Strangeness balance in HADES experiments and the ${\Xi }^{-}$ enhancement

The High Acceptance Di-Electron Spectrometer (HADES) data on strangeness production in Ar + KCl collisions at 1.76$A$ GeV are analyzed within a minimal statistical model. In the model the total negative strangeness content is fixed by the observed $K^{+}$ multiplicities. Particles with negative strangeness are assumed to remain in chemical equilibrium with themselves and in thermal equilibrium with the environment until a common freeze-out. Exact strangeness conservation in each collision event is explicitly preserved. This implies that $\Xi$ baryons can be released only in events where two or more kaons are produced. An increase of the fireball volume due to application of a centrality trigger in HADES experiments is taken into account. We find that experimental ratios of $K^{-}/K^{+}$, $\Lambda /K^{+}$, and $\Sigma /K^{+}$ can be satisfactorily described provided in-medium potentials are taken into account. However, the calculated ${\Xi }^{-}/\Lambda /K^{+}$ ratio proves to be significantly smaller compared to the measured value (eight times less than the experimental median value and three times less than the lower error bar). Various scenarios to explain observed $\Xi$ enhancement are discussed. Arguments are given in favor of the $\Xi$ production in direct reactions. The rates of the possible production processes are estimated and compared.

Figure 1

The ratios (51), (53), (54), and (56) as functions of the freeze-out temperature for the freeze-out density $0.6{\rho }_0$ in comparison with the empirical ratios (7) shown by dotted lines. The shaded regions are the experimental error intervals. Dashed curves are calculated in the absence of in-medium potentials, whereas solid lines are calculated with the scalar and vector potentials. For the $K^{-}/K^{+}$ ratio, solid lines labeled as 75 and 150 are computed with $U_{\overline{K}}=-75$ and $-150$ MeV, respectively. For the ratios involving hyperons, solid lines are calculated for $U_{\overline{K}}=-75$ MeV. Dash-double-dotted lines depict ratios with only nucleon potentials included. On the $\Sigma /K^{+}$ plot, two dotted lines show the central values given in Eqs. (7c) and (8) labeled as “(Hades)” and “(iso)” respectively.

Figure 2

Ratio (75) plotted as function of the $\Xi$ baryon freeze-out temperature $T_{\mathrm{fo}}^{\left(\Xi \right)}$. The corresponding $\Xi$ baryon freeze-out density is calculated according to the polytropic relation ${\rho }_{B,\mathrm{fo}}^{\left(\Xi \right)}\propto T_{\mathrm{fo}}^{\left(\Xi \right)\alpha }$; see text for details. Two curves are drawn for assumed values of the maximal temperature and density.

Figure 3

Mass spectrum (energy $E$) of strangeness–2 states with baryon numbers 0, 1, and 2 counted from the nonstrange ground states with the energy $E_0$ (shown on top of the figure).