Finite volume and magnetic field effects on the two-pion correlation function in relativistic heavy-ion collisions

Alejandro Ayala,Santiago Bernal-Langarica,Cristian Villavicencio

doi:10.1103/physrevd.105.056001

Abstract

We study the combined effects of a finite volume and an external magnetic field on the charged two-pion correlation function. For these purposes, we consider a dilute system of pions where the finite volume effects are introduced computing the pion wave functions with rigid boundary conditions in a cylindrical geometry in the presence of a uniform and constant magnetic field. We find that for slow pions, namely, for the case where the average pair momentum is small, the correlation function shows a large distortion, as opposed to the case where the average pair momentum is large. For a finite density system, the intercept of the correlation function is reduced, signaling the increasing importance of the pion ground state contribution. An increasing strength of the magnetic field reduces the importance of the ground state and the intercept becomes closer to 2.

Highlights

The properties of relativistic pion systems have attracted attention over several years in different contexts, ranging from the early universe [1,2] and astrophysics [3,4] to relativistic heavy-ion collisions [5–7]
We have considered the dilute limit of the pion system computing their wave functions in the presence of the magnetic field assuming cylindrical symmetry with rigid boundary conditions
To include the effects of a finite density, we introduce a chemical potential associated with the approximately conserved charged pion number

Summary

INTRODUCTION

The properties of relativistic pion systems have attracted attention over several years in different contexts, ranging from the early universe [1,2] and astrophysics [3,4] to relativistic heavy-ion collisions [5–7]. A natural question that emerges is what is the effect of the magnetic field produced in this kind of collisions on the formation of the condensate in a finite volume system. This question has been partially addressed in Ref. Finite size effects on the height of this intercept, when a sizable fraction of pions are in the lowest energy state, have been studied in Ref. The work is organized as follows: In Sec. II we formulate the way the finite volume pion states can be obtained in the presence of a magnetic field.

TWO-PION CORRELATION FUNCTION IN A FINITE VOLUME AND WITHIN A MAGNETIC FIELD

MAGNETIC FIELD AND FINITE VOLUME EFFECTS

Zero chemical potential

Fixed pion number

SUMMARY AND CONCLUSIONS