Contributions of orderO(mquark2)toKl3form factors and unitarity of the CKM matrix

The form factors for the ${K}_{l3}$ semileptonic decay are computed to order $\mathcal{O}{(p}^{4})$ in generalized chiral perturbation theory. The main difference with the standard $\mathcal{O}{(p}^{4})$ 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 ${V}_{\mathrm{us}},$ the ratio ${F}_{K}{/F}_{\ensuremath{\pi}}, {K}_{l3}$ decay rates and the scalar form factor slope ${\ensuremath{\lambda}}_{0}.$ This framework easily accommodates the precise value for ${V}_{\mathrm{ud}}$ deduced from superallowed nuclear \ensuremath{\beta} decays.