Sigma and hydrodynamic modes along the critical line

Assuming a tricritical point of two-flavor QCD in the space of temperature, baryon number chemical potential, and quark mass, we study the change of the associated soft mode along the critical line within the Ginzburg-Landau approach and the Nambu-Jona-Lasinio model. The ordering density along the chiral critical line is the scalar density whereas a linear combination of the scalar, baryon number, and energy densities becomes the proper ordering density along the critical line with finite quark masses. It is shown that the critical eigenmode shifts from the sigma-like fluctuation of the scalar density to a hydrodynamic mode at the tricritical point, where we have two ordering densities, the scalar density and a linear combination of the baryon number and energy densities. We argue that the appearance of the critical eigenmode with hydrodynamic character is a logical consequence of divergent susceptibilities of the conserved densities.