Calculation of Equation of State of QCD at Finite Chemical Potential and Temperature

In this paper, using path integral techniques we derive a model-independent formula for the pressure density P（μ, T） （or equivalently the partition function） of Quantum Chromodynamics （QCD）, which gives the equation of state （EOS） of QCD at finite chemical potential and temperature. In this formula the pressure density P（μ, T） consists of two terms： the first term （p（μ, T）｜T=0） is a μ-independent （but T-dependent） constant; the second term is totally determined by G[μ, T]（p, ωn） （the dressed quark propagator at finite μ and finite T）, which contains all the nontrivial μ-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson-Schwinger （DS） approach and under the approximation of neglecting the μ-dependence of the dressed gluon propagator, we show that G[μ, T]（p,ωn） can be obtained from G[T]（p,ωn ） （the dressed quark propagator at μ= 0） by the substitution ωn →ωn ＋ iμ. This result facilitates numerical calculations considerably. By this result, once C [T] （p, ωn） is known, one can determine the EOS of QCD under the above approximations （up to the additive term p（μ, T）｜T=0）. Finally, a comparison of the present EOS of QCD and the EOS obtained in the previous literatures in the framework of the rainbow-ladder approximation of the DS approach is given. It is found that the EOS given in the previous literatures does not satisfy the thermodynamic relation ρ（μ,T） =δp（μ,T）/δμ｜T.     

A Model Study of Equation of State of QCD at Finite Chemical Potential and Zero Temperature

In this paper, we give a direct method for calculating the partition function, and hence the equation of state （EOS） of QCD at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms： the first term P（μ）｜μ=0 （the pressure density at μ = 0） is a μ-independent constant; the second term, which is totally determined by G[μ] （p） （the dressed quark propagator at finite μ）, contains all the nontrivial μ-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71 （2005） 015205], G[μ]（p） is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 67 （2003） 054019]. From this the full analytic expression of the EOS of QCD at finite μ and zero T is obtained （apart from the constant term P（μ）｜μ=0, which can in principle be caJculated from the CJT effective action）. A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.     

QCD at finite temperature and density within the fRG approach: an overview

In this paper, we present an overview on recent progress in studies of QCD at finite temperature and densities within the functional renormalization group (fRG) approach. The fRG is a nonperturbative continuum field approach, in which quantum, thermal and density fluctuations are integrated successively with the evolution of the renormalization group (RG) scale. The fRG results for the QCD phase structure and the location of the critical end point (CEP), the QCD equation of state (EoS), the magnetic EoS, baryon number fluctuations confronted with recent experimental measurements, various critical exponents, spectral functions in the critical region, the dynamical critical exponent, etc, are presented. Recent estimates of the location of the CEP from first-principle QCD calculations within fRG and Dyson–Schwinger equations, which pass through lattice benchmark tests at small baryon chemical potentials, converge in a rather small region at baryon chemical potentials of about 600 MeV. A region of inhomogeneous instability indicated by a negative wave function renormalization is found with μ_B ≳ 420 MeV. It is found that the non-monotonic dependence of the kurtosis of the net-proton number distributions on the beam collision energy observed in experiments could arise from the increasingly sharp crossover in the regime of low collision energy.     

2+1维格点QCD真空波函数的计算

用改进的格点哈密顿量和截断本征方程法计算2+1维QCD真空波函数,结果显示出良好的标度行为.     

QCD phase diagram at finite isospin and baryon chemical potentials with the self-consistent mean field approximation

The self-consistent mean field approximation of the two-flavor NJL model,with a free parameter a to reflect the competition between the "direct" channel and the "exchange" channel,is employed to study the QCD phase structure at finite iso spin chemical potential μ_I,finite bary on chemical potential μ_B and finite temperature T,and especially to study the location of the QCD critical point.Our results show that in order to match the corresponding lattice results of iso spin density and energy density,the contributions of the "exchange" channel need to be considered in the framework of the NJL model,and a weighting factor α=0.5 should be taken.It is also found that for fixed isospin chemical potentials,the lower temperature of the phase transition is obtained with increasing a in the T-μ_I plane,and the largest difference of the phase transition temperature with different a's appears at μ_I~1.5 mπ.At μ_I=0 the temperature of the QCD critical end point(CEP) decreases with increasing a,while the critical baryon chemical potential increases.At high isospin chemical potential(μ_I=500 MeV),the temperature of the QCD tricritical point(TCP) increases with increasing a,and in the low temperature regions the system will transition from the pion superfluidity phase to the normal phase as μ_B increases.At low density,the critical temperature of the QCD phase transition with different a's rapidly increases with μ_I at the beginning,and then increases smoothly around μ_I 300 MeV.In the high baryon density region,the increase of the iso spin chemical potential will raise the critical baryon chemical potential of the phase transition.     

QCD thermodynamics with dynamical overlap fermions

We study QCD thermodynamics using two flavors of dynamical overlap fermions with quark masses corresponding to a pion mass of 350 MeV. We determine several observables on _Nt=6$N_t=6$ and 8 lattices. All our runs are performed with fixed global topology. Our results are compared with staggered ones and a nice agreement is found.     

QCD Phase Transitions and Bag Constants at Finite Chemical Potential

The global colour model at finite temperature is further extended to study the systems at finite chemical potential. The deconfinement and chiral phase transition at finite chemical potential and at temperature T = 0 K are studied simultaneously. Meanwhile the evolution of the bag constants at finite chemical potential is calculated. The dependences of results on the model parameters are discussed in detail     

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.     

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

In terms of the Nambu-Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple localgauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalarfields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential isgiven which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinementbehavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can bemelted away under high temperatures.     

