2,620 research outputs found
Time evolution of the chiral phase transition during a spherical expansion
We examine the non-equilibrium time evolution of the hadronic plasma produced
in a relativistic heavy ion collision, assuming a spherical expansion into the
vacuum. We study the linear sigma model to leading order in a large-
expansion. Starting at a temperature above the phase transition, the system
expands and cools, finally settling into the broken symmetry vacuum state. We
consider the proper time evolution of the effective pion mass, the order
parameter , and the particle number distribution. We
examine several different initial conditions and look for instabilities
(exponentially growing long wavelength modes) which can lead to the formation
of disoriented chiral condensates (DCCs). We find that instabilities exist for
proper times which are less than 3 fm/c. We also show that an experimental
signature of domain growth is an increase in the low momentum spectrum of
outgoing pions when compared to an expansion in thermal equilibrium. In
comparison to particle production during a longitudinal expansion, we find that
in a spherical expansion the system reaches the ``out'' regime much faster and
more particles get produced. However the size of the unstable region, which is
related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps
Lifetime of a Disoriented Chiral Condensate
The lifetime of a disoriented chiral condensate formed within a heat bath of
pions is calculated assuming temperatures and densities attainable at present
and future heavy-ion colliders. A generalization of the reduction formula to
include coherent states allows us to derive a formula for the decay rate. We
predict the half-life to be between 4 and 7 fm/c, depending on the assumed pion
density. We also calculate the lifetime in the presence of higher resonances
and baryons, which shortens the lifetime by at most 20%.Comment: 9 pages, 3 figures, REVTeX, Eq. (3) modifie
Dissipative Field Theory with Caldeira-Leggett Method and its Application to Disoriented Chiral Condensation
The effective field theory including the dissipative effect is developed
based on the Caldeira-Leggett theory at the classical level. After the
integration of the small field fluctuations considered as the field radiation,
the integro-differential field equation is given and shown to include the
dissipative effects. In that derivation, special cares should be taken for the
boundary condition of the integration. Application to the linear sigma model is
given, and the decay process of the chiral condensate is calculated with it,
both analytically in the linear approximation and numerically. With these
results, we discuss the stability of chiral condensates within the quenched
approximation.Comment: 16pages, ReV-Te
Pion Breather States in QCD
We describe a class of pionic breather solutions (PBS) which appear in the
chiral lagrangian description of low-energy QCD. These configurations are
long-lived, with lifetimes greater than fm/c, and could arise as
remnants of disoriented chiral condensate (DCC) formation at RHIC. We show that
the chiral lagrangian equations of motion for a uniformly isospin-polarized
domain reduce to those of the sine-gordon model. Consequently, our solutions
are directly related to the breather solutions of sine-gordon theory in 3+1
dimensions. We investigate the possibility of PBS formation from multiple
domains of DCC, and show that the probability of formation is non-negligible.Comment: 9 pages, 4 figure
Anomalous Transverse Distribution of Pions as a signal for the production of DCC's
We give evidence that the production of DCC's during a non-equilibrium phase
transition can lead to an anomalous transverse distribution of secondary pions
when compared to a more conventional boost invariant hydrodynamic flow in local
thermal equilibrium. Our results pertain to the linear model,treated
in leading order in large-, in a boost invariant approximation. We also show
that the interpolating number density of the field theory calculation plays the
role of a classical relativistic phase space number distribution in determining
the momentum distribution of pions in the center of mass frame.Comment: 10 pages, LaTex and 3 eps figure
Initial Time Singularities in Non-Equilibrium Evolution of Condensates and Their Resolution in the Linearized Approximation
The real time non-equilibrium evolution of condensates in field theory
requires an initial value problem specifying an initial quantum state or
density matrix. Arbitrary specifications of the initial quantum state (pure or
mixed) results in initial time singularities which are not removed by the usual
renormalization counterterms. We study the initial time singularities in the
linearized equation of motion for the scalar condensate in a renormalizable
Yukawa theory in 3+1 dimensions. In this renormalizable theory the initial time
singularities are enhanced. We present a consistent method for removing these
initial time singularities by specifying initial states where the distribution
of high energy quanta is determined by the initial conditions and the
interaction effects. This is done through a Bogoliubov transformation which is
consistently obtained in a perturbative expansion.The usual renormalization
counterterms and the proper choice of the Bogoliubov coefficients lead to a
singularity free evolution equation. We establish the relationship between the
evolution equations in the linearized approximation and linear response theory.
