Measurement of the ratio scrB(${\mathit{D}}^{+}$→${\mathrm{\pi }}^0$${\mathit{l}}^{+}$ν)/scrB(${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$${\mathit{l}}^{+}$ν)

Using the CLEO-II detector, the branching ratio of the Cabibbo suppressed decay ${\mathit{D}}^{+}$→${\mathrm{\pi }}^0$ ${\mathit{l}}^{+}$ν, relative to the branching ratio of the Cabibbo favored decay ${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$ ${\mathit{l}}^{+}$ν, is measured to be B(${\mathit{D}}^{+}$→${\mathrm{\pi }}^0$ ${\mathit{l}}^{+}$ν)/B(${\mathit{D}}^{+}$→K${\mathrm{¯}}^0$ ${\mathit{l}}^{+}$ν) =(8.5±2.7±1.4)%. From this ratio, the product of the ratio of Cabibbo-Kobayashi-Maskawa (CKM) matrix elements, ‖${\mathit{V}}_{\mathit{c}\mathit{d}}$/${\mathit{V}}_{\mathit{c}\mathit{s}}$ ${\mathrm{\Vert }}^2$, and the form factors at ${\mathit{q}}^2$=0, ‖${\mathit{f}}_{+}^{\mathrm{\pi }}$(0)/${\mathit{f}}_{+}^{\mathit{K}}$(0)${\mathrm{\Vert }}^2$, is determined to be ‖${\mathit{V}}_{\mathit{c}\mathit{d}}$/${\mathit{V}}_{\mathit{c}\mathit{s}}$ ${\mathrm{\Vert }}^2$‖${\mathit{f}}_{+}^{\mathrm{\pi }}$(0)/${\mathit{f}}_{+}^{\mathit{K}}$(0)${\mathrm{\Vert }}^2$ =0.085±0.027±0.014.