Disoriented Chiral Condensates Research Articles

Disoriented chiral condensates, pion probability distributions, and parallels with disordered systems

A general expression is discussed for pion probability distributions coming from relativistic heavy ion collisions. The general expression contains as limits: 1) The disoriented chiral condensate (DCC), 2) the negative binomial distribution and Pearson type III distribution, 3) a binomial or Gaussian result, 4) and a Poisson distribution. This general expression approximates other distributions such as a signal to noise laser distribution. Similarities and differences of the DCC distribution with these other distribution are studied. A connection with the theory of disordered systems will be discussed which include spin-glasses, randomly broken objects, random and chaotic maps.

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 D$\chi$C 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 $R$, 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 $k$ pions with lowest $p_T$ are all neutral. We find that, given such cuts, $<R>$ can be substantially different from 1/3. For example, for a single D$\chi$C domain without contamination due to incoherently emitted pions, $<R>$ is 3/5 given the pion with lowest $p_T$ is neutral, and 5/7 given the two pions with lowest $p_T$ are both neutral, {\it etc.}. The effects of multi-domain D$\chi$C formation and noise due to incoherent pion emission can be systematically incorporated. Potential applications to experiments and their limitations are briefly discussed.

Mean Field Theory for Collective Motion of Quantum Meson Fields

Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schroedinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the variational wavefunctional can be rewritten in a compact form similar to the Hartree-Bogoliubov equations in quantum many-body theory and this result is used to recover the covariance of the theory. We then apply this method to the O(N) model and present analytic solutions of the mean field evolution equations for an N-component scalar field. These solutions correspond to quantum rotations in isospin space and represent generalizations of the classical solutions obtained earlier by Anselm and Ryskin. As compared to classical solutions new effects arise because of the coupling between the average value of the field and its quantum fluctuations. We show how to generalize these solutions to the case of mean field dynamics at finite temperature. The relevance of these solutions for the observation of a coherent collective state or a disoriented chiral condensate in ultra-relativistic nuclear collisions is discussed.

Localized domains of disoriented chiral condensates

A new method to search for localized domains of disoriented chiral condensates (DCC) has been proposed by utilizing the ( η− φ) phase space distributions of charged particles and photons. Using the discrete wavelet transformation (DWT) analysis technique, it has been found that the presence of DCC domains broadens the distribution of wavelet coefficients in comparison to that of normal events. Strength contours have been derived from the differences in rms deviations of these distributions by taking into account the size of DCC domains and the probability of DCC production in ultra-relativistic heavy ion collisions. This technique can be suitably adopted to experiments measuring multiplicities of charged particles and photons.

Disoriented chiral condensate dynamics with the SU(3) linear sigma model

The SU(3) extension of the linear sigma model is employed to elucidate the effect of including strangeness on the formation of disoriented chiral condensates. By means of a Hartree factorization, approximate dispersion relations for the 18 scalar and pseudoscalar meson species are derived and their self-consistent solution makes it possible to trace out the thermal path of the two order parameters as well as delineate the region of instability within which spontaneous pair creation becomes possible. The results depend significantly on the employed sigma mass, with the highest values yielding the largest regions of instability. An approximate solution of the equations of motion for the order parameter in scenarios emulating uniform scaling expansions show that even with a rapid quench only the pionic modes grow unstable. Nevertheless, the rapid and oscillatory relaxation of the order parameters leads to enhanced production of both pions and (to a lesser degree) kaons.

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.

Effect of friction on disoriented chiral condensate formation

We investigate the effect of friction on the DCC domain formation. We solve the Newton equation of motion for the O(4) fields, with a quenched initial condition. The initial fields are randomly distributed in a Gaussian form. In a one-dimensional expansion, on the average, large DCC domains cannot be formed. However, in some particular orbits, large instabilities may occur. This possibility also greatly diminishes with the introduction of friction. But, if the friction is large, the system may be overdamped and then there is a possibility of large DCC domain formation in some events.

Admixture of disoriented chiral condensate domains

Admixture of disoriented chiral condensate domains

Time development of vacuum structure in chiral phase transitions

The conditions for the restoration of chiral symmetry and the subsequent formation of the disoriented chiral condensates in ultrarelativistic nucleus-nucleus collisions are studied by using the linear $\ensuremath{\sigma}$ model. A rapid increase of temperature in the initial thermalization stage is parametrized so as to simulate the result of the parton cascade model. The subsequent decrease of temperature in the cooling stage is described in terms of the one- or three-dimensional scaling hydrodynamics. The effective potential at each temperature is calculated in the massless free particle approximation. Those ingredients are used to solve numerically the equation of motion for the chiral condensates. In general, solutions exhibit characteristic damped oscillations of which patterns are very sensitive to the maximum temperature ${T}_{m}$ and the time when the maximum temperature is attained. In particular, it is found that the maximum temperature must be much higher than the critical temperature ${T}_{c}$ in order that the chiral symmetry is restored temporarily, e.g., ${T}_{m}&gt;~175$ MeV for ${T}_{c}\ensuremath{\sim}123$ MeV with longitudinal expansion. Moreover, it is suggested that the disoriented chiral condensates will be formed most easily in the $\ensuremath{-}\ensuremath{\sigma}$ direction.