Dynamical Model of QCD Vacuum and Color Thaw at Finite Temperatures

In terms of the Nambu Jona-Lasinio (NJL) mechanism, the dynamical symmetry breaking of a simple local gauge model is investigated. An important relation between the vacuum expectation value of gauge fields and scalar fields is derived by solving the Euler equation for the gauge fields. Based on this relation the SU(3) gauge potential is given which can be used to explain the asymptotic freedom and confinement of quarks in a hadron. The confinement behavior at finite temperatures is also investigated and it is shown that color confinement at zero temperature can be melted away under high temperatures.     

Calculation of Quark-Number Susceptibility at Finite Chemical Potential and Temperature

We use the direct method proposed by He et al. [Phys. Lett. B 680 （2009） 432） to calculate the quark-number susceptibility （QNS） at finite temperature and the chemical potential in the quasi-particle model. In our approach the QNS is given by a formula solely involving the dressed quark propagator at finite chemical potential μ and temperature Τ. The QNS at finite μ and Τ is calculated in the quasi-particle model. It is found that at high temperatures the QNS tends to the ideal quark gas result. At very small temperatures the QNS vanishes. This vanishing behavior in the low-temperature region is consistent with the lattice results. For μ∈ [0,180] MeV, our results show that there exists a rapid increase of QNS near some temperatures. The temperature at which the rapid increase occurs shifts to smaller values with the increasing quark chemical potential. This rapid increase could be regarded as a signal of a crossover.     

Lattice QCD Calculation of ππ Scattering Length

We study s-wave pion-pion scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV.In the "Asqtad" improved staggered fermion formulation,we measure full ππ four-point correlators for isospin I = 0 and 2 channels,and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results.Extrapolating to the physical pion mass yields scattering lengths as mπaI=2 0 = 0.041 6(2) and m π a I =0 0 = 0.186(2) for isospin I = 2 and 0 channels,respectively.Our lattice simulation for ππ scattering length in I = 0 channel is an exploratory study,where we include the disconnected contribution,and our preliminary result is near to its experimental value.These simulations are carried out with MILC 2 + 1 flavor gauge configurations at lattice spacing a ≈ 0.15 fm.     

Calculation of equation of state of QCD at zero temperature and finite chemical potential

In this paper we calculate the equation of state (EOS) of QCD at zero temperature and finite chemical potential by using several models of quark propagators including the Dyson-Schwinger equations (DSEs) model, the hard-dense-loop (HDL) approximation and the quasi-particle model. The results are analyzed and compared with the known results in the literature.     

On the QCD phase structure from effective models

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.     

Finite-size behavior near the critical point of QCD phase-transition

It is pointed out that the finite-size effect is not negligible in locating the critical point of quantum colordynamics (QCD) phase transitions at current relativistic heavy ion collisions. The finite-size scaling form of the critical related observable is suggested. Its fixed point behavior at critical incident energy can be served as a reliable identification of a critical point and nearby boundary of QCD phase transition. How to experimentally find the fixed point behavior is demonstrated by using 3D-Ising model as an example. The validity of the method at finite detector acceptances at RHIC is also discussed.     

Calculation of equation of state of QCD at zero temperature and finite chemical potential

In this paper we calculate the equation of state （EOS） of QCD at zero temperature and finite chemical potential by using several models of quark propagators including the Dyson-Schwinger equations （DSEs） model,the hard-dense-loop （HDL） approximation and the quasi-particle model.The results are analyzed and compared with the known results in the literature.     

The Strength of First and Second Order Phase Transitions from Partition Function Zeroes

We present a numerical technique employing the density of partition function zeroes (i) to distinguish between phase transitions of first and higher order, (ii) to examine the crossover between such phase transitions and (iii) to measure the strength of first and second order phase transitions in the form of latent heat and critical exponents. These techniques are demonstrated in applications to a number of models for which zeroes are available.     

Proof of factorization of fragmentation function in non-equilibrium QCD

In this paper, we prove factorization of fragmentation function in non-equilibrium QCD by using Schwinger-Keldysh closed-time path integral formalism. We use the background field method of QCD in a pure gauge in path integral approach to prove factorization of fragmentation function in non-equilibrium QCD. Our proof is valid in any arbitrary gauge fixing parameter α. This may be relevant to study hadron production from quark-gluon plasma at high energy heavy-ion colliders at RHIC and LHC.     

微扰QCD方法计算稀有衰变B+→D+s(-K)*0

在标准模型中,稀有衰变道B+→D+s(-K)*0只有通过纯湮没图才可以发生.这样这个衰变道的分支比很小.利用基于kT因子化的微扰方法给出分支比的预测,发现它在10-8的量级上.这个衰变道估计在将来的LHC上得到测量,对检验标准模型以及探寻新物理有着重要的意义.     

Quark Gluon Condensate, Virtuality and Susceptibility of QCD Vacuum

We study vacuum of QCD in this work. The structure of non-local quark vacuum condensate, values of various local quark and gluon vacuum condensates, quark-gluon mixed vacuum condensate, quark and gluon virtuality in QCD vacuum state, quark dynamical mass and susceptibility of QCD vacuum state to external field are predicted by use of the solutions of Dyson-Schwinger equations in ＂rainbow＂ approximation with a modeling gluon propagator and three different sets of quark-quark interaction parameters. Our theoretical predictions are in good agreement with the correspondent empirical values used widely in literature, and many other theoretical calculations. The quark propagator and self-energy functions are also obtained from the numerical solutions of Dyson Schwinger equations. This work is centrally important for studying non-perturbative QCD, and has many important applications both in particle and nuclear physics.