Strangeness fluctuations fromK−πinteractions

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...

Excluded-volume effects for a hadron gas in Yang-Mills theory

“…Even though this could seem unjustified, it is presently not clear how higher-mass resonances in a certain channel would interact, as compared with the ground state; in general, there is the possibility that they may have a smaller cross section, which would be encoded in a smaller effective radius. This could be particularly relevant for a correct inclusion of exotic resonances, for which the repulsive channels are known to be as relevant as the attractive ones [50]. In the case of mass-dependent eigenvolumes, we label the parametrization in terms of the radius of the ground-state J P ¼ 0 þ particle, in order to have an immediate comparison to the fixed-radius scenario.…”

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.…”

Flavor Correlations and the QCD Phase Structure

“…However, owing to the large width of the κ meson and the significant non-resonant background, the HRG model does not provide an accurate description of the interaction contributions. In fact, a consistent treatment of all Kπ S-wave interactions within the S-matrix approach shows that a simplified (HRG) treatment of the interactions The strange susceptibility (left) [26] and the p T spectrum of ρ 0 in thermal equilibrium (T = 155 MeV) and the daughter π + originating from ρ 0 → π + π − decay (right) [27].…”

“…In Ref. [26], we focus on the strange scalar channel and its contribution to strangeness susceptibilities.…”