Abstract
We analyze the chiral phase structure of the Nambu–Jona-Lasinio model at finite temperature and density by using the functional renormalization group (FRG). The renormalization group (RG) equation for the fermionic effective potential V(σ;t) is given as a partial differential equation, where σ:=ψ¯ψ and t is a dimensionless RG scale. When the dynamical chiral symmetry breaking (DχSB) occurs at a certain scale tc, V(σ;t) has singularities originated from the phase transitions, and then one cannot follow RG flows after tc. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales. It is shown that the weak solution of the RG equation correctly captures vacuum structures and critical phenomena within the pure fermionic system. We show the chiral phase diagram on temperature, chemical potential and the four-Fermi coupling constant.
Highlights
Solving Quantum Chromodynamics (QCD) is a challenging problem in elementary particle physics
We introduce the weak solution method to the renormalization group (RG) equation in order to follow the RG flows after the DχSB and to evaluate the dynamical mass and the chiral condensate in low energy scales
We have studied the chiral phase structure of the NJL model at finite temperature and density using the functional renormalization group (FRG)
Summary
Solving Quantum Chromodynamics (QCD) is a challenging problem in elementary particle physics. We call the RG equation applied the weak solution method “weak renormalization group equation” It has been shown in [37] that the weak solution method can address the chiral phase transitions of both second- and firstorder and evaluate the physical values such as the dynamical mass and the chiral condensate. We analyze the DχSB in the NJL model at finite temperature and density using the FRG with the weak solution method. It should be emphasized that we will obtain the chiral phase diagram of the NJL model using the FRG without the auxiliary field method. The main purpose of this paper is to show that one can obtain the chiral phase diagram with both second- and first-order phase transitions by the weak solution method without the help of the auxiliary field method. In the appendix B, the convexity and concavity of the beta function is discussed
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