https://doi.org/10.1140/epjc/s10052-009-1231-8
Regular Article - Theoretical Physics
The speed of sound in hadronic matter
1
Dipartimento di Fisica, Università di Catania and INFN Sezione di Catania, 95123, Catania, Italy
2
Physics Department, University of Cape Town, Cape Town, South Africa
3
Fakultät für Physik, Universität Bielefeld, 33501, Bielefeld, Germany
4
Department of Physics, Pennsylvania State University, Hazleton Campus, Hazleton, PA, 18202, USA
* e-mail: dmiller@physik.uni-bielefeld.de
Received:
21
July
2009
Revised:
21
August
2009
Published online:
15
January
2010
We calculate the speed of sound c s in an ideal gas of resonances, whose mass spectrum is assumed to have the Hagedorn form ρ(m)∼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 resonance effects dominate, which causes 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.
© Springer-Verlag / Società Italiana di Fisica, 2010