2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229803We update the determination of |V_us| using semielectronic and semimuonic decays of K mesons. A modest improvement of 15% with respect to its present value is obtained for the error bar of this matrix element when we combine the four available semileptonic decays. The combined effects of long-distance radiative corrections and nonlinear terms in the vector form factors can decrease the value of |V_us| by up to 1%. Refined measurements of the decay widths and slope form factors in the semimuonic modes and a more accurate calculation of vector form factors at zero momentum transfer can push the determination of |V_us| at a few of percent level.19 pages, 2 figuresHigh Energy Physics - Phenomenologytext