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In this contribution we present results from Au+Au collisions at √SNN = 2.42 GeV as well as Ag+Ag collisions at √SNN = 2.42 and 2.55 GeV measured by HADES. We focus on three different observables: electromagnetic probes, collective and bulk-matter phenomena and strangeness production which are discussed in the following.

I review recent theory progress reported at the 19th International Conference on Strangeness in Quark Matter (SQM), and discuss open questions to be addressed by the coming editions of SQM.

Strangness production processes can balance natural strangeness decay in the early hadronic Universe. Comparing to the characteristic Hubble time 1/ H , the reaction rates for μ ± + ν μ → K ± , l − + l + → ϕ, and π+π → K in sequence become slower than expansion rate at T = 33.9 MeV, T = 25MeV and T = 20MeV respectively. This means that in the antibaryon annihilation epoch near to T ≃ 40MeV strangeness is in chemical equilibrium.

Prominent phenomena observed in high-energy hadronic collisions, such as the strangeness enhancement in small collision systems with increasing multiplicity and the production of loosely bound states in collisions where extreme temperatures are reached, are still mysterious and at the center of the experimental programs of several scientific Collaborations. In this contribution, recent experimental results from the ALICE and STAR Collaborations on these two fronts are presented and discussed.

Recent LHCb data for B− → J/ψΛp¯ show a clear peak structure at the ΞcD¯ threshold in the J/ψ invariant mass (MJ/ψΛ) distribution. In their amplitude analysis, LHCb identified the peak with the first hidden-charm pentaquark with strangeness PψsΛ(4338). We conduct a coupled-channel amplitude analysis of the LHCb data by simultaneously fitting the MJ/ψΛ,MJ/ψp¯,MΛp¯, and cosθK* distributions. Rather than the Breit-Wigner fit employed in the LHCb analysis, we consider relevant threshold effects and a unitary ΞcD¯ − ΛcD¯s coupled-channel scattering amplitude from which PψsΛ poles are extracted for the first time. In our default fit, the PψsΛ(4338) pole is almost a ΞcD¯ bound state at (4338:2±1:4)−(1:9±0:5) i MeV. Our default model also fits a large fluctuation at the ΛcD¯s threshold, giving a ΛcD¯s virtual state, PψsΛ(4255), at 4254:7±0:4 MeV. We also found that the PψsΛ(4338) peak cannot solely be a kinematical effect, and a nearby pole is needed.

We investigate baryon-baryon (BB) interactions in the strangeness S = −2 sector via the coupled-channel HAL QCD method which enables us to extract the scattering observables from Nambu-Bethe-Salpeter (NBS) wave function on the lattice. The simulations are performed with (almost) physical quark masses (m π = 146MeV) and a huge lattice volume of La = 8.1fm. We discuss the fate of H-dibaryon state through the ΛΛ and NΞ coupled-channel scatterings

High-energy cosmic rays are observed indirectly by detecting the extensive air showers initiated in Earth’s atmosphere. The interpretation of these observations relies on accurate models of air shower physics, which is a challenge and an opportunity to test QCD under extreme conditions. Air showers are hadronic cascades, which give rise to a muon component through hadron decays. The muon number is a key observable to infer the mass composition of cosmic rays. Air shower simulations with state-of-the-art QCD models show a significant muon deficit with respect to measurements; this is called the Muon Puzzle. By eliminating other possibilities, we conclude that the most plausible cause for the muon discrepancy is a deviation in the composition of secondary particles produced in high-energy hadronic interactions from current model predictions. The muon discrepancy starts at the TeV scale, which suggests that this deviation is observable at the Large Hadron Collider. An enhancement of strangeness production has been observed at the LHC in high-density events, which can potentially explain the puzzle, but the impact of the effect on forward produced hadrons needs further study, in particular with future data from oxygen beam collisions.

The production of Ξ(1321)- and Ξ¯(1321)+ hyperons in inelastic p+p interactions is studied in a fixed target experiment at a beam momentum of 158 Ge/c. Double differential distributions in rapidity y and transverse momentum pT are obtained from a sample of 33M inelastic events. They allow to extrapolate the spectra to full phase space and to determine the mean multiplicity of both Ξ- and Ξ¯+. The rapidity and transverse momentum spectra are compared to transport model predictions. The Ξ- mean multiplicity in inelastic p+p interactions at 158 Ge/c is used to quantify the strangeness enhancement in A+A collisions at the same centre-of-mass energy per nucleon pair.

In these proceedings, we present the measurements of charged K+ − K+ and neutral KS0, - KS0 correlation functions from Au+Au fixed-target collisions at √sNN = 3.0, 3.2, 3.5, 3.9 and 4.5 GeV at STAR. This is the first such systematic measurement of correlation functions involving strangeness in the high baryon density region. The source size values do not exhibit a clear energy dependence, and the transverse mass dependence of source size for kaons does not align with the trend observed for pions. Parameters extracted from UrQMD transport model calculations qualitatively capture the measured values.

Strangeness production has been suggested as a sensitive probe to the early dynamics of the deconfined matter created in heavy-ion collisions. In this presentation, we report new measurements of strange hadron (Ks0, Λ ¯Λ, Ξ, ¯Ξ, ϕ) production in Au+Au collisions at √SNN = 14.6, 19.6 GeV from STAR BESII and Ω(¯Ω) production in Au+Au collisions at √SNN = 200 GeV, including rapidity spectra, nuclear modification factors RCP and Ω-to-ϕ ratios. Benefiting from the iTPC upgrade, the strangeness measurements are now extended from mid-rapidity (|y| < 0.5, BES-I) to a larger rapidity range (|y| < 1.0).