Using a $281{\mathrm{pb}}^{-1}$ data sample collected at the $\psi (3770)$ with the CLEO-$c$ detector, we present the first absolute branching fraction measurement of the decay $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$ at a statistical significance of about 4.0 standard deviations. We find 10 candidates consistent with the decay $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$. The probability that a background fluctuation accounts for this signal is less than $4.1\times {10}^{-5}$. We find $\mathcal{B}(D^0\to K^{-}{\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e)=[{2.8}_{-1.1}^{+1.4}(\mathrm{stat})\pm 0.3(\mathrm{syst})]\times {10}^{-4}$. By restricting the invariant mass of the hadronic system to be consistent with $K_1(1270)$, we obtain the product of branching fractions $\mathcal{B}\mathbf{(}{D}^0\to K_1^{-}(1270)e^{+}{\nu }_e\mathbf{)}\times \mathcal{B}\mathbf{(}{K}_1^{-}(1270)\to K^{-}{\pi }^{+}{\pi }^{-}\mathbf{)}=[{2.5}_{-1.0}^{+1.3}(\mathrm{stat})\pm 0.2(\mathrm{syst})]\times {10}^{-4}$. Using $\mathcal{B}(K_1^{-}(1270)\to K^{-}{\pi }^{+}{\pi }^{-})=(33\pm 3)\%$, we obtain $\mathcal{B}(D^0\to K_1^{-}(1270)e^{+}{\nu }_e)=[{7.6}_{-3.0}^{+4.1}(\mathrm{stat})\pm 0.6(\mathrm{syst})\pm 0.7]\times {10}^{-4}$. The last error accounts for the uncertainties in the measured $K_1^{-}(1270)\to K^{-}{\pi }^{+}{\pi }^{-}$ branching fractions.

• Received 29 May 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.191801