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Meson resonance gas in a relativistic quark model: scalar vs vector confinement and semishort range correlations

Smooth transitions from hadronic matter to hot and dense matter of quantum chromodynamics accompany continuous transformations in effective degrees of freedom. The microscopic descriptions should include relativistic quarks interacting inside of hadrons. In this work we construct a schematic constituent quark model with relativistic kinematics which captures the global trends of meson spectra in the light, strange, and charm quark sectors. We examine the roles of the scalar- and vector-confining potentials as well as semishort range correlations in estimating the strength of central, spin-spin, and spin-orbit interactions. The quark dynamics in low-lying mesons is very sensitive to relativistic kinematics and short range interactions, while in high-lying mesons are sensitive to the composition of scalar- and vector-confinement. After expressing mesons in terms of quark wave functions, we use them to describe the quark occupation probability in a meson resonance gas, and discuss how it can be related to its counterpart in a quark-gluon-plasma.