Weak solution method of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking and its application to beyond the ladder analysis in QCD

The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DCSB) in QCD. We show that the DCSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.Comment: 6 pages, 3 figures, contribution to SCGT12 "KMI-GCOE Workshop on Strong Coupling Gauge Theories in the LHC Perspective", 4-7 Dec. 2012, Nagoya Universit

Phase structure of NJL model with weak renormalization group

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 $V(\sigma;t)$ is given as a partial differential equation, where $\sigma:=\bar \psi\psi$ and $t$ is a dimensionless RG scale. When the dynamical chiral symmetry breaking (D$\chi$SB) occurs at a certain scale $t_c$, $V(\sigma;t)$ has singularities originated from the phase transitions, and then one cannot follow RG flows after $t_c$. In this study, we introduce the weak solution method to the RG equation in order to follow the RG flows after the D$\chi$SB 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.Comment: 32 pages, 12 figures; Version published in Nuclear Physics

Analysis of Spontaneous Mass Generation by Iterative Method in the Nambu-Jona-Lasinio Model and Gauge Theories

We propose a new iterative method to directly calculate the spontaneous mass generation due to the dynamical chiral symmetry breaking. We can conclude the physical mass definitely without recourse to any other consideration like the free energy comparison.Comment: 6 pages, 7 figures, contribution to SCGT12 "KMI-GCOE Workshop on Strong Coupling Gauge Theories in the LHC Perspective", 4-7 Dec. 2012, Nagoya Universit