Bose-Einstein condensation in the relativistic pion gas: Thermodynamic limit and finite size effects

Abstract

We consider the Bose-Einstein condensation (BEC) in a relativistic pion gas. The thermodynamic limit when the system volume $V$ goes to infinity as well as the role of finite size effects are studied. At $V\ensuremath{\rightarrow}\ensuremath{\infty}$ the scaled variance for particle-number fluctuations, $\ensuremath{\omega}=\ensuremath{\langle}\ensuremath{\Delta}{N}^{2}\ensuremath{\rangle}/\ensuremath{\langle}N\ensuremath{\rangle}$, converges to finite values in the normal phase above the BEC temperature, $Tg{T}_{C}$. It diverges as $\ensuremath{\omega}\ensuremath{\propto}{V}^{1/3}$ at the BEC line $T={T}_{C}$, and $\ensuremath{\omega}\ensuremath{\propto}V$ at $Tl{T}_{C}$ in a phase with the BE condensate. Possible experimental signals of the pion BEC in finite systems created in high-energy proton-proton collisions are discussed.