Search for the rare leptonic decays $B^{+}\to l^{+}{\nu }_l$ ($l=e,\mu$)

We have performed a search for the rare leptonic decays $B^{+}\to {\ell }^{+}{\nu }_{\ell }$($l=e,\mu$), using data collected at the ${\rm Y}(4S)$ resonance by the BABAR detector at the PEP-II storage ring. In a sample of $468\times {10}^6$ $B\overline{B}$ pairs we find no evidence for a signal and set an upper limit on the branching fractions $\mathcal{B}(B^{+}\to {\mu }^{+}{\nu }_{\mu })<1.0\times {10}^{-6}$ and $\mathcal{B}(B^{+}\to e^{+}{\nu }_e)<1.9\times {10}^{-6}$ at the 90% confidence level, using a Bayesian approach.

Figure 1

Lowest order SM Feynman diagram for the purely leptonic decay $B^{+}\to l^{+}{\nu }_l$.

Figure 2

Distributions of signal (a),(b) and background (c),(d) $m_{\mathrm{ES}}$ (left) and $p_{\mathrm{FIT}}$ (right) for $B^{+}\to {\mu }^{+}{\nu }_{\mu }$ from MC simulation [(a)–(c)] and from $m_{\mathrm{ES}}$ sideband $5.17<m_{\mathrm{ES}}<5.2\mathrm{GeV}/c^2$ (d).

Figure 3

Distributions of signal (a),(b) and background (c),(d) $m_{\mathrm{ES}}$ (left) and $p_{\mathrm{FIT}}$ (right) for $B^{+}\to e^{+}{\nu }_e$ from MC simulation.

Figure 4

Final fit to the data projected on $m_{\mathrm{ES}}$ (left) and $p_{\mathrm{FIT}}$ (right) distributions for $B^{+}\to {\mu }^{+}{\nu }_{\mu }$ events (a),(b) and $B^{+}\to e^{+}{\nu }_e$ events (c),(d): The solid blue line is the total PDF, the dashed red line is the background PDF, and the dashed-dotted black line is the signal PDF.