Contributions of order ${\cal O}(m_{\rm quark}^2)$ to $K_{\ell 3}$ form   factors and unitarity of the CKM matrix
  The form factors for the $K_{\ell 3}$ semileptonic decay are computed to order $O(p^4)$ in generalized chiral perturbation theory. The main difference with the standard $O(p^4)$ expressions consists in contributions quadratic in quark masses, which are described by a single divergence-free low-energy constant, $A_3$. A new simultaneous analysis is presented for the CKM matrix element $V_{us}$, the ratio $F_K/F_{\pi}$, $K_{\ell 3}$ decay rates and the scalar form factor slope $\lambda_0$. This framework easily accommodates the precise value for $V_{ud}$ deduced from superallowed nuclear $\beta$-decays. 
N.H. Fuchs (Purdue), M. Knecht (CPT Marseille), J. Stern (IPN-Orsay)