10%
5%
k(dh)
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.
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 nonmonotonic 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
●5%
○10%
αξ
Npart
Phys. Rev. C 76, 034903 (2007)
Kensuke Homma / Hiroshima Univ.
5% bin width
5% bin width
Kensuke Homma / Hiroshima Univ.
Kensuke Homma / Hiroshima Univ.
Npart~90 in
eBJt~2.4GeV/fm2/c
Phys. Rev. C 76, 034903 (2007)
αξ
<mc>/<mc>@AuAu200
Normalized mean
multiplicity to that
of top 5% in
Phys. Rev. C 76, 034903 (2007)
Kensuke Homma / Hiroshima Univ.
Kensuke Homma / Hiroshima Univ.
Npart ~90
Kensuke Homma / Hiroshima Univ.
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.
Kensuke Homma / Hiroshima Univ.
Kensuke Homma / Hiroshima Univ.
102
Npart
arXiv:0801.0220v1 [nuclex]
Npart~90 in
eBJt~2.4GeV/fm2/c
If we put a biased line …
Kensuke Homma / Hiroshima Univ.
Npart ~90
KET/nq
Npart ~90
Kensuke Homma / Hiroshima Univ.
Kensuke Homma / Hiroshima Univ.
Kensuke Homma / Hiroshima Univ.
Measurement of transverse energy ET
Preliminary
Npart~90 corresponds to etBJ~2.4GeV/fm2/c
Kensuke Homma / Hiroshima Univ.
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.
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
1D 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.
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(1dh/DhPHENIX)
L=240
Kensuke Homma / Hiroshima Univ.
Hit map
Dead map
256 f bins
256 h bins
3sigma cut as the central cut
to define dead map.
Today only 3sigma result will be shown.
Number of bins
Number of hits (counts*events per minimum bin size)
Kensuke Homma / Hiroshima Univ.
Example of 5% most central sample
L=72
L=0
dh=0.7
L=28(1dh/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.
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.
10% bin width
5% bin width
10% bin width
Kensuke Homma / Hiroshima Univ.