Scaled variables and the quark-hadron duality
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Regular Article - Theoretical Physics
Scaled variables and the quark-hadron duality A. S. Parvan1,2,a 1 2
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia Department of Theoretical Physics, Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
Received: 21 February 2020 / Accepted: 18 July 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020 Communicated by Xin-Nian Wang
Abstract The thermodynamic quantities of the ideal gas of hadrons and the (2 + 1)-flavor lattice QCD scaled by the effective degeneracy factors of the corresponding models are compared. We have found that in terms of the scaled variables the quark-hadron duality of the lattice QCD and the hadron resonance gas (HRG) model disappears. However, we have revealed that the scaled variables lead to the quarkhadron duality of the lattice QCD and the quantum ideal gas of kaons and antikaons, namely, the ideal gas of those hadrons that contain all the three quarks u, d, s and their antiquarks. Satisfactory agreement between the scaled results of the kaon ideal gas and the lattice QCD data is achieved at large values of the volume in the entire temperature range. In the ideal gas of kaons there is no any phase transition. Nevertheless, in our calculations the scaled thermodynamic quantities of the ideal gas and the lattice QCD follow the same qualitative behavior and are consistent with each other especially at high temperatures in the perturbative region and the Stefan–Boltzmann limit.
1 Introduction Perturbative calculations of low-energy hadronic observables from quantum chromodynamics (QCD), the theory of strong interactions, are not possible due to the fact that QCD does not contain a small dimensionless coupling constant. Thus, the lattice QCD (LQCD) [1], which is one of the approaches of this theory, is used to proceed by defining QCD on a lattice of spacetime points, and then extrapolating observables to a continuum limit. In the LQCD calculations there is no any hadronic degree of freedom. This approach is formulated entirely in terms of quark and gluon fields. The main thermodynamic quantities, which are calculated in the framework of the LQCD, are pressure, energy density and entropy density. Their temperature and density dependence commonly suma e-mail:
marized as the equation of state (EoS) of quarks and gluons [2–8] provides the most basic description of the equilibrium thermodynamic properties of strong-interaction matter. The fastest growth of reduced energy density ε/T 4 with temperature in LQCD is interpreted as a phase transition from the hadronic phase to the state of quark-gluon plasma (QGP) [9]. Since LQCD theory does not contain hadronic degrees of freedom, the existence of the hadronic phase state is deduced indirectly from a comparison of the bulk thermodynamic quantities of LQCD with the results of other thermodynamic models, e.g. the hadron resonance gas (HRG) model [4,10–14]. Connection of ha
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