Validity of reducing dynamical degrees of freedom in the coupled n–σ system under limited scale separation

Ascertain whether, in heavy-ion collision scenarios where scale separation is limited, one can consistently reduce dynamical degrees of freedom in the coupled chiral condensate–baryon density (n–σ) system—such as integrating out the σ field as a fast mode—without losing essential physics relevant to critical fluctuations.

Background

Many studies simplify the dynamics near the QCD critical point by treating σ as a fast mode and focusing on conserved-charge diffusion (model B). However, heavy-ion collisions feature short lifetimes and comparable microscopic and macroscopic time scales, which may invalidate such reductions.

Clarifying when (or if) the σ degree of freedom can be safely eliminated is essential for constructing reliable dynamical frameworks that capture critical phenomena in realistic collision conditions.