$\Delta S=0$ Effective Weak Chiral Lagrangian from the Instanton Vacuum

Abstract

We investigate the $\Delta S=0$ effective chiral Lagrangian from the instanton vacuum. Based on the $\Delta S=0$ effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving effective weak chiral Lagrangian from the instanton vacuum to order ${\cal O}(p^2)$ and the next-to-leading order in the $1/N_c$ expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak penguin operators appear in the next-to-leading order in the $1/N_c$ expansion for the $\Delta S =0$ effective weak chiral Lagrangian, while they are in the leading order terms in the $\Delta S = 1$ case. Three different types of the form factors are employed and we find that the dependence on the different choices of the form factor is rather insensitive. The low-energy constants of the Gasser-Leutwyler type are determined and discussed in the chiral limit.