Functional renormalization group study of the jet quenching parameter near the QCD critical end point

We investigate the jet quenching parameter $\hat{q}$ in the QCD phase diagram within a QCD-assisted low-energy effective theory using the functional renormalization group (fRG). Following the formalism that relates $\hat{q}$ to the spectral functions of the chiral order-parameter field, we compute the $\sigma$ and $\pi$ meson contributions to $\hat{q}$ at finite temperature and baryon chemical potential from analytically continued mesonic two-point functions. We find that $\hat{q}$ receives appreciable contributions mainly above the chiral phase boundary and exhibits a pronounced enhancement at large baryon chemical potential as the chiral crossover sharpens toward the critical end point (CEP), a behavior consistent with the picture of partonic critical opalescence (PCO), a pronounced enhancement of jet transverse momentum broadening induced by the critical $\sigma$ field fluctuations.