Chiral phase transitions in quantum chromodynamics at finite temperature: Hard-thermal-loop resummed Dyson-Schwinger equation in the real time formalism

Chiral phase transition in thermal QCD is studied by using the Dyson-Schwinger (DS) equation in the real time hard thermal loop approximation. Our results on the critical temperature and the critical coupling are significantly different from those in the preceding analyses in the ladder DS equation, showing the importance of properly taking into account the essential thermal effects, namely the Landau damping and the unstable nature of thermal quasiparticles.     

A survey of lattice results on finite temperature quantum chromodynamics

The talk summarizes some new results of lattice investigations of QCD at finite temperature. The topics discussed cover the flavor dependence of the critical temperature and the equation-of-state as well as hadronic correlation functions.     

带有2+1味道Wilson费米子的格点量子色动力学在有限温度、有限密度下的相变

利用格点规范理论研究了带有2＋1味道费米子的量子色动力学在有限密度及温度下的相变问题,研究了去禁闭相变与化学势和裸质量参数之间的依赖关系,并利用有限体积效应分析以及Monte Carlo模拟的演化序列所反映出的特点对相变的类型做了确认,给出了相结构图. 关键词： 格点量子色动力学 相变     

First and second order phase transitions in gauge theories at finite temperature

We consider in general the nature of the phase transition which occurs in 4D gauge theories coupled to scalar and spinor fields at finite temperature. It is shown that the critical behavior can be isolated in an effective 3D theory of the zero frequency mode whose lagrangian may be calculated explicitly in weak coupling perturbation theory. This lagrangian, in turn, may be investigated by means of standard ?-expansion techniques. Theories with an asymptotically free gauge coupling constant possess no stable fixed point in the ?-expansion and are inferred to have weakly first-order phase transitions; theories not satisfying this condition may have second-order transitions.     

Net-proton measurements at RHIC and the quantum chromodynamics phase diagram

Two measurements related to the proton and antiproton production near midrapidity in \(\sqrt {s_{{NN}}} = 7.7\) , 11.5, 19.6, 27, 39, 62.4 and 200 GeV Au+Au collisions using the STAR detector at the Relativistic Heavy Ion Collider (RHIC) are discussed. At intermediate impact parameters, the net-proton midrapidity dv ₁/dy, where v ₁ and y are directed flow and rapidity, respectively, shows non-monotonic variation as a function of beam energy. This non-monotonic variation is characterized by the presence of a minimum in dv ₁/dy between \(\sqrt {s_{NN}} = 11.5\) and 19.6 GeV and a change in the sign of dv ₁/dy twice between \(\sqrt {s_{{NN}}}\) = 7.7 and 39 GeV. At small impact parameters the product of the moments of net-proton distribution, kurtosis × variance (κ σ ²) and skewness × standard deviation (S σ) are observed to be significantly below the corresponding measurements at large impact parameter collisions for \(\sqrt {s_{{NN}}}\) = 19.6 and 27 GeV. The κ σ ² and S σ values at these beam energies deviate from the expectations from Poisson statistics and that from a hadron resonance gas model. Both these measurements have implications towards understanding the quantum chromodynamics (QCD) phase structures, the first-order phase transition and the critical point in the high baryonic chemical potential region of the phase diagram.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

The quark-nucleon phase diagram and quantum chromodynamics

The temperature dependence of a conjectured first-order phase transition between nuclear matter and quark-gluon matter is calculated for temperatures below T = 200 MeV. On the nuclear side a rather successful meson-nucleon mean field theory is applied while quark-gluon matter at large densities and finite temperatures is described perturbatively by quantum chromodynamics. Outside the finite volume of hot and dense quark-gluon matter the physical vacuum is characterized, by the newly determined bag parameter Λ_B = 235 MeV. We observe a dramatic drop in the density of nuclear matter at the phase transition point as the temperature increases, if the scale parameter Λ of QCD is chosen as Λ = 100 MeV. For larger values of Λ the effect is less pronounced. Further work is required to settle this problem.     

Nonperturbative approach to chiral phase transition in chromodynamics

A nonperturbative approach aimed at the localization of the QCD chiral phase transition atT, π≠0 is presented. We identify this transition with the dynamical quark mass peculiarity which results from the selfconsistent solution of the Schwinger-Dyson equation for the quark propagator. The specific model of the effective quark-gluon interaction, based both on the peculier interpolation for the running coupling constant and on the nonperturbative gluon magnetic and electric masses is exploited. The numerical estimates of the phase diagram are presented and it is shown that phase peculiarities are determined not only by the ultraviolet properties of QCD but also by its infrared structure. The obtained results are discussed, compared with other approaches and a possible interpretation is given.     

