Calculating the Decay Constant f_π : Particles and Fields

概要

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We calculate physical quantities accompanying dynamical chiral symmetry breaking in QCD like theories. To emphasize the consistency of our approximation with chiral symmety, we first derive an effective action for a bilocal auxiliary field standing for ψ(x)ψ^^-(y), from which the Schwinger-Dyson equation for fermion self-energy Σ and the Bethe-Salpeter equation for the Nambu-Goldstone bound state follow. An expression for the decay constant (usually called f_π) is given exactly to the ladder approximation by solving the Bethe-Salpeter equation. Numerical calculation is done for Σ, f_π, <ψ^^-ψ>_R, with various β-functions of the gauge coupling constant. We find that f_π/<ψ^^-ψ>_R, f_π/Λ_<QCD> are rather stable against the infrared cutoff parameter, while Σ-function itself depends strongly on the infrared cutoff.
理論物理学刊行会の論文
1990-10-25