Measurement of Structure-Dependent K+→μ+νμγ Decay

We report the first measurement of a structure-dependent component in the decay $K^{+}\to {\mu }^{+}{\nu }_{\mu }\gamma$. Using the kinematic region where the muon kinetic energy is greater than 137 MeV and the photon energy is greater than 90 MeV, we find that the absolute value of the sum of the vector and axial-vector form factors is $|F_V{+F}_A|=0.165\mathrm{}\pm 0.007\pm 0.011$. This corresponds to a branching ratio of $B\left({\mathrm{SD}}^{+}\right)=(1.33\pm 0.12\pm 0.18)\times {10}^{-5\mathrm{}}$. We also set the limit $-0.04<F_V{-F}_A<0.24\mathrm{}$ at $90\%$ C.L.