Larger domains from resonant decay of disoriented chiral condensates

Abstract

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. ͓S0556-2821͑99͒03911-9͔PACS number͑s͒: 25.75.Ϫq Experiments at the Relativistic Heavy Ion Collider at Brookhaven and at the Large Hadron Collider at CERN may soon be able to probe many questions in strong-interaction physics which have until now been studied only on paper or simulated on a lattice. One major area of study concerns the QCD chiral phase transition. In relativistic heavy ion collisions, it is possible that non-equilibrium dynamics could produce ''disoriented chiral condensates'' ͑DCCs͒, domains in which a particular direction of the pion field develops a nonzero expectation value ͓1-3͔. These domains would then decay to the usual QCD vacuum by radiating soft pions. Preliminary searches for DCCs by the MiniMax Collaboration in pp collisions at Fermilab have thus far not found evidence for the production and decay of DCCs ͓4͔, though they are far more likely to be created in upcoming heavy ion collisions. Thus, understanding their possible formation and likely decay signatures in anticipation of further experimental work is of key importance.If these domains grow to sufficient size ͑on the order of 3-7 fm͒, such an experimental event would be marked by a particular clustering pattern: some regions within the detector would measure a large number of charged pions but few neutral pions, while other regions of the detector would measure predominantly neutral pions with few charged pions ͓2͔. Defining R to be the ratio of neutral pions to total pions, Rϵn o /(n oϩ n ϩϩ n Ϫ) , it has been demonstrated that the probability for measuring various ratios R in DCC events obeys P(R)ϭ(4R) Ϫ1/2 , which, especially for small-R, may be easily distinguished from the isospin-invariant result of P(R)→␦(RϪ1/3) ͓2͔. ͑Detecting the decay of such DCCs could be improved by measuring the two-pion correlation functions ͓5͔, and from enhanced dilepton and photoproduction ͓6͔, in addition to studying the fraction of neutral pions produced.͒ The production and subsequent relaxation of such DCCs may also explain the so-called ''Centauro'' highenergy cosmic ray events, in which very large numbers of charged pions are detected with only very few neutral pions ͓2,7͔.However, as emphasized in ͓8,9͔, if the disoriented domains do not grow to such large scales within heavy ion collisions, such exper...

High-Dimensional Chaotic and Attractor Systems

“…It manifests itself as a rapid growth of a physical field at an exponential rate. Recently this phenomenon has been used to explain some physical processes such as reheating in the early universe [KLS94, Kai97] and in phase transitions in disordered chiral condensates [Kai99]. At the same time a lot of attention has been given to the study of chaotic systems, i.e., systems whose trajectories in phase-space diverge exponentially, but at the same time remain within a bounded region.…”

Microscopic dynamics of disoriented chiral condensate formation

“…This implies that the j (k ជ )'s and the j (k ជ )'s are independent Gaussian numbers of variances N͗ j 2 ͘ and 14 Such a probability distribution for the ␣'s is called the P-representation of the density operator ͓17͔: a very large class of quantum density operators can be written ϭ͐d 2 ␣ P ␣ (␣)͉␣͗͘␣͉. 15 Note that although our initial state is a thermal collection of quanta, these are not zero temperature pions ͑this means that their dispersion relations are not those of free pions͒. That is why the initial neutral fraction distribution is not the same as Eq.…”

Parametric resonance at the critical temperature in high energy heavy ion collisions

“…The time development of the chiral condensate has been studied in terms of DCC and the possibility of soft mode enhancement by parametric resonance was suggested [1]. Parametric resonance in the last stage of high energy heavy ion collisions was discussed [1][2][3][4][5][6][7] and amplified modes were extracted. A parametric resonance is expected even in the chiral phase transition because the oscillation of the chiral condensate (momentum k = 0) may amplify nonzero (k = 0) modes.…”

“…The study of parametric resonance at finite temperature in chiral phase transition has never been examined, while that at zero temperature [1][2][3][4][5][6][7] has been performed. Parametric resonance may occur even when the temperature is not zero if the condensates moves periodically like a sine function.…”