Pinning down the kaon form factors in K⁺→μ⁺ν_μγ decay

We find that the normal muon polarization in the decay K→μν_μγ is very sensitive to the values of the kaon vector F_V and axial-vector F_A form factors. It is shown that the ongoing KEK-E246 experiment can definitely determine the signs of the sum of the form factors if their difference is fixed from other considerations. This method can also verify the form factor values and signs obtained from the K⁺→l⁺ν_le⁺e^- decays. A new experiment with sensitivity to the normal and transverse muon polarizations of about 10^-4 will provide a unique possibility to determine the F_V and F_A values with a few percent accuracy.