Comparison of accelerator and cosmic ray data

The final results of the MiniMax experiment at Fermilab where a search was made for evidence of Disoriented Chiral Condensates is reported; the negative conclusions are in contrast with the recent positive results reported by the Brazilian cosmic ray group. Accelerator results relating to the Pomeron and to hard diffraction are noted. Attention is drawn to the conspicuous lack of forward production data from accelerators which are particularly relevant to both the interpretation of cosmic ray physics and to non-perturbative QCD Strong Interaction physics.

DCC pion production from classical sources

We propose a scenario of DCC (disoriented chiral condensate) pion production. As the simplest realization of this scenario we consider the linear sigma model $O(2)$ in two dimensions. Through a numerical evolution of the classical equation of motion we evaluate the energy exchange between the sigma and the pion fields. Using our simulations we estimate the number and spectrum of emitted pions.

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 $10^3$ 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.

Search for disoriented chiral condensate in cosmicγ-hadron families

We present a systematic study of the large asymmetries in neutral pion fraction distribution in high energy cosmic ray families $(100 \mathrm{TeV}&lt;{E}_{\mathrm{vis}}&lt;700 \mathrm{TeV})$ detected at high mountain altitudes at Pamir (4300 m, 595 ${\mathrm{g}/\mathrm{c}\mathrm{m}}^{2}).$ With this in mind we have constructed robust observables, ratios of factorial moments, in experimental and simulated families in a similar way. We have found that our experimental data do not exclude the possibility of a DCC formation mechanism in high energy interactions.

Search for Disoriented Chiral Condensates in 158 AGeV Pb+Pb collisions

The restoration of chiral symmetry and its subsequent breaking through a phase transition has been predicted to create regions of Disoriented Chiral Condensates (DCC). This phenomenon has been predicted to cause anomalous fluctuations in the relative production of charged and neutral pions in high-energy hadronic and nuclear collisions. The WA98 experiment has been used to measure charged and photon multiplicities in the central region of 158 AGeV Pb+Pb collisions at the CERN SPS. In a sample of 212646 events, no clear DCC signal can be distinguished. Using a simple DCC model, we have set a 90% C.L. upper limit on the maximum DCC production allowed by the data.

Quantum transport theory and nonequilibrium chiral condensates

Quantum transport theory and disoriented chiral condensate (DCC) in the Nambu-Jona-Lasinio model are investigated. The kinetic equations are derived in covariant and equal-time formulations. It is found that DCC is closely connected with the fluctuation of quark spin density. For the longitudinally expanding system, which models a highenergy nucleus-nucleus collision, a DCC present initially is quickly dissolved due to the expansion and the collision processes. However, the quantum off-shell effect leads to a strong fluctuation of DCC.

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 $7\mathrm{fm}/c$, 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 $20%$.

Forming disoriented chiral condensates through fluctuations

Using the influence functional formalism, classical equations of motion for the O(N) model are derived in the presence of a heat bath, in both the symmetric phase as well as the phase of spontaneously broken symmetry. The heat bath leads to dissipation and fluctuation terms in the classical equations of motion, which are explicitly computed to lowest order in perturbation theory. In the broken phase these terms are found to be large for the sigma field, even at zero temperature, due to the decay process sigma -> pi pi, while they are small for the pi fields at temperatures below T_c = 160 MeV. It is shown that in large volumes the presence of dissipation and fluctuations suppresses the formation of disoriented chiral condensates (DCC's). In small volumes, however, fluctuations become sufficiently large to induce the formation of DCC's even if chiral symmetry has not been restored in the initial stage of the system's evolution.

A Self-Consistent Treatment of Disoriented Chiral Condensates

A system with disoriented chiral condensates (DCCs) is considered in the presence of residual thermal pion distributions. By self-consistently solving the coupled equations for the condensates, the thermal pion distributions, and the self-energies, it is observed that the neutral pion fraction f as a signal of DCCs is erased by the thermal pions.

Anomaly induced domain formation of disoriented chiral condensates

We discuss the effect of chiral anomaly as a possible mechanism for triggering formation of domains of disoriented chiral condensate (DCC) in relativistic heavy ion collisions. The anomalous $\pi^0 \to 2 \gamma$ coupling and the strong, Lorentz contracted electromagnetic fields of the heavy ions combine to produce the ``anomaly kick'' to the field configuration of the neutral pion field. We implement the effect of anomaly kick in our numerical simulation of the linear sigma model in a schematic way which preserves its characteristic features: the effect is coherent over a large region of space but is opposite in sign above and below the ion scattering plane. We demonstrate by detailed simulations with longitudinal expansion that the DCC domain formation is dramatically enhanced by the anomaly kick in spite of its small absolute magnitude. We examine the behavior of various physical quantities such as pion fields, the axial vector currents, and their correlation functions. Our results also provide useful insight into the mechanism and properties of DCC domain formation, in general. Finally, we discuss some experimental observables which can signal the anomaly induced formation of DCC.

THERMAL FLUCTUATIONS OF DISORIENTED CHIRAL CONDENSATE DOMAINS

We argue that disoriented chiral condensate (DCC) domains are not well defined for temperatures above the Ginzburg temperature T G (≃0.7 T c ). Above T G , the dynamics of DCC domains is dominated by thermal fluctuations leading to fluctuating orientation of the chiral field in a given domain. It implies that disorientation of chiral field, and hence DCC formation may happen even in relatively lower energy collisions where the temperature only reaches T G , and never rises to T c . It also means that detection of DCC cannot be taken as a signal for an intermediate chirally symmetric phase of matter. Using these considerations, we estimate the probability distribution for DCC domains as a function of the chiral angle.