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System-size dependence of particle ratio fluctuations
D. Kresan for the NA49 Collaboration
GSI, Darmstadt, Germany; now at Justus Liebig Universität Gießen, Germany
Introduction
Results
The exploration of the QCD phase diagram particularly the search for a (1st order) phase
transition from hadronic to partonic degrees of freedom and possibly a critical endpoint, is one
of the most challenging tasks in present heavy ion physics. One of the important observables
are event-by-event fluctuations of e.g. particle ratios.
The NA49 experiment at the CERN SPS [1] and
the STAR experiment at RHIC have measured the
energy dependence of the K/ and p/ ratio
fluctuations [2,3]. Increase of the first variable
towards lower energies, observed by NA49, is
under vivid discussion. The data are neither
reproduced by UrQMD or HSD simulations [4,5].
The p/ ratio fluctuations indicate correlations.
They are in a good agreement with model
calculations and are explained as originated from
nucleon resonance decays, producing pairs of
pion and proton.
One expectation for the dynamical fluctuation
measure of the K/ ratio fluctuations is that they
scale with average kaon multiplicity in the
detector acceptance [6,7]. Such a contribution is
inherently included in the definition of dynamical
fluctuations. This hypothesis can be tested by
measuring the fluctuations at fixed beam energy
while varying the centrality of the collisions, thus
changing the kaon multiplicity keeping all other
parameters fixed. Such a measurement will help
to understand the energy dependence of the
signal from the experimental side.
In this analysis the Pb + Pb collisions at the beam energy of 158A GeV were considered.
Analysis method
In the presented analysis hadrons were identified by the simultaneous measurements of
momentum and specific energy loss (dE/dx) [8]. As this measurement allows no track-by-track
PID in the momentum range accessible to NA49, an elaborate event-by-event fitting method has
been developed:
The measured centrality dependence of the particle ratio fluctuations in Pb + Pb collisions at
158A GeV shows a systematic increase of the absolute value towards lower centralities.
The size of the centrality bin was chosen to be 5%. Published values are from [2]. The shaded
band shows the systematic error
K/
K/p
p/
Scaling of fluctuations
One of the possible explanations for such an increase is the scaling of the dynamical
fluctuations with average particle multiplicities in the detector acceptance. In the approximation
of large multiplicities [7] dyn for example for the K/ ratio fluctuations can be written as:
 
 dyn K  
var  N K   N K
NK
2

var  N   N
N
2
covN K , N 
2
N K N
This term can be simplified due to the fact that NK << N
 
 dyn K  
var N K   N K
NK
2

var N K   N K
NK
According to this equation, scaling is expected with 1/NK. This can be tested by comparing the
energy and centrality dependence of the K/ ratio fluctuations in dependence on NK.
From a similar line of argumentation one expects that for the p/ ratio fluctuations shows that
the correlation term dominates. Therefore scaling is tested versus NpN.
For both, K/ and p/ ratio fluctuations a common scaling of the energy and centrality
dependence with the average number of produced particles in the acceptance is observed.
For the K/p ratio fluctuations the energy and centrality dependences do not follow a common
scaling, which is under ongoing investigation.
First, inclusive dE/dx distributions are fitted in small phase space bins. The result of this can be
recalculated as inclusive probability density distribution which is then used to estimate particle
numbers in single events. In this event-by-event fits the Maximum Likelihood Method is used
fixing positions and widths of the peaks in the dE/dx distribution and iteratively varying only the
yields.
Due to lower statistics in peripheral collisions, one loses some fraction of phase-space coverage
of kaons in the PDFs. Thus the available acceptance does change by going from most central to
semi-peripheral bins. In order to exclude the possible influence of this acceptance shift, results
shown as blue triangles are calculated with a constant, i.e. the smallest, acceptance for all
centrality bins.
ptot=3.3GeV/c,pt=0.3GeV/c,=0.393rad
Fluctuations in the measured event-byevent particle ratio distributions are
defined as the ratio of width (root-meansquared) and mean:
The observed scaling of the K/ ratio fluctuations with average kaon multiplicity explains the
observed rise of the fluctuations towards lower energies as a statistical effect caused by the
lower number of produced kaons.
The measurement of the p/ ratio fluctuations indicates that in both dependences the
covariance of pions and protons can be approximated by the geometrical mean of their
multiplicities:
0.5
RMS

MEAN

N p N
p


 dyn      2


N p N
The background, i.e. the statistical
fluctuations due to finite number statistics
and detector resolution, was estimated with
mixed events, which by construction do not
contain two- and many-particle correlations.
 dyn  sign  data   mix  
This strongly supports the hypothesis that they originate from nucleon resonance decays.
2
data

2
mix
In order to estimate the systematic error, two analyses were carried out, one with loose and
another with tighter track selection cuts. The final result is the mean, and the systematic
error is half the difference between the two of them. In addition numerous checks were done
investigating the influence of variations in the particle identification procedure, acceptance,
centrality bin size etc.
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References
[1] S. Afanasev et al., Nucl. Instrum. Meth. A 430 (1999) 210
[2] C. Alt et al., Phys. Rev. C 79, 044910 (2009)
[3] J.Phys.G35
[4] J.Phys.G36:125106,2009
[5] Prog. Part. Nucl. Phys. 41
[6] V. Koch and T. Schuster, Phys. Rev. C 81 (2010) 034910
[7] D. Kresan and V. Friese, PoS FRNC2006 (2006) 017
[8] S. Wenig, Nucl. Instrum. Meth. A 409 (1998) 100