Search for the decay modes $B^{\mathbf{\pm }}\to h^{\mathbf{\pm }}\tau \ell$

We present a search for the lepton flavor violating decay modes $B^{\pm }\to h^{\pm }\tau \ell$ ($h=K$, $\pi$; $\ell =e$, $\mu$) using the BABAR data sample, which corresponds to $472\times {10}^6$ $B\overline{B}$ pairs. The search uses events where one $B$ meson is fully reconstructed in one of several hadronic final states. Using the momenta of the reconstructed $B$, $h$, and $\ell$ candidates, we are able to fully determine the $\tau$ four-momentum. The resulting $\tau$ candidate mass is our main discriminant against combinatorial background. We see no evidence for $B^{\pm }\to h^{\pm }\tau \ell$ decays and set a 90% confidence level upper limit on each branching fraction at the level of a few times ${10}^{-5}$.

Figure 1

Distributions of $m(K\pi )$ for the (a, b) $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$; ${\tau }^{-}\to (n{\pi }^0){\pi }^{-}{\nu }_{\tau }$ and (c, d) $B^{+}\to K^{+}{\tau }^{+}{\mu }^{-}$; ${\tau }^{+}\to (n{\pi }^0){\pi }^{+}{\overline{\nu }}_{\tau }$ channels. The top row shows the data (points) compared with the background MC (solid line). The area of the background MC distribution has been normalized to the area of the data distribution. The bottom row shows the (b) $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$ and (d) $B^{+}\to K^{+}{\tau }^{+}{\mu }^{-}$ signal MC. The normalization of the bottom row is arbitrary. The dotted vertical line is at $1.95\mathrm{GeV}/c^2$, which is the minimum allowed value of $m(K\pi )$ for the signal selection. The peak in the top row just below $1.95\mathrm{GeV}/c^2$ is from ${\overline{D}}^0\to K^{+}{\pi }^{-}$ decays.

Figure 2

Distributions of the three-component $\Delta E_{D\ell \nu }$ unbinned maximum likelihood fits of the data for the (a) $B\to D^{(*)0}\mu \nu$ and (b) $B\to D^{(*)0}e\nu$ control samples. In each plot, the points represent the data, the solid blue curve is the sum of all PDFs, the long-dashed green curve is the $D^0$ component, the dash-dotted purple curve is the $D^{*0}$ component, and the dotted blue curve is the $D^{**0}$ component, which also includes any residual combinatorial background.

Figure 3

Distributions of $|\cos {\theta }_{\mathrm{thr}}|$ for background (top) and signal MC (bottom), for the $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$; ${\tau }^{-}\to (n{\pi }^0){\pi }^{-}{\nu }_{\tau }$ channel. The points (solid line) in the top figure are the data (background MC). The background MC has been normalized to match the area of the data distribution. The normalization of the signal MC is arbitrary. The solid red curve is the result of the polynomial fit of the MC distribution.

Figure 4

Distributions of $\sum _{}^{}{E}_{\mathrm{cal}}$ for background (top) and signal MC (bottom), for the $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$ mode; ${\tau }^{-}\to e^{-}{\overline{\nu }}_e{\nu }_{\tau }$ (left), ${\tau }^{-}\to {\mu }^{-}{\overline{\nu }}_{\mu }{\nu }_{\tau }$ (middle), and ${\tau }^{-}\to (n{\pi }^0){\pi }^{-}{\nu }_{\tau }$ (right). The events where $\sum _{}^{}{E}_{\mathrm{cal}}=0$ have been separated from the main distribution and plotted in a bin below zero for clarity. The points (solid line) in the top figure are the data (background MC). The background MC has been normalized to match the area of the data distribution. The normalization of the signal MC is arbitrary. The solid red curve is the result of the polynomial fit of the MC distribution.

Figure 5

Likelihood ratio ($L_R$) output distributions of background (top) and signal MC (bottom), for the $B^{+}\to K^{+}{\tau }^{-}{\mu }^{+}$; ${\tau }^{-}\to (n{\pi }^0){\pi }^{-}{\nu }_{\tau }$ channel. The points (solid line) in the top figure are the data (background MC). The background MC has been normalized to match the area of the data distribution. The normalization of the signal MC is arbitrary.

Figure 6

Observed distributions of the $\tau$ invariant mass for the $B\to K\tau \ell$ modes. The distributions show the sum of the three $\tau$ channels $(e,\mu ,\pi )$. The points with error bars are the data. The solid line is the background MC which has been normalized to the area of the data distribution. The dashed vertical lines indicate the $m_{\tau }$ signal window range. The inset shows the $m_{\tau }$ distribution for signal MC.

Figure 7

Observed distributions of the $\tau$ invariant mass for the $B\to \pi \tau \ell$ modes. The distributions show the sum of the three $\tau$ channels $(e,\mu ,\pi )$. The points with error bars are the data. The solid line is the background MC which has been normalized to the area of the data distribution. The dashed vertical lines indicate the $m_{\tau }$ signal window range. The inset shows the $m_{\tau }$ distribution for signal MC.