335 research outputs found
Multiplicity Fluctuations in Limited Segments of Momentum Space in Statistical Models
Multiplicity fluctuations in limited segments of momentum space are
calculated for a classical pion gas within the statistical model. Results for
the grand canonical, canonical, and micro-canonical ensemble are obtained,
compared and discussed. We demonstrate that even in the large volume limit
correlations between macroscopic subsystems due to energy and momentum
conservation persist. Based on the micro-canonical formulation we make
qualitative predictions for the rapidity and transverse momentum dependence of
multiplicity fluctuations. The resulting effects are of similar magnitude as
the predicted enhancement due to a phase transition from a quark-gluon plasma
to a hadron gas phase, or due to the critical point of strongly interacting
matter, and qualitatively agree with recently published preliminary
multiplicity fluctuation data of the NA49 SPS experiment.Comment: 23 pages, 4 figure
On the sign of kurtosis near the QCD critical point
We point out that the quartic cumulant (and kurtosis) of the order parameter
fluctuations is universally negative when the critical point is approached on
the crossover side of the phase separation line. As a consequence, the kurtosis
of a fluctuating observable, such as, e.g., proton multiplicity, may become
smaller than the value given by independent Poisson statistics. We discuss
implications for the Beam Energy Scan program at RHIC.Comment: 4 pages, 2 figure
Large QCD at non-zero chemical potential
The general issue of large QCD at nonzero chemical potential is
considered with a focus on understanding the difference between large QCD
with an isospin chemical potential and large QCD with a baryon chemical
potential. A simple diagrammatic analysis analogous to `t Hooft's analysis at
implies that the free energy with a given baryon chemical potential is
equal to the free energy with an isospin chemical potential of the same value
plus corrections. Phenomenologically, these two systems behave quite
differently. A scenario to explain this difference in light of the diagrammatic
analysis is explored. This scenario is based on a phase transition associated
with pion condensation when the isospin chemical potential exceeds ;
associated with this transition there is breakdown of the expansion--in
the pion condensed phase there is a distinct expansion including a
larger set of diagrams. While this scenario is natural, there are a number of
theoretical issues which at least superficially challenge it. Most of these can
be accommodated. However, the behavior of quenched QCD which raises a number of
apparently analogous issues cannot be easily understood completely in terms of
an analogous scenario. Thus, the overall issue remains open
Multiplicity Fluctuations in Au+Au Collisions at RHIC
The preliminary data of the PHENIX collaboration for the scaled variances of
charged hadron multiplicity fluctuations in Au+Au at GeV are
analyzed within the model of independent sources. We use the HSD transport
model to calculate the participant number fluctuations and the number of
charged hadrons per nucleon participant in different centrality bins. This
combined picture leads to a good agreement with the PHENIX data and suggests
that the measured multiplicity fluctuations result dominantly from participant
number fluctuations. The role of centrality selection and acceptance is
discussed separately.Comment: 7 pages, 3 figures, submitted to Phys. Rev. C (Rapid Communication
Using Higher Moments of Fluctuations and their Ratios in the Search for the QCD Critical Point
The QCD critical point can be found in heavy ion collision experiments via
the non-monotonic behavior of many fluctuation observables as a function of the
collision energy. The event-by-event fluctuations of various particle
multiplicities are enhanced in those collisions that freeze out near the
critical point. Higher, non-Gaussian, moments of the event-by-event
distributions of such observables are particularly sensitive to critical
fluctuations, since their magnitude depends on the critical correlation length
to a high power. We present quantitative estimates of the contribution of
critical fluctuations to the third and fourth moments of the pion, proton and
net proton multiplicities, as well as estimates of various measures of
pion-proton correlations, all as a function of the same five non-universal
parameters, one of which is the correlation length that parametrizes proximity
to the critical point. We show how to use nontrivial but parameter independent
ratios among these more than a dozen fluctuation observables to discover the
critical point. We also construct ratios that, if the critical point is found,
