Pion decay constant at finite temperature

The values of the pion decay constant, and of the bilinear fermionic condensate, for temperatures from zero up to the critical temperature for chiral phase transition, are calculated using our composite operator approach to finite temperature QCD. For small temperatures our results agree with those found with other approaches. Near the critical temperature we recover the universal behaviour typical of second order phase transition. We have assumed that effects responsible for deconfinement do not strongly perturb our chiral approach for two and possibly three flavours.     

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a 5% change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.     

改进的PNJL模型下QCD的相图

Polyakov-Nambu-Jona-Lasinio（PNJL）模型是研究强相互作用物质性质的使用最为广泛的有效模型之一。在PNJL模型的基础上考虑了手征凝聚和Polyakov圈之间的纠缠作用,并且引入了化学势修正的Polyakov有效势,由此得到了化学势依赖的entangled PNJL（μEPNJL）模型。在平均场框架下的计算结果表明:相较于原始的PNJL模型,由μEPNJL模型计算得到的临界点（CEP）朝着温度更高、化学势更小处移动,并且手征对称性恢复相变和退禁闭相变在较大的化学势范围内都重合得很好。通过与STAR合作组在相对论重离子对撞机（RHIC）上进行的净质子数分布的测量结果相比,可以发现,通过适当的参数调节,由μEPNJL模型计算得到的CEP更加靠近实验预言的CEP可能存在的区域。Polyakov-Nambu-Jona-Lasinio (PNJL) model is one of the most popular effective quark models to investigate the properties of strongly interacting matter. Based on the PNJL model, we consider the entanglement interactions between the chiral condensate and Polyakov-loop, as well as the chemical potential modification of Polyakov-loop potential simultaneously, which is named μEPNJL model. Compared with the original PNJL model, the calculations in the mean field approximation show that the critical end point (CEP) given in the μEPNJL model moves towards higher temperature and smaller chemical potential in the T-μ phase diagram. Besides, the chiral symmetry restoration and deconfinement phase transition coincide well in a wide range of chemical potential. Comparing our calculations with the measurement of the moments of net-proton multiplicity distributions at Relativistic Heavy-Ion Collider (RHIC) by STAR Collaboration, we find that the CEP given by μEPNJL model can be closer to the range predicted by the experiment through appropriate parameter adjustment.     

The Effects of the Pion String at Heavy ion Collisions

We study the possible signals of the pion string associated with the QCD chiral phase transition in LHC Pb–Pb collision at energy s=5.5 TeV.We follow the Kibble–Zurek mechanism to discuss the production and evolution of the pion string.We will show that if the QCD chiral phase transition really takes place in the LHC Pb-Pb collision process and the phase transition is in the second order,the pion string will be inevitably produced and subsequently decay.The main effect of this phenomenon is that there is a generation of a large number of pions in the final state produced by the decay of the pion string, and these pions are mostly distributed in a low momentum region with p～143MeV; also there are lots of neutral pions distributed in a low momentum region with the mean momentum at p～21MeV.     

Generalized Beth–Uhlenbeck approach to mesons and diquarks in hot,dense quark matter

An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the Gaussian approximation for the meson and diquark fields and it is given in the Beth–Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson–diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by π$\pi$ in accordance with Levinson’s theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth–Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.     

Pion propagation near the QCD chiral phase transition

We point out that, in analogy with spin waves in antiferromagnets, all parameters describing the real-time propagation of soft pions at temperatures below the QCD chiral phase transition can be expressed in terms of static correlators. This allows, in principle, the determination of the soft pion dispersion relation on the lattice. Using scaling and universality arguments, we determine the critical behavior of the parameters of pion propagation. We predict that, when the critical temperature is approached from below, the pole mass of the pion drops despite the growth of the pion screening mass. This fact is attributed to the decrease of the pion velocity near the phase transition.     

Classical pion fields in the presence of a source

A classical pion field that is similar to a disoriented chiral condensate is considered in the presence of an external source. The field is similar to the condensate in that the isotopic orientation of the field in the whole space is determined by a single vector. Within the nonlinear sigma model, classical solutions are considered both in the chiral limit, where the pions are massless, and in the case of a finite pion mass. In either case, the classical filed is similar to the Coulomb field of a charged particle; however, the nonlinear pion interaction results in the existence of several solutions. In the massless case and in the case where the source is sufficiently small, there are a great number of classical solutions characterized by finite discrete energies. In the more realistic case of heavy ions, there are no stable solutions of this type; however, long-lived quasistationary states, which slowly decay, emitting very soft pions, can be formed. The structure and the energies of these solutions are studied numerically.     

Effects of mesonic correlations in the QCD phase transition

The finite-temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T _c the pressure is well described by the mean-field-approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed. The text was submitted by the authors in English.     

Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model

Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ-T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the Bose-Einstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.     

