Measurement of $K^{0}_{\mu3}$ form factors

22 pages 7 figuresThis paper reports on a new high precision measurement of the form factors of the K_{L}\to \pi^{\pm} \mu^{\mp} \nu_{\mu} decay. The data sample of about 2.3$\times 10^{6}$ events was recorded in 1999 by the NA48 experiment at CERN. Studying the Dalitz plot density we measured a linear, $\lambda^{'}_{+} = (20.5\pm 2.2_{stat} \pm 2.4_{syst})\times 10^{-3}$, and a quadratic, $\lambda^{''}_{+} = (2.6\pm 0.9_{stat} \pm 1.0_{syst})\times 10^{-3}$ term in the power expansion of the vector form factor. No evidence was found for a second order term for the scalar form factor; the linear slope was determined to be $\lambda_{0} = (9.5\pm 1.1_{stat} \pm 0.8_{syst})\times 10^{-3}$. Using a linear fit our results were: $\lambda_{+} = (26.7\pm 0.6_{stat} \pm 0.8_{syst} )\times 10^{-3}$ and, $\lambda_{0} = (11.7\pm 0.7_{stat} \pm 1.0_{syst})\times 10^{-3}$. A pole fit of the form factors yields: $m_V = (905 \pm 9_{stat} \pm 17_{syst})$ MeV/c$^2$ and $m_S = (1400 \pm 46_{stat} \pm 53_{syst})$ MeV/c$^2$