Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-12-25
Phys.Rev. C59 (1999) 1722-1734
Physics
High Energy Physics
High Energy Physics - Phenomenology
32 pages, LaTex, 11 figures
Scientific paper
10.1103/PhysRevC.59.1722
We study the finite quark mass effects of the low-energy QCD using the improved ladder Schwinger-Dyson and Bethe-Salpeter equations which are derived in the manner consistent with the vector and axial-vector Ward-Takahashi identities. The non-perturbative mass-independent renormalization allows us to calculate the quark condensate for a non-zero quark mass. We explicitly show that the PCAC relation holds. The key ingredients are the Cornwall-Jackiw-Tomboulis effective action, the generalized Noether current and the introduction of the regularization function to the Lagrangian. The reasonable values of the pion mass, the pion decay constant and the quark condensate are obtained with a rather large $\Lambda_{QCD}$. The pion mass square and the pion decay constant are almost proportional to the current quark mass up to the strange quark mass region. It suggests that the chiral perturbation is applicable up to the strange quark mass region. We study the validity of the approximation often used in solving the Bethe-Salpeter equations too.
Naito Kenichi
Nemoto Yukio
Oka Makoto
Takizawa Motokazu
Yoshida Koji
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