The Speed of Sound in Hadronic Matter

Abstract

We calculate the speed of sound $c_s$ in an ideal gas of resonances whose mass spectrum is assumed to have the Hagedorn form $\rho (m)\sim m^{-a}\exp bm$, which leads to singular behavior at the critical temperature $T_c=1/b$. With $a=4$ the pressure and the energy density remain finite at $T_c$, while the specific heat diverges there. As a function of the temperature the corresponding speed of sound initially increases similarly to that of an ideal pion gas until near $T_c$ where the resonance effects dominate causing $c_s$ to vanish as $(T_c-T{)}^{1/4}$. In order to compare this result to the physical resonance gas models, we introduce an upper cut-off M in the resonance mass integration. Although the truncated form still decreases somewhat in the region around $T_c$, the actual critical behavior in these models is no longer present.

Comments: 11 Pages, 9 Figures and 17 References