Search for the decay $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}$ using data from the Belle and Belle II experiments

We report a search for the rare decay $B^{+}\to K^{+}{\tau }^{+}{\tau }^{-}$ using $1.2\times {10}^9$ $\mathrm{{\rm Y}}(4S)$ mesons produced near threshold in electron-positron collisions and collected by the Belle and Belle~II experiments. We fully reconstruct the hadronic decay of one $B$ meson produced in the $\mathrm{{\rm Y}}(4S)\to B^{+}{B}^{-}$ decay, and search for $B^{\pm }\to K^{\pm }{\tau }^{+}{\tau }^{-}$ candidates among the remaining collision products, reconstructing a charged kaon and leptonic decays of the $\tau$ leptons. We optimize the selection for best sensitivity and look for an excess over background at low values of the residual energy detected in the calorimeter after full event reconstruction. We observe no significant excess and set the limit $\mathcal{B}(B^{+}\to K^{+}{\tau }^{+}{\tau }^{-})<0.56\times {10}^{-3}$ at the 90% confidence level, improving on the only previous result by a factor of four.