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Bardeen-Buras-G\'{e}rard have proposed a large N$_c$ method to evaluatehadronic weak matrix elements to attack for instance the determination of the$\Delta I= \frac{1}{2}$-rule and $\mathrm{Re}(\frac{\epsilon'}{\epsilon})$.Here we test this method to the determination of the form factor parameters$a_+$ and $b_+$ in the decays $K^+ \rightarrow \pi^+ \ell^+ \ell^- $ and $K_S\rightarrow \pi ^0 \ell^+ \ell^-$. The results are encouraging: in particularafter a complete treatment of Vector Meson Dominance (VMD).

$K \rightarrow \pi \ell^+ \ell^-$ form factor in the Large-N$_c$ and cut-off regularization method