Chiral QCD phase transition in nuclear collisions

The characteristic aspects of multiparticle states generated at , as a result of chiral QCD phase transition, are studied in the framework of the O(4) theory. Predictions concerning critical events, in connection with current and future experiments with ultrarelativistic heavy ions, are presented. Received: 9 June 1997 / Revised version: 18 July 1997 / Published online: 26 February 1998     

Chiral phase transition in lattice QCD with Wilson quarks

The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extensionN _t=4. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.     

Chiral phase transition in lattice QCD with dynamical quarks

The effect of virtual light quark loops on the chiral phase transition in lattice QCD with staggered fermions is investigated by employing the pseudo-fermion Monte Carlo method on a 6³ × 2 lattice. The variation in the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ is found to become less sharp than the quenched case, indicating a second order chiral phase transitioon in the full theory.     

Chiral phase transition in lattice QCD with Wilson quarks

The nature of the chiral phase transition in lattice QCD is studied for the cases of 2, 3 and 6 flavors with degenerate Wilson quarks, mainly on a lattice with the temporal direction extensionN _t=4. We find that the chiral phase transition is continuous for the case of 2 flavors, while it is of first order for 3 and 6 flavors.     

Correlation function for topological charge densities within the instanton model in QCD

The QCD sum rule for the correlation of topological charge densities χ(Q ²) and for the longitudinal part of the correlation function for singlet axial currents (the latter is related to the former) is considered within the instanton model. The constant f _η′ of η′-meson coupling to the singlet axial current is determined. Its value appears to be in good agreement with that determined recently from the relation between the proton-spin fraction Σ carried by u, d, and s quarks and the derivative of the QCD topological susceptibility χ′(0). On the basis of the same sum rule, the η-η′ mixing angle θ₈ is found within the model employing two mixing angles. The value of θ₈ coincides with that in effective chiral theory. The correlation function for topological charge densities χ(Q ²) at large Q ² is calculated. It is shown that the Q ² dependence at high Q ² matches well with that at low Q ², the latter being determined by the known values χ′(0) and by the contributions of the π and η mesons.     

Pion distribution amplitudes within the instanton model of QCD vacuum

The pion transition form factor for the process γ*γ* → π⁰ at spacelike values of photon momenta is calculated within the effective quark-meson model with the interaction induced by instanton exchange. The leading and next-to-leading order power asymptotics of the form factor and the relation between the light-cone pion distribution amplitudes of twists 2 and 4 and the dynamically generated quark mass are found.     

QCD phase transition in the inhomogeneous universe

We investigate a new mechanism for the cosmological QCD phase transition: inhomogeneous nucleation. The primordial temperature fluctuations, measured to be deltaT/T approximately 10(-5), are larger than the tiny temperature interval in which bubbles would form in the standard picture of homogeneous nucleation. Thus the bubbles nucleate at cold spots. We find the typical distance between bubble centers to be a few meters. This exceeds the estimates from homogeneous nucleation by 2 orders of magnitude. The resulting baryon inhomogeneities may affect primordial nucleosynthesis.     

Explore the QCD phase transition phenomena from a multiphase transport model

We study the phase structure of QCD matter in the framework of a multiphase transport model by implementing a strong local parton density fluctuation scenario. Our calculations on the beam energy dependence of net-proton high moment show that local parton density fluctuation only has a small effect. But it becomes important when all baryons are included. We then study the effect on elliptic flow and find that an enhanced local parton density fluctuation leads to a significant effect on protons but a small effect on pions. Our study provides a reference of transport dynamics on QCD phase transition phenomena and will be relevant for the upcoming phase II of the beam energy scan program at RHIC.     

Quantum critical phase and Lifshitz transition in an extended periodic Anderson model

We study the quantum phase transition in f-electron systems as a quantum Lifshitz transition driven by selective-Mott localization in a realistic extended Anderson lattice model. Using dynamical mean-field theory (DMFT), we find that a quantum critical phase with anomalous ω/T scaling separates a heavy Landau-Fermi liquid from ordered phase(s). This non-Fermi liquid state arises from a lattice orthogonality catastrophe originating from orbital-selective Mott localization. Fermi surface reconstruction occurs via the interplay between and penetration of the Green function zeros to the poles, leading to violation of Luttinger's theorem in the strange metal. We show how this naturally leads to scale-invariant responses in transport. Thus, our work represents a specific DMFT realization of the hidden-FL and FL* theories, and holds promise for the study of 'strange' metal phases in quantum matter.     

QCD chiral phase transition and critical exponents within the nonextensive Polyakov-Nambu-Jona-Lasinio model

We present a nonextensive version of the Polyakov-Nambu-Jona-Lasinio model that is based on nonextentive statistical mechanics.This new statistics model is characterized by a dimensionless nonextensivity parameter q that accounts for all possible effects violating the assumptions of the Boltzmann-Gibbs(BG) statistics(for q→ 1,it returns to the BG case).Based on the nonextensive Polyakov-Nambu-Jona-Lasinio model,we discussed the influence of nonextensive effects on the curvature of the phase diagram at μ=0 and especially on the location of the critical end point(CEP).A new and interesting phenomenon we found is that with an increase in q,the CEP position initially shifts toward the direction of larger chemical potential and lower temperature.However,when q is larger than a critical value q_c,the CEP position moves in the opposite direction.In other words,as q increases,the CEP position moves in the direction of smaller chemical potential and higher temperature.This U-turn phenomenon may be important for the search of CEP in relativistic heavy-ion collisions,in which the validity of BG statistics is questionable due to strong fluctuations and long-range correlations,and nonextensive effects begin to manifest themselves.In addition,we calculated the influence of the nonextensive effects on the critical exponents and found that they remain almost constant with q.     

The chiral phase transition in QCD

The Chiral Phase Transition in QCD is studied analytically by looking at truncations of the Schwinger-Dyson equation for the quark self-mass. We find that the usual implementation of the gluon propagator at non-zero temperature is far too simple. When the gluons are given the correct qualitative non-zero temperature behaviour, the calculation of the critical temperature changes significantly.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Self-consistent theory of localization for the Anderson model

The self-consistent theory of electron localization in a random system in the form proposed by Vollhardt and Wölfle is generalized for the analysis of localization in the Anderson model. We derive the general equations appropriate for the system with rather general form of the electronic spectrum. Explicit calculations are restricted to the lattices of cubic symmetry and use the effective mass approximation to obtain the final results. Anderson's critical ratio for the localization of all the electronic states in the tight-binding band is evaluated and found to be in surprisingly good agreement with the results of numerical analysis of localization in the Anderson model.