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

Abstract

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

Comments: 9 pages, two columns, 5 figures