Meson Scattering in a Pion Superfluid

TL;DR

This paper investigates how pion-pion scattering behavior changes in a pion superfluid, revealing a BCS-BEC crossover at the quark level through the Nambu--Jona-Lasinio model.

Contribution

It demonstrates that boson-boson scattering amplitude decreases monotonically with isospin density, indicating a BCS-BEC crossover in the pion superfluid.

Findings

Scattering amplitude drops with decreasing isospin density

Amplitude vanishes at phase transition boundary

Evidence of BCS-BEC crossover in pion superfluid

Abstract

Instead of the fermion-fermion scattering which identifies the BCS-BEC crossover in cold atom systems, boson-boson scattering is measurable and characterizes the BCS-BEC crossover at quark level. We study $\pi$-$\pi$ scattering in a pion superfluid described by the Nambu--Jona-Lasinio model. We found that the scattering amplitude drops down monotonically with decreasing isospin density and finally vanishes at the boundary of the phase transition. This indicates a BCS-BEC crossover in the pion superfluid.