$ΔS=0$ Effective Weak Chiral Lagrangian from the Instanton Vacuum

Details $ΔS=0$ Effective Weak Chiral Lagrangian from the Instanton Vacuum $ΔS=0$ Effective Weak Chiral Lagrangian from the Instanton Vacuum

2004-05-22

arxiv.org/abs/hep-ph/0405217v2

Eur.Phys.J.C45:451-457,2006

Physics

High Energy Physics

High Energy Physics - Phenomenology

Final version accepted for publication in Eur. Phys. J. C

Scientific paper

10.1140/epjc/s2005-02442-3

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.

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