can be used to overconstrain the values of the non-universal parameters.Comment: 16 pages, 5 figures. Version to appear in PRD. Footnote and reference
adde
Anomalous Multiplicity Fluctuations from Phase Transitions in Heavy Ion Collisions
Event-by-event fluctuations and correlations between particles produced in
relativistic nuclear collisions are studied. The fluctuations in positive,
negative, total and net charge are closely related through correlations. In the
event of a phase transitions to a quark-gluon plasma, fluctuations in total and
net charge can be enhanced and reduced respectively which, however, is very
sensitive to the acceptance and centrality. If the colliding system experiences
strong density fluctuations due, e.g., to droplet formation in a first-order
phase transition, all fluctuations can be enhanced substantially. The
importance of fluctuations and correlations is exemplified by event-by-event
measurement of the multiplicities of 's and charged particles since
these observables should anti-correlate in the presence of co-mover or
anomalous absorption.Comment: revised version to appear in Phys. Rev. C, 5 page
Particle number fluctuations in nuclear collisions within excluded volume hadron gas model
The multiplicity fluctuations are studied in the van der Waals excluded
volume hadron-resonance gas model. The calculations are done in the grand
canonical ensemble within the Boltzmann statistics approximation. The scaled
variances for positive, negative and all charged hadrons are calculated along
the chemical freeze-out line of nucleus-nucleus collisions at different
collision energies. The multiplicity fluctuations are found to be suppressed in
the van der Waals gas. The numerical calculations are presented for two values
of hard-core hadron radius, fm and 0.5 fm, as well as for the upper
limit of the excluded volume suppression effects.Comment: 19 pages, 4 figure
Phase diagram of Nambu-Jona-Lasinio model with dimensional regularization
We investigate the phase diagram on temperature-chemical potential plane in
the Nambu-Jona-Lasinio model with the dimensional regularization. While the
structure of the resulting diagram shows resemblance to the one in the
frequently used cutoff regularization, some results of our study indicate
striking difference between these regularizations. The diagram in the
dimensional regularization exhibits strong tendency of the first order phase
transition.Comment: 9 pages, 9 figure
Probing the QCD Critical Point with Higher Moments of Net-proton Multiplicity Distributions
Higher moments of event-by-event net-proton multiplicity distributions are
applied to search for the QCD critical point in the heavy ion collisions. It
has been demonstrated that higher moments as well as moment products are
sensitive to the correlation length and directly connected to the thermodynamic
susceptibilities computed in the Lattice QCD and Hadron Resonance Gas (HRG)
model. In this paper, we will present measurements for kurtosis (),
skewness () and variance () of net-proton multiplicity
distributions at the mid-rapidity () and GeV/ for
Au+Au collisions at =19.6, 39, 62.4, 130 and 200 GeV, Cu+Cu
collisions at =22.4, 62.4 and 200 GeV, d+Au collisions at
=200 GeV and p+p collisions at =62.4 and 200 GeV.
The moment products and of net-proton
distributions, which are related to volume independent baryon number
susceptibility ratio, are compared to the Lattice QCD and HRG model
calculations. The and of net-proton
distributions are consistent with Lattice QCD and HRG model calculations at
high energy, which support the thermalization of the colliding system.
Deviations of and for the Au+Au collisions at
low energies from HRG model calculations are also observed.Comment: 10 pages, 8 figures, Proceedings of 27th Winter Workshon on Nuclear
Dynamics. Feb. 6-13 (2011
Evolution of fluctuations near QCD critical point
We propose to describe the time evolution of quasi-stationary fluctuations
near QCD critical point by a system of stochastic
Boltzmann-Langevin-Vlasov-type equations. We derive the equations and study the
system analytically in the linearized regime. Known results for equilibrium
stationary fluctuations as well as the critical scaling of diffusion
coefficient are reproduced. We apply the approach to the long-standing question
of the fate of the critical point fluctuations during the hadronic rescattering
stage of the heavy-ion collision after chemical freezeout. We find that if
conserved particle number fluctuations survive the rescattering, so do, under a
certain additional condition, the fluctuations of non-conserved quantities,
such as mean transverse momentum. We derive a simple analytical formula for the
magnitude of this "memory" effect.Comment: 13 pages, as published, typos corrected, some definitions made more
explici
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