Determination of the K$0\atop{L}$ → π^-μ⁺v_μ form factor xi(q²) by muon polarization measurements

The polarization of the muon in the decay K$sup 0$/sub L/ $Yields$ $pi$$sup -$$mu$$sup +$$nu$/sub $mu$/ was measured as a function of q$sup 2$, the four-momentum transferred to the lepton pair. The kinematic information was used to compute the polarization expected on the basis of various assumed values of the form factor xi(q$sup 2$). By comparing the interpolated curve of the polarization as a function of xi(q$sup 2$) to the experimentally measured polarization, one has determined xi(q$sup 2$) as a function of q$sup 2$. If one parameterizes the q$sup 2$ dependence of xi by xi(q$sup 2$) = xi(0) + $lambda$ q$sup 2$/m$sup 2$/sub $pi$/, then xi(0) = 0.178 +- 0.105 - 3.80 $lambda$. (auth