Dynamical generation of the constituent mass in expanding plasma

Abstract

We investigate dynamics of the chiral transition in expanding quark-antiquark plasma produced in an ultra-relativistic heavy ion collision. The chiral symmetry break-down and dynamical generation of the constituent quark mass are studied within the linear sigma model and Nambu-Jona-Lasinio model. Time dependence of the quark and antiquark densities is obtained from the scaling solution of the relativistic Vlasov equation. Fast initial growth and strong oscillations of the constituent quark mass are found in the linear sigma model as well as in the NJL model, when derivative terms are taken into account.PACS numbers: 25.75.+r, 11.30.Rd, 12.38Mh, 24.85.+p Keywords: non-equilibrium chiral transition, constituent quarks, pion field oscillations, relativistic heavy ion collisions, scaling expansion.Introduction.-It is commonly believed that colour deconfinement and chiral symmetry restoration take place at early stages of ultra-relativistic heavy-ion collisions. At intermediate stages of the reaction the quark-gluon plasma may be formed and evolve through the states close to thermodynamical equilibrium. However, at later stages of the expansion the transition to the hadronic phase with broken chiral symmetry should take place. The breakdown of chiral symmetry will possibly lead to such interesting phenomena as formation of disoriented chiral condensates (DCCs) and classical pion fields as well as clustering of quarks and antiquarks. These phenomena were studied recently in many publications [1][2][3][4][5][6][7][8][9][10][11][12][13][14], using QCD motivated effective models, such as the linear and non-linear sigma models and the Nambu-Jona-Lasinio (NJL) model. Of course, these models have some significant shortcomings, e.g. they do not possess colour confinement and the NJL-model is non-renormalizable. The key point is, however, that these models obey the same chiral symmetry as the QCD Lagrangian.In most applications of the sigma model the quark degrees of freedom are disregarded (see e.g. [2-9,14]). The inclusion of quarks [10, 11] makes it possible to study the hadronization

On Dark Matter Identification

“…One could then also hope to gain more information about the properties of QGP near the QCD phase transition, such as the growth of the effective quark masses and hence, indirectly, about the screening of colour gluons [19] [21]. In the linear sigma model, where massive qq -pairs play the role of pions and the sigma meson that of a Higgs boson, however, by contrast to the EW transition, the dimensionless coupling has attained a value λ > 1 [10].…”

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

“…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].…”

“…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.…”

“…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.…”

“…To illustrate the above idea, we applied the linear s model coupled to a heat bath [5,16]. The Lagrangian of the linear sigma model with quark degrees of freedom reads L q ͓ig m ≠ m 2 g͑s 1 ig 5 t ?…”