The equilibrium and dynamical cumulants of QCD chiral order parameter with parametric Landau free energy

Abstract By linearly parameterizing the QCD Landau free energy near critical point in baryon chemical potential and temperature plane, we study fluctuations of chiral order parameter field (the $$\sigma $$ σ field) equilibrium case dynamical phase transition, respectively. setting system size to typical QGP fireball ( $$\approx 10^3$$ ≈ 10 3 fm $$^3$$ ), show that case, discontinuity first transition region is replaced by smooth crossover, corresponding are broadened. Meanwhile, quartic cumulant $$\kappa _4$$ κ 4 generally negative line. We further derive evolution Fokker–Plank framework, based on which deduce cumulants field. Assuming decreases as a known function time, numerically evaluate confirm present clear memory effects. Moreover, effects side stronger than crossover side, at hypothetical freeze-out line rich non-monotonic structures.