QCD手征相变中的π介子增强(英文)

讨论了在LHC的Pb-Pb碰撞过程中,如果QGP SU(2)手征相变出现二级相变,那么系统将会有π弦产生,并且π弦最终将衰变为π介子。于是以上效应将导致在低动量区域（p~150—400 MeV）内的π介子增强。对应于不同的冷却温度T_f=130,120,110 MeV,产生于π弦衰变的π介子的数量分别是Nt≈270,150, 60. It is pointed out that if the QGP SU(2) chiral phase transition in the LHC Pb Pb collision process is taken place and the phase transition is in the second order, then pion strings will be formed, and decay. These phenomena lead to the pion enhancement in the low momentum region(p150—400 MeV) and the number of pions produced from pion string decay can be estimated about Nt≈270, 150, 60 for different freeze temperature Tf=130, 120, 110 MeV respectively.     

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     

A generalized Uhlenbeck and Beth formula for the third cluster coefficient

Relatively recently (Amaya-Tapia et al., 2011), we presented a formula for the evaluation of the third Bose fugacity coefficient–leading to the third virial coefficient–in terms of three-body eigenphase shifts, for particles subject to repulsive forces. An analytical calculation for a 1-dim. model, for which the result is known, confirmed the validity of this approach. We now extend the formalism to particles with attractive forces, and therefore must allow for the possibility that the particles have bound states. We thus obtain a true generalization of the famous formula of Uhlenbeck and Beth (Uhlenbeck and Beth, 1936; Beth and Uhlenbeck, 1937) and of Gropper (Gropper, 1936, 1937) for the second virial. We illustrate our formalism by a calculation, in an adiabatic approximation, of the third cluster in one dimension, using McGuire’s model as in our previous paper, but with attractive forces. The inclusion of three-body bound states is trivial; taking into account states having asymptotically two particles bound, and one free, is not.     

Pion and σ-meson Properties in a Strong Magnetic Field

With the Nambu-Jona-Lasinio (NJL) model we calculate the properties of pion and σ-meson at finite temperature and finite magnetic field. The obtained temperature and magnetic field strength dependence of the constituent quark mass M, the pion and σ-meson masses and the neutral pion decay constant indicates that, in the simple four fermion interaction model, there exists the magnetic catalysis effect. It also shows that the Gell-Mann-Oakes-Renner relation is violated obviously with the increasing of the temperature, and the effect of the magnetic field becomes pronounced only around the critical temperature. The deviation of the critical temperatures obtained with different criteria indicates that the chiral phase transition driven by the temperature in the magnetic field strength region we have considered is in fact a crossover.     

Pion condensation at finite temperature: (I). Mean field theory

The pion-condensed state of neutron-rich matter at finite temperature is calculated within the framework of a simple σ-model, treating the pion field as a mean field. At high densities the matter is condensed with a spatially non-uniform condensate. However, we find the unexpected result that as the density is lowered, at any finite temperature, pure neutron matter always makes a transition to a state with a spatially uniform condensate. Pure neutron matter, within mean field theory, is condensed at all non-zero temperatures and densities. Matter with a small proton fraction at zero temperature has a qualitatively similar phase diagram, except that it is normal when both the temperature and density are sufficiently low.     

Finite size effect on dissociation and diffusion of chiral partners in Nambu-Jona-Lasinio model

The masses of pion and sigma meson modes, along with their dissociation in the quark medium, provide detailed spectral structures of the chiral partners. Collectivity has been observed in pA and pp systems both at LHC and RHIC. In this research, we studied the restoration of chiral symmetry by investigating the finite size effect on the detailed structure of chiral partners in the framework of the Nambu-Jona-Lasinio model. Their diffusion and conduction have been studied using this dissociation mechanism. It is determined that the masses, widths, diffusion coefficients, and conductivities of chiral partners merge at different temperatures in the restoration phase of chiral symmetry. However, merging points are shifted to lower temperatures when finite size effect is introduced into the picture. The strengths of diffusions and conductions are also reduced once the finite size is introduced in the calculations.     

Chiral condensate and chemical freeze-out

We consider a chemical freeze-out mechanism which is based on a strong medium dependence of the rates for inelastic flavor-equilibrating collisions based on the delocalization of hadronic wave functions and growing hadronic radii when approaching the chiral restoration. We investigate the role of mesonic (pion) and baryonic (nucleon) fluctuations for melting the chiral condensate in the phase diagram in the (T, μ)-plane. We apply the PNJL model beyond mean-field and present an effective generalization of the chiral perturbation theory result which accounts for the medium dependence of the pion decay constant while preserving the GMOR relation. We demonstrate within a schematic resonance gas model consisting of a variable number of pionic and nucleonic degrees of freedom that within the above model a quantitative explanation of the hadonic freeze-out curve and its phenomenological conditions can be given.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Possible pseudogap phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally, and quarks acquire constituent masses in the pseudogap phase, despite the fact that chiral symmetry is restored.