Nonlinear evolution of the momentum dependent condensates in strong interaction: The “pseudoscalar laser”

Abstract

We discuss the relaxation of the scalar and pseudoscalar condensates after a rapid quench from an initial state with fluctuations. If we include not only the zero-mode but also higher modes of the condensates in the classical evolution, we observe parametric amplification of those "hard" modes. Thus, they couple nonlinearly to the "soft" modes. As a consequence, domains of coherent π-field emerge long after the initial spinodal decomposition. The momentum-space distribution of pions emerging from the decay of that momentumdependent condensate is discussed.The exciting speculation that the dynamics of spontaneous breaking of chiral symmetry could reorient the condensates in QCD as compared to the physical vacuum has stimulated many studies, see e.g. [1][2][3][4][5][6][7], and [8] for reviews. However, for the chiral symmetry breaking process in strong interaction the spinodal decomposition after a rapid "quench" does not yield a large correlation length [9]. Accordingly, a simulation [4] of the classical equations of motion of the linear σ-model on a 3d-lattice with spacing a = 1 fm confirmed that in the strongcoupling case no large domains form in which the π-field were essentially uniform, see also [5].We shall confirm that result but also argue that if the cutoff for the Fourier modes of the classical order parameter of chiral symmetry is pushed to larger values by some physical mechanism, e.g. parametric resonance [10][11][12], domains much bigger than the Compton wavelength of the pion can form over time-scales ≫ 1 fm. Thus, the "pseudoscalar laser" is a non-linear phenomenon developing long after spinodal decomposition.Our rather simple idea is that parametric resonance leads to large occupation numbers of "hard" modes of the scalar and pseudoscalar condensates, which then couple non-linearly to the "soft" modes. Thus, the same mechanism that is responsible for the explosive heating of the universe after inflation [10] (see also [13] were the inflaton decay was studied via a simulation on the lattice, similar to our studies here) leads to the formation of domains where the pseudoscalar condensate exhibits coherent oscillations with big amplitude around its vacuum value. Those domains could be produced in the laboratory in collisions of protons [1] or heavier nuclei [2] at high energies.As an effective theory of the chiral symmetry breaking dynamics [14] we apply the linear σ-model [15]The potential exhibiting the spontaneously broken symmetry isHere q is the constituent-quark field q = (u, d). The scalar field σ and the pseudoscalar field π = (π 1 , π 2 , π 3 ) together form a chiral field Φ = (σ, π). The parameters of the Lagrangian are usually chosen such that the chiral SU L (2) ⊗ SU R (2) symmetry is spontaneously broken in the vacuum and the expectation values of the condensates are σ = f π and π = 0, where f π = 93 MeV is the pion decay constant. The explicit symmetry breaking term is determined by the PCAC relation which gives H = f π m 2 π , where m π = 138 MeV is the pion mass. Then one findsπ , wh...

Hydrodynamics near a chiral critical point

“…We employed the same small grid spacing ∆x = 0.3 fm as for the fluid. Although the mean fields vary on a larger scale, it is important to allow for non-linear amplification of harder fluctuations which can couple to the soft modes and affect the dynamical relaxation to the vacuum state with broken symmetry, see for example [36] and [37].…”

Non-Equilibrium Phenomena in the QCD Phase Transition

“…In this sense our study is close to the real world. As a consequence, the pion production in our model is not as pronounced as in other models [6,9,10]. However, the momentum distribution of the produced pions possesses fingerprints of the zone structure of the amplification regions in momentum space: a cluster of pions with low momenta is formed.…”

“…These initial conditions differ from the ones assumed for particle production through inflaton decay in cosmology [8], and in some works on QCD [9,10], as in those cases the initial particle number is taken to be zero.…”

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

“…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.…”