Search for $B^+ to e^+ u$ and $B^+ to mu^+ u$ decays using hadronic tagging

We present a search for the rare leptonic decays $B^+ to e^+ u_e$ and $B^+ to mu^+ u_mu$, using the full $Upsilon(4S)$ data sample of $772times 10^6$ $Bbar{B}$ pairs collected with the Belle detector at the $rm {small KEKB}$ asymmetric-energy $e^+ e^-$ collider. One of the $B$ mesons from the $Upsilon(4S) to Bbar{B}$ decay is fully reconstructed in a hadronic mode, while the recoiling side is analyzed for the signal decay. We find no evidence of a signal in any of the decay modes. Upper limits of the corresponding branching fractions are determined as ${cal B}(B^+ to e^+ u_e)<3.5times 10^{-6}$ and ${cal B}(B^+ to mu^+ u_mu)<2.7 times 10^{-6}$ at 90$%$ confidence level.