Measurement of the Hadronic Form Factors in Ds -> phi e nu Decays

Based on the measured four-dimensional rate for $D_{s}^+ to \phi e^+ \nu_e$ decays, we have determined the ratios of the three hadronic form factors, r_V=V(0)/A_1(0)= 1.636 \pm 0.067 \pm 0.038 and r_2=A_2(0)/A_1(0)= 0.705 \pm 0.056 \pm 0.029, using a simple pole ansatz for the $q^2$ dependence, with fixed values of the pole masses for both the vector and axial form factors. By a separate fit to the same data, we have also extracted the pole mass for the axial form factors, $m_A$: r_V=V(0)/A_1(0)= 1.633 \pm 0.081 \pm 0.068 ,r_2=A_2(0)/A_1(0)= 0.711 \pm 0.111 \pm 0.096 and m_A=(2.53^{+0.54}_{-0.35}\pm 0.54){{GeV/}c^2}