Repulsive interactions and their effects on the thermodynamics of a hadron gas

Abstract

We compare two approaches in modeling repulsive interactions among hadrons: the excluded volume approximation and the S-matrix formalism. These are applied to study the thermodynamics of the πN ∆ system. It is shown that the introduction of an extraneous repulsion between pions and nucleons via the excluded volume approach, in addition to the interaction that generates the ∆-resonance, is incompatible with the analysis based on the physical phase shift of pion-nucleon scattering in the P33 channel. This finding suggests that the repulsive force between hadrons is interaction-channel dependent and is hence unlikely to be captured by a single phenomenological parameter. The S-matrix approach employed here can be used, however, to provide useful estimates of the magnitude of the effective eigenvolume.

Balance of attractive and repulsive hadronic interactions: The influence of hadronic spectrum and excluded-volume effects on lattice thermodynamics, and consequences for experiments

“…In addition we show a systematic study of repulsive interactions modelled by means of Excluded-Volume (EV) effects, in which we explore the specific effective hard-core sizes of hadrons depending on mass and quark content, allowing for example to a distinct behaviour between light and strange sectors. The use of EV effects can be justified through the S-matrix approach, which correctly includes repulsive channels via experimentally measured phase shifts and gives results compatible with the hard-core approach [12]. Using NN phase shifts, it has recently been shown how observables calculated on the lattice which are usually interpreted as a signal for deconfinement are indeed strictly connected to repulsive hadronic interactions [13].…”

Thermal properties of S = − 1 Hyperons: an S-matrix approach

“…the phase shift is known), model parameters (e.g. couplings, masses, etc) need to be adjusted to reproduce the known phase shift for consistency [17,18]. This is automatically fulfilled by the S-matrix approach as the empirical data is used as input.…”

Overlap between Lattice QCD and HRG with in-medium effects and parity doubling

“…Nevertheless, our results do not rule out the manifestation of parity doublers. Several studies [19,20] have revealed that the conventional treatment of the particles in the HRG is not sufficient and a proper inclusion of the width improves the thermodynamics. Although those analysis have been limited to the S −matrix approaches where interactions are incorporated via the two-body scattering phase shift in the vacuum, a consistent treatment of the resonance widths at finite temperature and densities should clarify the consequences of the partial restoration of the chiral symmetry in the baryonic sector of correlations and fluctuations.…”

“…Then, the partition function of the interacting hadronic system can be written as a mixture of free gases of all stable and resonant hadrons [18]. The validity of the vanishing-width approximation for the fluctuations has been recently examined based on the S-matrix formalism for K-π [19] and π-N-∆ [20] systems. It has been found that an explicit treatment of the width can have a substantial effect on the fluctuations.…”

“…Particularly interesting quantities are those involving net-baryon number, baryon-charge (BQ) and baryon-strangeness (BS) correlations. Since mesons do not contribute to these quantities, one may gain access to a role of baryonic degrees of freedom and interactions which are not visible in the equation of state and other meson-dominated quantities due to their heavy masses [17].…”