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Contribution of the Sixth Order Effective Chiral Lagrangian to the $πK$ Scattering at Large $N_c$

Using the method of asymptotic sum rules we estimated the size of $O(m_s p_π^4)$ and $O(m_s^2 p_π^2)$ corrections to $πK$ scattering amplitude in large $N_c$ limit. These corrections arise from the sixth order effective chiral lagrangian (EChL). Our method enables us to estimate the corresponding terms of the sixth order EChL in leading order of $1/N_c$ expansion in model independent way. We found that the corrections numerically are suppressed in spite of naive expectation of 30--35\%. Our estimation gives the value of these corrections about 5--10\% .