Strangeness production in low energy heavy ion collisions via Hagedorn resonances

Background: Statistical models are successfully used to describe particle multiplicities in (ultra)relativistic heavy ion collisions. Transport models usually lack the ability to describe special aspects of the results of these experiments, as the fast equilibration and some multiplicity ratios.

Purpose: An alternative, unorthodox picture of the dynamics of heavy ion collisions is developed using the concept of Hagedorn states.

Method: A prescription of the bootstrap of Hagedorn states respecting the conserved quantum numbers baryon number $B$, strangeness $S$, isospin $I$ is implemented into the GiBUU transport model.

Results: Using a strangeness saturation suppression factor suitable for nucleon-nucleon collisions, recent experimental data for the strangeness production by the HADES collaboration in Au + Au and Ar + KCl is reasonably well described. The experimentally observed exponential slopes of the energy distributions are nicely reproduced.

Conclusions: A dynamical model using Hagedorn resonance states, supplemented by a strangeness saturation suppression factor, is able to explain essential features (multiplicities, exponential slope) of experimental data for strangeness production in nucleus-nucleus collisions close to threshold.

Figure 1

The energy density as function of the temperature for ${\mu }_B=0$ (red curves) and ${\mu }_B=0.85\mathrm{GeV}$ (blue curves) with vanishing net strangeness density. Solid curves show results including Hagedorn states, dashed curves a hadron gas only.

Figure 2

The mass distribution for vanishing baryochemical potential. The gray area shows the hadronic contribution, while the lines indicate the results for given $\epsilon$.

Figure 3

Same as Fig. 2, but for ${\mu }_B=0.85\mathrm{GeV}$.

Figure 4

The boundary $\epsilon =1\mathrm{GeV}{\mathrm{fm}}^{-3}$ in the $T-\mu$ plane. Also shown the freeze-out curve from Refs. [2, 34].

Figure 5

The averaged number of negative charged hadrons $h^{-},K$ mesons, and $\mathrm{\Lambda }$ baryons from a Hagedorn state $(B,S,I,(Q\left)\right)=(2,0,1,(2\left)\right)$ decay compared to experimental data from $p+p$ collisions as a function of $\sqrt{s}$ (data compilation, Refs. [36, 37]). The strangeness suppression is ${\gamma }_s=0.3$.

Figure 6

The mass distribution of hadrons and Hagedorn states at different time steps of the calculation for $\mathrm{Au}(1.23\mathrm{AGeV}$)Au (0–$40\%$) collisions. The maximal overlap of the nuclei is at $t=12.0\mathrm{fm}$.

Figure 7

The evolution of Hagedorn states (excluding known hadrons) with different baryon number $B$ for $\mathrm{Au}(1.23\mathrm{AGeV}$)Au (0–$40\%$) collisions. The maximal overlap of the nuclei is at $t=12.0\mathrm{fm}$. (The number of hadrons is too large to be visible in this plot.)

Figure 8

Comparison of calculated and measured multiplicities in $\mathrm{Au}(1.23\mathrm{AGeV}$)Au (0–$40\%$) [19, 42] and $\mathrm{Ar}(1.76\mathrm{AGeV}$)KCl (min. bias) [18]. The strangeness suppression is ${\gamma }_s=0.3$.

Figure 9

Comparison of calculated and measured multiplicities in $\mathrm{Au}(1.23\mathrm{AGeV}$)Au (0–$40\%$) [19, 42] and $\mathrm{Ar}(1.76\mathrm{AGeV}$)KCl (min. bias) [18]. GiBUU is used in its defaults; microcanonical prescription.

Figure 10

Transverse mass spectra at midrapidity for $\mathrm{Au}(1.23\mathrm{AGeV}$)Au (0–$40\%$). Symbols show experimental data [19, 42] (solid: midrap, open: next-to-midrap). The dotted curve shows the $K^{-}$ spectrum without $\varphi$ decays. Normalization of theoretical curves arbitrary.

Figure 11

Same as Fig. 10, but with GiBUU in its defaults. ($\varphi$ decay contribution to the $K^{-}$ spectrum not visible.)