Thermalization of hadrons via Hagedorn states

Hagedorn states are characterized by being very massive hadron-like resonances and by not being limited to quantum numbers of known hadrons. To generate such a zoo of different Hagedorn states, a covariantly formulated bootstrap equation is solved by ensuring energy conservation and conservation of baryon number $B$, strangeness $S$, and electric charge $Q$. The numerical solution of this equation provides Hagedorn spectra, which also enable us to obtain the decay width for Hagedorn states needed in cascading decay simulations. A single Hagedorn state cascades by various two-body decay channels subsequently into final stable hadrons. All final hadronic observables such as masses, spectral functions, and decay branching ratios for hadronic feed-down are taken from a hadronic transport model. Strikingly, the final energy spectra of resulting hadrons are exponential, showing a thermal-like distribution with the characteristic Hagedorn temperature.

Figure 1

Meson-like $(B=S=Q=0)$ (upper part) and baryonic ($B=1$, $S=0$, $Q=1$) (lower part) Hagedorn spectra for two different radii with corresponding (fitted) Hagedorn temperatures. The black line represents the sum of spectral functions of hadrons with the given quantum numbers.

Figure 2

Total decay width of charge neutral Hagedorn state for two different radii.

Figure 3

Hadronic multiplicities after a cascade decay of Hagedorn state with radius $R=0.8\mathrm{fm}$ and $B=S=Q=0$ (upper part) and $B=1$, $S=-3$, $Q=-1$ (lower part) and the following hadronic feed-down.

Figure 4

Energy spectra of hadrons stemming from cascade decay of a charge neutral Hagedorn state with radius $R=0.8\mathrm{fm}$ and initial masses $M_{HS}=4\mathrm{GeV}$ and $M_{HS}=8\mathrm{GeV}$.

Figure 5

Hadronic ratios stemming from cascade decay of a charge neutral Hagedorn state with radius $R=0.8\mathrm{fm}$.