Search for the decay modes $D^0\to e^{\mathbf{+}}{e}^{\mathbf{-}}$, $D^0\to {\mu }^{\mathbf{+}}{\mu }^{\mathbf{-}}$, and $D^0\to e^{\mathbf{\pm }}\mu \mathbf{\mp }$

We present searches for the rare decay modes $D^0\to e^{+}{e}^{-}$, $D^0\to {\mu }^{+}{\mu }^{-}$, and $D^0\to e^{\pm }{\mu }^{\mp }$ in continuum $e^{+}{e}^{-}\to c\overline{c}$ events recorded by the BABAR detector in a data sample that corresponds to an integrated luminosity of $468{\mathrm{fb}}^{-1}$. These decays are highly Glashow–Iliopoulos–Maiani suppressed but may be enhanced in several extensions of the standard model. Our observed event yields are consistent with the expected backgrounds. An excess is seen in the $D^0\to {\mu }^{+}{\mu }^{-}$ channel, although the observed yield is consistent with an upward background fluctuation at the 5% level. Using the Feldman–Cousins method, we set the following 90% confidence level intervals on the branching fractions: $\mathcal{B}(D^0\to e^{+}{e}^{-})<1.7\times {10}^{-7}$, $\mathcal{B}(D^0\to {\mu }^{+}{\mu }^{-})$ within $[0.6,8.1]\times {10}^{-7}$, and $\mathcal{B}(D^0\to e^{\pm }{\mu }^{\mp })<3.3\times {10}^{-7}$.

Figure 1

Reconstructed $D^0$ mass (left) and $\Delta m$ (right) for the three signal channels: $D^0\to e^{+}{e}^{-}$ (top), $D^0\to {\mu }^{+}{\mu }^{-}$ (middle), and $D^0\to e^{\pm }{\mu }^{\mp }$ (bottom). The solid (black) histogram is the signal MC sample, the dashed (blue) histogram is the $D^0\to {\pi }^{+}{\pi }^{-}$ MC sample reconstructed as $D^0\to {\ell }^{+}{\ell }^{-}$, and the dotted (red) histogram is the $D^0\to K^{-}{\pi }^{+}$ MC sample reconstructed as $D^0\to {\ell }^{+}{\ell }^{-}$. The $D^0\to {\ell }^{+}{\ell }^{-}$ and $D^0\to {\pi }^{+}{\pi }^{-}$ distributions have been normalized to unit area. The $D^0\to K^{-}{\pi }^{+}$ normalization is arbitrary.

Figure 2

Fisher discriminant, $\mathcal{F}$, distributions for the $B\overline{B}$ MC sample (dashed blue line), the $D^0\to {\mu }^{+}{\mu }^{-}$ signal MC sample (solid black line), and the continuum MC sample (dotted red line). The $\mathcal{F}$ distributions for $D^0\to e^{+}{e}^{-}$ and $D^0\to e^{\pm }{\mu }^{\mp }$ are similar to those of $D^0\to {\mu }^{+}{\mu }^{-}$.

Figure 3

Distributions of $|\cos ({\theta }_{\mathrm{hel}})|$ for the three signal channels: $D^0\to e^{+}{e}^{-}$ (left), $D^0\to {\mu }^{+}{\mu }^{-}$ (center), and $D^0\to e^{\pm }{\mu }^{\mp }$ (right). The top distributions show Monte Carlo distributions for the combinatorial $B\overline{B}$ (dashed blue lines) and continuum (dotted red lines) backgrounds. The bottom distributions show the signal Monte Carlo samples with arbitrary normalization.

Figure 4

Data distributions of $\Delta m$ vs the reconstructed $D^0$ mass (top row), projections of the $D^0$ mass (middle row), and $\Delta m$ (bottom row). The columns contain the distributions for the $D^0\to e^{+}{e}^{-}$ (left), $D^0\to {\mu }^{+}{\mu }^{-}$ (center), and $D^0\to e^{\pm }{\mu }^{\mp }$ (right) decay modes. The shaded $D^0$ mass ($\Delta m$) distributions represent the subset of events that fall in the $\Delta m$ ($D^0$ mass) signal window. In the top row, the dotted (black) box indicates the signal region and the dashed (red) box indicates the sideband region. In the middle and bottom rows, the vertical dotted black lines indicate the boundaries of the signal region.