Fast dynamical evolution of a hadron resonance gas via Hagedorn states

Hagedorn states are the key to understanding how all hadrons observed in high-energy heavy-ion collisions seem to reach thermal equilibrium so quickly. An assembly of Hagedorn states is formed in elementary hadronic or heavy-ion collisions at hadronization. Microscopic simulations within the transport model UrQMD allow us to study the time evolution of such a pure nonequilibrated Hagedorn state gas to a thermally equilibrated hadron resonance gas by using dynamics, which unlike strings fully respect detailed balance. Propagation, repopulation, rescatterings, and decays of Hagedorn states provide the yields of all hadrons up to a mass of $m=2.5\mathrm{GeV}$. Ratios of feed-down-corrected hadron multiplicities are compared to corresponding experimental data from the ALICE Collaboration at LHC. The quick thermalization within $t=1–2\mathrm{fm}/c$ of the emerging hadron resonance gas exposes Hagedorn states as a tool to understand hadronization.

Figure 1

Mass distribution of HS in thermal equilibrium $\left(t=20\mathrm{fm}/c\right)$ for energy densities in the range $\epsilon =0.3–2.0\mathrm{GeV}/{\mathrm{fm}}^3$.

Figure 2

Fraction (a) of total multiplicities, energy, and mass occupied by HS in thermal equilibrium $\left(t\ge 5\mathrm{fm}/c\right)$ as function of energy density. Boltzmann slopes (temperatures) of hadrons (b) as function of energy density in thermal equilibrium $\left(t=20\mathrm{fm}/c\right)$. Red solid line denotes the Hagedorn temperature $T_H$.

Figure 3

Time evolution of total (feed-down-corrected) multiplicities (a) of ${\pi }^{+}, K^{+}, p$, and ${\mathrm{\Lambda }}^0$ at energy density $\epsilon =1.0\mathrm{GeV}/{\mathrm{fm}}^3$. Time evolution of feed-down contributions (b) from resonance decay (R) and from HS decays (HS) for same hadrons as mentioned above. In the case of HS direct multiplicities were considered.

Figure 4

Total multiplicity dependence on energy density of ${\pi }^{+}, K^{+}, p$, and ${\mathrm{\Lambda }}^0$ close to chemical equilibrium $\left(t=5\mathrm{fm}/c\right)$. In the case of HS dynamical multiplicities were considered.

Figure 5

Hadronic multiplicities from dynamical box simulation (ordinate) for $\epsilon =1.0\mathrm{GeV}/{\mathrm{fm}}^3\left(T\approx 0.154\mathrm{GeV}\right)$ at $t=20\mathrm{fm}/c$ and corresponding thermal model (abscissa) for $T=0.154\mathrm{GeV}$ and $V=1000{\mathrm{fm}}^3$. Statistical errors in simulations are for ${\mathrm{\Omega }}^{-}$ roughly $25\%$ and for others less than $5\%$.