Functional renormalization group study of phonon mode effects on the chiral critical point

We apply the functional renormalization group (FRG) equation to analyze the nature of the quantum chromodynamics (QCD) critical point beyond the mean-field approximation by taking into consideration the fact that the soft mode associated with the QCD critical point is a linear combination of fluctuations of the chiral condensate and the quark-number density, rather than pure chiral fluctuations. We first construct an extended quark-meson model, in which a new field φ corresponding to the quark-number density is introduced to the conventional one, composed of chiral fields (σ, π) and quarks. The fluctuations of the quark-number density as well as the chiral condensate are taken into account by solving the FRG equation, which contains σ and φ as coupled dynamical variables. It is found that mixing of the two dynamical variables causes a kind of level repulsion between the curvature masses, which in turn leads to an expansion of the critical region of the QCD critical point, depending on the coupling constants in the model yet to be determined from microscopic theories or, hopefully, by experiments. (author)