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Register a new userQuark cluster expansion model for interpreting finite-T lattice QCD thermodynamics
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We present a unified approach to the thermodynamics of hadron-quark-gluon matter at finite temperatures on the basis of a quark cluster expansion in the form of a generalized Beth-Uhlenbeck approach with a generic ansatz for the hadronic phase shifts that fulfills the Levinson theorem. The change in the composition of the system from a hadron resonance gas to a quark-gluon plasma takes place in the narrow temperature interval of $150 - 185$ MeV where the Mott dissociation of hadrons is triggered by the dropping quark mass as a result of the restoration of chiral symmetry. The deconfinement of quark and gluon degrees of freedom is regulated by the Polyakov loop variable that signals the breaking of the $Z(3)$ center symmetry of the color $SU(3)$ group of QCD. We suggest a Polyakov-loop quark-gluon plasma model with $mathcal{O}(alpha_s)$ virial correction and solve the stationarity condition of the thermodynamic potential (gap equation) for the Polyakov loop. The resulting pressure is in excellent agreement with lattice QCD simulations up to high temperatures.
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Over the past few years new physics methods and algorithms as well as the latest supercomputers have enabled the study of the QCD thermodynamic phase transition using lattice gauge theory numerical simulations with unprecedented control over systematic errors. This is largely a consequence of the ability to perform continuum extrapolations with physical quark masses. Here we review recent progress in lattice QCD thermodynamics, focussing mainly on results that benefit from the use of physical quark masses: the crossover temperature, the equation of state, and fluctuations of the quark number susceptibilities. In addition, we place a special emphasis on calculations that are directly relevant to the study of relativistic heavy ion collisions at RHIC and the LHC.
The QCD equation of state at finite baryon density is studied in the framework of a Cluster Expansion Model (CEM), which is based on the fugacity expansion of the net baryon density. The CEM uses the two leading Fourier coefficients, obtained from lattice simulations at imaginary $mu_B$, as the only model input and permits a closed analytic form. Excellent description of the available lattice data at both $mu_B = 0$ and at imaginary $mu_B$ is obtained. We also demonstrate how the Fourier coefficients can be reconstructed from baryon number susceptibilities.
Taylor expansion of the equation of state of QCD suffers from shortcomings at chemical potentials $mu_B geq (2-2.5)T$. First, one faces difficulties inherent in performing such an expansion with a limited number of coefficients; second, higher order coefficients determined from lattice calculations suffer from a poor signal-to-noise ratio. In this work, we present a novel scheme for extrapolating the equation of state of QCD to finite, real chemical potential that can extend its reach further than previous methods. We present continuum extrapolated lattice results for the new expansion coefficients and show the thermodynamic observables up to $mu_B/Tle3.5$.
We compute the coefficients of the effective mass operator of the 1/Nc expansion for negative parity L=1 excited baryons using the Isgur-Karl model in order to compare the general approach, where the coefficients are obtained by fitting to data, with a specific constituent quark model calculation. We discuss the physics behind the fitted coefficients for the scalar part of the most general two-body quark-quark interaction. We find that both pion exchange and gluon exchange lead to the dominance of the same operator at the level of the effective mass operator, which is also observed from data.
Since the incident nuclei in heavy-ion collisions do not carry strangeness, the global net strangeness of the detected hadrons has to vanish. We investigate the impact of strangeness neutrality on the phase structure and thermodynamics of QCD at finite baryon and strangeness chemical potential. To this end, we study the low-energy sector of QCD within a Polyakov loop enhanced quark-meson effective theory with 2+1 dynamical quark flavors. Non-perturbative quantum, thermal, and density fluctuations are taken into account with the functional renormalization group. We show that the impact of strangeness neutrality on thermodynamic quantities such as the equation of state is sizable.
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