No abstract

Motivated by recent lattice QCD studies, we explore the effects of interactions on strangeness fluctuations in strongly interacting matter at finite temperature. We focus on S-wave Kπ scattering and discuss the role of the K * 0 (800) and K * (1430) resonances within the S-matrix formulation of thermodynamics. Using the empirical Kπ phase shifts as input, we find that the Kπ S-wave interactions provide part of the missing contribution to the strangeness susceptibility. Moreover, it is shown that the simplified treatment of the interactions in this channel, employed in the hadron resonance gas approach, leads to a systematic overestimate of the strangeness fluctuations. In particular, the HRG results for the strangeness and mixed strangeness-baryon number susceptibilities (χ SS and χ BS ) are clearly below those of the lattice, while the results for the thermodynamic pressure and the baryon number susceptibility are in good agreement.This motivates the search for hitherto unknown strange hadrons, which could reduce or eliminate this discrepancy. In the PDG database, there are around twenty unconfirmed states with a mass below 2.0 GeV. Although these are not established resonances, the interactions in the corresponding scattering channels may yield important contribution to thermodynamic quantities.More generally, a possible origin of the discrepancy is interaction strength in channels carrying net strangeness that so far have not been accounted for. Given the corresponding empirical scattering phase shifts, both confirmed and unconfirmed resonances as well as nonresonant interactions can be handled in a unified, modelindependent way, using the S-matrix approach of Ref. [3].The strange scalar channel, with the unconfirmed K * 0 (800) resonance, a.k.a. κ, is a prime candidate. Since the corresponding phase shifts for S-wave Kπ scattering are fairly well determined, this channel is well suited for the S-matrix approach. In addition, the counterpart of κ in the scalar-isoscalar channel, the f 0 (500), a.k.a. σ, though considered to be established [4], is unlike a typical resonance. Since the ππ S-wave phase shifts are known with reasonable accuracy, also this channel is a prime candidate for the S-matrix approach to thermodynamics. In this study we focus on the strange scalar channel and its contribution to strangeness susceptibilities.With the relatively low mass of the interaction strength in the κ channel, it potentially has a large impact on the thermodynamics, in particular on χ SS , owing to the moderate suppression by the Boltzmann factor. In Fig. 1, we illustrate the effect of the κ resonance on pressure and strangeness fluctuation within the HRG approach. For the PDG particle spectrum, we use only confirmed baryons (i.e. three and four star resonances) and established mesons. The contribution of κ to the thermodynamics is approximated by that of an ideal gas of zero-width mesons with mass m κ = 0.682 GeV and degeneracy four. Indeed, the inclusion of this single state improves the HRG result on χ SS dramatica...

We study the mean-field thermodynamics and the characteristics of the net-baryon number fluctuations at the phase boundaries for the chiral and deconfinement transitions in the Hybrid Quark-Meson-Nucleon model. The chiral dynamics is described in the linear sigma model, whereas the quark confinement is manipulated by a medium-dependent modification of the particle distribution functions, where an additional scalar field is introduced. At low temperature and finite baryon density, the model predicts a first-, second-order chiral phase transition, or a crossover, depending on the expectation value of the scalar field, and a first-order deconfinement phase transition. We focus on the influence of the confinement over higher-order cumulants of the net-baryon number density. We find that the cumulants show a substantial enhancement around the chiral phase transition, they are not as sensitive to the deconfinement transition.

Based on recent lattice QCD (LQCD) results obtained at finite temperature, we discuss modeling of the hadronic phase of QCD in the framework of hadron resonance gas (HRG) with discrete and continuous mass spectra. We focus on fluctuations of conserved charges, and show how a common limiting temperature can be used to constrain the Hagedorn exponential mass spectrum in different sectors of quantum number, through a matching of HRG and LQCD. For strange baryons, the extracted spectra are found to be consistent with all known and expected states listed by the Particle Data Group (PDG). The strange-mesonic sector, however, requires additional states in the intermediate mass range beyond that embodied in the database.

The influence of the finite width of ρ meson on the pion momentum distribution is studied quantitatively in the framework of the S-matrix approach combined with a blast-wave model to describe particle emissions from an expanding fireball. We find that the proper treatment of resonances which accounts for their production dynamics encoded in data for partial wave scattering amplitudes can substantially modify spectra of daughter particles originating in their two body decays. In particular, it results in an enhancement of the low-pT pions from the decays of ρ mesons which improves the quantitative description of the pion spectra in heavy ion collisions obtained by the ALICE collaboration at the LHC energy. Recent measurements of the transverse momentum, p T -distributions of identified particles produced in √ s N N = 2.76 TeV Pb+Pb collisions at CERN Large Hadron Collider (LHC) [1] revealed an excess of lowmomentum (p T < ∼ 0.3 GeV) pions over the conventional fluid-dynamical calculations [1-3].It is well known that pions originating from decays of resonances have a steeper p T -distribution than the thermal pions [4], and that they provide a dominant contribution to the spectrum at low transverse momentum. Thus, resonance decays require a particular attention when modeling spectra of particles originating from an expanding thermal fireball.In fluid-dynamical calculations, the interacting hadrons are usually described by the hadron resonance gas (HRG), where the system is modeled as a gas of free hadrons with resonances considered as particles with vanishing widths.This approximation yields reasonable description of the bulk properties of the hadronic medium [5][6][7][8]. The HRG model also provides a very satisfactory description of particle yields measured in heavy ion collisions [9][10][11][12][13][14][15][16][17], as well as the hadronic equation of state and some fluctuation observables obtained in lattice QCD (LQCD) [18][19][20][21][22]. However, as we show in this letter, when p T -differential observables are involved, a more refined approach may be necessary.To properly address the dynamics of hadrons, the effect of resonance width must be included. A conventional way is to impose a Breit-Wigner distribution on the resonance mass. Unfortunately, this approach proves to be too crude in many circumstances. For example, for a broad resonance like the σ meson [23], or the (yet-to-beconfirmed) κ meson [24], the Breit-Wigner approach can give misleading results on the resonance contribution to the thermodynamics.We thus take a more fundamental approach to evaluate the properties of interacting hadrons based on the S-matrix formulation of Dashen, Ma and Bernstein [25]. For elastic scatterings, the interaction part of the partition function reduces to the Beth-Uhlenbeck form for the second virial coefficient, expressed in terms of the scattering phase shifts [26]. In the context of heavy-ion physics, this approach has been applied to evaluate the contribution of πN [5,7,27], ππ [5,23], and πK interactions [5,24] ...

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.

We extend the recently developed hybrid quark-meson-nucleon model by augmenting a six-point scalar interaction and investigate the consequences for neutron-star sequences in the mass-radius diagram. The model has the characteristic feature that, at increasing baryon density, the chiral symmetry is restored within the hadronic phase by lifting the mass splitting between chiral partner states (parity doubling), before quark deconfinement takes place. At low temperature and finite baryon density, the model predicts a first-, second-order chiral phase transition, or a crossover, depending on the expectation value of the scalar field, and a first-order deconfinement phase transition. We discuss two sets of free parameters, which result in compact-star mass-radius relations that are at tension with the combined constraints for maximum-mass (2 M ) and the compactness (GW170817). We find that the most preferable mass-radius relations result in isospin-symmetric phase diagram with rather low temperature for the critical point of the chiral phase transition.

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.