First-Order Chiral Phase Transition May Naturally Lead to a “Quenched” Initial Condition and Strong Soft-Pion Fields

Abstract

We propose a novel mechanism for disoriented chiral condensate (DCC) formation in a first-order chiral phase transition. In this case the effective potential for the chiral order parameter has a local minimum at F ϳ 0 in which the chiral field can be "trapped." If the expansion is fast, a bubble of disoriented chiral field can emerge and decouple from the rest of the fireball. The bubble may overshoot the mixed phase and supercool until the barrier disappears, when the potential resembles that at T 0. This situation corresponds to the initial condition realized in a "quench." Thus, the subsequent alignment in the vacuum direction leads to strong amplification of low-momentum modes of the pion field. We propose that these DCCs could accompany the previously suggested baryon rapidity fluctuations. 11.30.Qc, 11.30.Rd, 24.85. + p Relativistic heavy-ion collisions might offer the interesting opportunity to study chiral symmetry restoration at nonzero temperature and density, which could possibly lead to the formation of domains of disoriented chiral condensate (DCC) [1][2][3][4][5]. The strongest amplification of the pion field is obtained for the so-called "quenched" initial condition [3]. It is assumed that the heat bath is removed instantaneously after restoration of chiral symmetry.However, dynamical simulations [4,5] show that the "quench" does not emerge naturally in a heavy-ion collision, if the chiral phase transition is second order or a smooth crossover. In this Letter, we instead propose a new approach to obtain the quenched initial conditions naturally in the presence of a first-order phase transition.It has been argued [6] that the phase transition for two massless quarks at baryon-chemical potential m 0 is second order which then becomes a smooth crossover for small quark masses. On the other hand, a first-order phase transition is predicted for small temperatures and large m. If, indeed, there is a smooth crossover for m 0 and nonzero T , and a first-order transition for small T and nonzero m, then the first-order phase transition line in the ͑m, T ͒ plane must end in a second-order critical point. This point is predicted to be at T ϳ 100 MeV and m ϳ 600 MeV. However, some lattice QCD results indicate a first-order transition even at vanishing baryon-chemical potential [7]. Such temperatures and baryon-chemical potentials can be reached in the central region of heavy-ion collisions in the forthcoming Pb͑40A GeV͒ 1 Pb experiments at the CERN-SPS [8], and in the fragmentation regions of more energetic collisions at the CERN-SPS, BNL-RHIC, and CERN-LHC ( p s Ӎ 20A, 200A, 5000A GeV) [9]. Furthermore, fluctuations in individual events can also provide rapidity bins with significantly higher m and lower T than on average [10][11][12][13]. In any case, the dynamical scenario for DCC formation described in this Letter applies to the case of a first-order chiral phase transition, and is qualitatively independent of the value of m. Our calculation described below has been performed at m 0, and the parameters ...

Chiral transition and the quark-gluon plasma

“…This sort of effective potential is commonly used as the thermodynamic potential in a phenomenological description of the chiral transition for an expanding quark-gluon plasma created in a high-energy heavy-ion collision [22][23][24][25][26]. However, the presence of a nontrivial background field configuration, e.g.…”

“…In particular, to study the mechanisms of bubble nucleation and spinodal decomposition in a hot expanding plasma, it is common to adopt the linear σ-model coupled to quarks, where the latter comprise the hydrodynamic degrees of freedom of the system [21][22][23][24][25][26]. The gas of quarks provides a thermal bath in which the longwavelength modes of the chiral field evolve, and the latter plays the role of an order parameter in a Landau-Ginzburg approach to the description of the chiral phase transition.…”

Nucleation in the chiral transition with an inhomogeneous background

“…The mechanism of chiral symmetry breaking and the study of the dynamics of phase conversion after a temperaturedriven chiral transition can be done conveniently within lowenergy effective models [1][2][3][4][5][6][7][8][9]. In particular, to study the mechanisms of bubble nucleation and spinodal decomposition in a hot expanding plasma [10], it is common to adopt the linear σ-model coupled to quarks [11].…”

“…This kind of effective potential is commonly used as the coarse-grained thermodynamic potential in a phenomenological description of the chiral transition for an expanding quarkgluon plasma [3][4][5][6].…”

Non-local effects at the onset of the chiral transition

“…Results from CERN-SPS and BNL-RHIC feature an explosive behavior in the hadronization process and seem to favor a very fast spinodal decomposition as the mechanism of phase conversion. Effective chiral field theory models for QCD also point to an explosive spinodal decomposition scenario [3,4].…”