Light quark masses in quantum chromodynamics and chiral symmetry breaking

We derive model independent lower bounds for the sums of effective quark masses \(\bar m_u + \bar m_d \) and \(\bar m_u + \bar m_s \) . The bounds follow from the combination of the spectral representation properties of the hadronic axial currents two-point functions and their behavior in the deep euclidean region (known from a perturbative QCD calculation to two loops and the leading non-perturbative contribution). The bounds incorporate PCAC in the Nambu-Goldstone version. If we define the invariant masses \(\hat m\) by $$\bar m_i = \hat m_i \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^{{{\gamma _1 } \mathord{\left/ {\vphantom {{\gamma _1 } {\beta _1 }}} \right. \kern-\nulldelimiterspace} {\beta _1 }}} $$ and <F ²> is the vacuum expectation value of $$F^2 = \Sigma _a F_{(a)}^{\mu v} F_{\mu v(a)} $$ , we find, e.g., $$\hat m_u + \hat m_d \geqq \sqrt {\frac{{2\pi }}{3} \cdot \frac{{8f_\pi m_\pi ^2 }}{{3\left\langle {\alpha _s F^2 } \right\rangle ^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} }}} $$ ; with the value <α _u F ²?0.04GeV⁴, recently suggested by various analysis, this gives $$\hat m_u + \hat m_d \geqq 35MeV$$ . The corresponding bounds on \(\bar m_u + \bar m_s \) are obtained replacingm _π ² f _π bym _K ² f _K . The PCAC relation can be inverted, and we get upper bounds on the spontaneous masses, \(\hat \mu \) : $$\hat \mu \leqq 170MeV$$ where \(\hat \mu \) is defined by $$\left\langle {\bar \psi \psi } \right\rangle \left( {Q^2 } \right) = \left( {{{\frac{1}{2}\log Q^2 } \mathord{\left/ {\vphantom {{\frac{1}{2}\log Q^2 } {\Lambda ^2 }}} \right. \kern-\nulldelimiterspace} {\Lambda ^2 }}} \right)^d \hat \mu ^3 ,d = {{12} \mathord{\left/ {\vphantom {{12} {\left( {33 - 2n_f } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {33 - 2n_f } \right)}}$$ .     

Infrared chiral anomaly at finite temperature

We study the Schwinger model at finite temperature and show that a temperature dependent chiral anomaly may arise from the long distance behavior of the electric field. At high temperature this anomaly depends linearly on the temperature T and is present not only in the two point function, but also in all even point amplitudes.     

Thermodynamics and bulk viscosity of approximate black hole duals to finite temperature quantum chromodynamics

We consider classes of translationally invariant black hole solutions whose equations of state closely resemble that of QCD at zero chemical potential. We use these backgrounds to compute the ratio zeta/s of bulk viscosity to entropy density. For a class of black holes that exhibits a first-order transition, we observe a sharp rise in zeta/s near Tc. For constructions that exhibit a smooth crossover, like QCD does, the rise in zeta/s is more modest. We conjecture that divergences in zeta/s for black hole horizons are related to extrema of the entropy density as a function of temperature.     

Chiral and deconfinement phase transitions of two-flavour QCD at finite temperature and chemical potential

We present results for the chiral and deconfinement transition of two flavor QCD at finite temperature and chemical potential. To this end we study the quark condensate and its dual, the dressed Polyakov loop, with functional methods using a set of Dyson-Schwinger equations. The quark propagator is determined self-consistently within a truncation scheme including temperature and in-medium effects of the gluon propagator. For the chiral transition we find a crossover turning into a first order transition at a critical endpoint at large quark chemical potential, μEP/TEP≈3. For the deconfinement transition we find a pseudo-critical temperature above the chiral transition in the crossover region but coinciding transition temperatures close to the critical endpoint.     

The deconfining phase transition in lattice quantum chromodynamics

We present a large-scale Monte Carlo calculation of the deconfining phase transition temperature in lattice quantum chromodynamics without fermions. Using the Wilson action, the transition temperature as a function of the lattice couplingg is consistent with scaling behavior dictated by the perturbativeα function for 6/g²>6.15. Speaker at the conference; on leave from CRIP, Budapest.     

Sign-posting the phase diagram of quantum chromodynamics

The good agreement between lattice predictions and data for the shape of the distribution of event-by-event fluctuations of the baryon number is discussed. Such comparisons can give fine probes of thermalization, and can be used to provide a direct determination of the cross-over temperature T _c of QCD. The logic of these comparisons and the systematics involved are discussed. The same methods can be used to further explore the phase diagram.     

Bag-model quantum chromodynamics at low energy

Gluon-exchange mediating quark-exchange scattering is the mechanism of lowest order in perturbative QCD that contributes to the strong interactions at low energy. When it is dressed with long-range quark-gluon correlations by means of bag-model wavefunctions, this quark interchange force becomes bilocal in the quark-gluon sector involving the whole bag and non-perturbative. When it is Fierz-rearranged, the quark-interchange amplitude takes on the usual local form for each hadron that is expected from the wealth of empirical knowledge at low energy. This quark interchange is calculated here in the MIT bag model, which is supplemented by tunneling rules, and then applied to elastic NN scattering, and subsequently toπN andππ scattering. For each reaction the OBE interaction is obtained in agreement with meson theoretic models. Repulsive axial-vector meson exchanges are predicted for NN scattering at short range. The chiral structure of the quark interchange force in conjunction with its tunneling aspects suggest an interpretation of the strong interactions at low energy as Josephson currents of non-Abelian superconductivity.