It is found that only a very specific form of the external source for linear
response leads to a real time evolution equation which is singularity free. We
focus on the evolution of spatially inhomogeneous scalar condensates by
implementing the initial state preparation via a Bogoliubov transformation up
to one-loop. As a concrete application, the evolution equation for an
inhomogenous condensate is solved analytically and the results are carefully
analyzed. Symmetry breaking by initial quantum states is discussed.Comment: LaTex, 26 pages, 2 .ps figure
Looking For Disoriented Chiral Condensates From Pion Distributions
We suggest two methods for the detection of the formation of disoriented
chiral condensates in heavy ion collisions. We show that the variance in the
number of charged pions (in a suitable range of momentum space) provides a
signature for the observation of a disoriented chiral condensate. The signal
should be observable even if multiple domains of DC form provided the
average number of pions per domain is significantly larger than unity. The
variance of the number charged pions alone provides a signal which can be used
even if the number of neutral pions cannot be measured in a given detector. On
the other hand, the probability distribution in , the proportion of neutral
pions to all pions emitted in heavy ion collisions in certain kinematic
regions, has been suggested as a signal of a disoriented chiral condensate.
Here we note that the signature can be greatly enhanced by making suitable cuts
in the data. In particular, we consider reducing the data set such that the
pions with lowest are all neutral. We find that, given such cuts,
can be substantially different from 1/3. For example, for a single D$\chi$C
domain without contamination due to incoherently emitted pions, is 3/5
given the pion with lowest is neutral, and 5/7 given the two pions with
lowest are both neutral, {\it etc.}. The effects of multi-domain DC
formation and noise due to incoherent pion emission can be systematically
incorporated. Potential applications to experiments and their limitations are
briefly discussed.Comment: 16 pages in REVTeX, 7 figures. Combined and updated version of
nucl-th/9903029 and nucl-th/9904074. Accepted by Phys. Rev.
Larger Domains from Resonant Decay of Disoriented Chiral Condensates
The decay of disoriented chiral condensates into soft pions is considered
within the context of a linear sigma model. Unlike earlier analytic studies,
which focused on the production of pions as the sigma field rolled down toward
its new equilibrium value, here we focus on the amplification of
long-wavelength pion modes due to parametric resonance as the sigma field
oscillates around the minimum of its potential. This process can create larger
domains of pion fluctuations than the usual spinodal decomposition process, and
hence may provide a viable experimental signature for chiral symmetry breaking
in relativistic heavy ion collisions; it may also better explain physically the
large growth of domains found in several numerical simulations.Comment: 4pp, 2 figs, Revtex. Minor revisions, conclusions unchange
The Chiral Phase Transition in Dissipative Dynamics
Numerical simulations of the chiral phase transition in the (3+1)dimensional
O(4)-model are presented. The evolutions of the chiral field follow purely
dissipative dynamics, starting from random chirally symmetric initial
configurations down to the true vacuum with spontaneously broken symmetry. The
model stabilizes topological textures which are formed together with domains of
disoriented chiral condensate (DCC) during the roll-down phase. The classically
evolving field acts as source for the emission of pions and mesons.
The exponents of power laws for the growth of angular correlations and for
emission rates are extracted. Fluctuations in the abundance ratios for neutral
and charged pions are compared with those for uncorrelated sources as potential
signature for the chiral phase transition after heavy-ion collisions. It is
found that the presence of stabilizing textures (baryons and antibaryons)
prevents sufficiently rapid growth of DCC-domain size, so observability of
anomalous tails in the abundance ratios is unlikely. However, the transient
formation of growing DCC domains causes sizable broadening of the distributions
as compared to the statistical widths of generic sources.Comment: 28 pages, 8 figure
Dynamical simulation of DCC formation in Bjorken rods
Using a semi-classical treatment of the linear sigma model, we simulate the
dynamical evolution of an initially hot cylindrical rod endowed with a
longitudinal Bjorken scaling expansion (a ``Bjorken rod''). The field equation
is propagated until full decoupling has occurred and the asymptotic many-body
state of free pions is then obtained by a suitable Fourier decomposition of the
field and a subsequent stochastic determination of the number of quanta in each
elementary mode. The resulting transverse pion spectrum exhibits visible
enhancements below 200 MeV due to the parametric amplification caused by the
oscillatory relaxation of the chiral order parameter. Ensembles of such final
states are subjected to various event-by-event analyses. The factorial moments
of the multiplicity distribution suggest that the soft pions are
non-statistical. Furthermore, their emission patterns exhibit azimuthal
correlations that have a bearing on the domain size in the source. Finally, the
distribution of the neutral pion fraction shows a significant broadening for
the soft pions which grows steadily as the number of azimuthal segments is
increased. All of these features are indicative of disoriented chiral
condensates and it may be interesting to apply similar analyses to actual data
from high-energy nuclear collision experiments.Comment: 38 pages total, incl 26 ps figures ([email protected]
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