Eur. Phys. J. C (2010) 66: 207-213
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

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 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.