Hadron liquid with a small baryon chemical potential at finite temperature Original Research Article

We discuss general properties of a system of heavy fermions (including antiparticles) interacting with rather light bosons. First, we consider one diagram of Φ. The fermion chemical potential is assumed to be small, μf≲T. Already for the low temperature, T≪min(Tbl.f,mb), the fermion mass shell proves to be partially blurred due to multiple fermion rescatterings on virtual bosons, mb is the boson mass, View the MathML source is the typical temperature corresponding to a complete blurring of the gap between fermion–antifermion continua, mf is the fermion mass. As the result, the ratio of the number of fermion–antifermion pairs to the number provided by the ordinary Boltzmann distribution becomes larger than unity (RN>1). For View the MathML source (hot hadron liquid, blurred boson continuum), View the MathML source is the effective boson mass, the abundance of all particles dramatically increases. Bosons behave as quasi-static impurities, on which heavy fermions undergo multiple rescatterings. The soft thermal loop approximation solves the problem. The effective fermion mass View the MathML source decreases with the temperature increase. For T≳Tbl.f fermions are essentially relativistic particles. Due to the interaction of the boson with fermion–antifermion pairs, View the MathML source decreases leading to the possibility of the “hot Bose condensation” for T>Tcb. The phase transition might be of the second order or of the first order depending on the species under consideration. We study in detail properties of the system of spin View the MathML source heavy fermions interacting with substantially lighter scalar neutral bosons (e.g., Nσ system). Correlation effects of higher order diagrams of Φ are evaluated resulting in a suppression of vertices for View the MathML source. The abundance of high-lying baryon resonances proves to be of the same order, as the nucleon–antinucleon abundance, or might be even higher for some species. Further we discuss the system of heavy fermions interacting with more light vector bosons (e.g., Nω and Nρ) and then, with pseudo-scalar bosons (e.g., Nπ). For the fermion–vector boson system correlation effects are incorporated by keeping the Ward identity. In case of the fermion–pseudo-scalar boson system correlation effects are rather small. Finally, we allow for all interactions. We estimate RN∼1.5 for T∼mπ/2; Tbl.f proves to be near Tcb; both values are in the vicinity of the pion mass mπ.