Measurement of $D^0\to \pi l\nu (Kl\nu )$ Form Factors and Absolute Branching Fractions

Using a $282{\mathrm{fb}}^{-1}$ data sample collected by the Belle experiment at the KEKB $e^{+}{e}^{-}$ collider, we study $D^0$ decays to $K^{-}{\ell }^{+}\nu$ and ${\pi }^{-}{\ell }^{+}\nu$ final states. The $D^0$ flavor and momentum are tagged through a full reconstruction of the recoiling charm meson and additional mesons from fragmentation. The reconstruction method provides very good resolution in neutrino momentum and in $q^2=(p_{\ell }+p_{\nu }{)}^2$. Normalizing to the total number of $D^0$ tags, we measure the absolute branching fractions to be $\mathcal{B}(D^0\to K\ell \nu )=(3.45\pm {0.07}_{\mathrm{stat}}\pm {0.20}_{\mathrm{syst}})\%$ and $\mathcal{B}(D^0\to \pi \ell \nu )=(0.255\pm {0.019}_{\mathrm{stat}}\pm {0.016}_{\mathrm{syst}})\%$ and the semileptonic form factors (within the modified pole model) $f_{+}^K(0)=0.695\pm {0.007}_{\mathrm{stat}}\pm {0.022}_{\mathrm{syst}}$ and $f_{+}^{\pi }(0)=0.624\pm {0.020}_{\mathrm{stat}}\pm {0.030}_{\mathrm{syst}}$.

Figure 1

Mass spectrum of ${\overline{D}}_{\mathrm{sig}}^0$ candidates.

Figure 2

Form factors for (a) $D^0\to K^{-}{\ell }^{+}\nu$, in $q^2$ bins of $0.067{\mathrm{GeV}}^2/c^2$ and (b) $D^0\to {\pi }^{-}{\ell }^{+}\nu$, in $q^2$ bins of $0.3{\mathrm{GeV}}^2/c^2$. Overlaid are the predictions of the simple pole model using the physical pole mass (dashed), and a quenched [3] (light gray), and unquenched [2] (dark gray) LQCD calculation. Each LQCD curve is obtained by fitting a parabola to values calculated at specific $q^2$ points. The shaded band reflects the theoretical uncertainty (without the Becirevic-Kaidalov–ansatz error for Ref. [2]) and is shown within the range of $q^2$ for which calculations are reported.