High statistics measurement of the K+-->pi0e+nu (K+e3) branching ratio.

E865 at the Brookhaven National Laboratory AGS collected about 70 000 K(+)(e3) events to measure the K(+)(e3) branching ratio relative to the observed K+-->pi(+)pi(0), K+-->pi(0)micro(+)nu, and K+-->pi(+)pi(0)pi(0) decays. The pi(0) in all the decays was detected using the e(+)e(-) pair from pi(0)-->e(+)e(-)gamma decay and no photons were required. Using the 2002 Particle Data Group branching ratios for the normalization decays, we obtain BR(K(+)(e3(gamma)))=(5.13+/-0.02(stat)+/-0.09(syst)+/-0.04(norm))%, where K(+)(e3(gamma)) includes the effect of virtual and real photons. This result is approximately 2.3sigma higher than the current Particle Data Group value. Implications for the V(us) element of the CKM matrix, and the matrix's unitarity are discussed.