Fast Equilibration of Hadrons in an Expanding Fireball

Because of long chemical equilibration times for standard hadronic reactions in a hadron gas in relativistic heavy ion collisions, it was suggested that hadrons are born into equilibrium after the quark gluon plasma is formed. We develop a dynamical scheme, using master equations, in which Hagedorn states contribute to fast chemical equilibration times of baryons and kaons, just below the critical temperature, estimates of which are derived analytically. The hadrons quickly equilibrate for an initial over- or underpopulation of Hagedorn states. Our particle ratios compared to BNL Relativistic Heavy Ion Collider show a close match.

Figure 1

Comparison of the total equilibrium number of pions $N_{\pi }^{\mathrm{eq}}$, Hagedorn states $\sum _i{N}_i^{\mathrm{eq}}$, and effective pions ${\tilde{N}}_{\pi ,B\overline{B}}^{\mathrm{eq}}$ and ${\tilde{N}}_{\pi ,K\overline{K}}^{\mathrm{eq}}$ as defined in Eq. (6).

Figure 2

Numerical and analytical results in a static environment, i.e., fixed volume and temperature, at $T=180\mathrm{MeV}$ when ${\beta }_i=1.3$ and $\alpha =0.7$.

Figure 3

Same as Fig. 2 with no initial baryons ($\varphi =0$).

Figure 4

Results for an expanding fireball when $\alpha =1$, $\beta =1$, and $\varphi =0$. The effective number of baryons ${\tilde{N}}_{B\overline{B}}^{\mathrm{eq}}$, kaons ${\tilde{N}}_{K\overline{K}}^{\mathrm{eq}}$, and pions ${\tilde{N}}_{\pi ,B\overline{B}}^{\mathrm{eq}}$ and ${\tilde{N}}_{\pi ,K\overline{K}}^{\mathrm{eq}}$ are given.

Figure 5

Comparison of the ratios obtained employing the expanding fireball picture for various initial conditions to data at $\sqrt{s}=200\mathrm{GeV}$ from PHENIX [21] and STAR [22].