We search for the rare decay B+→K+νν ̄ in a 362 fb-1 sample of electron-positron collisions at the δ (4S) resonance collected with the Belle II detector at the SuperKEKB collider. We use the inclusive properties of the accompanying B meson in δ (4S)→BB ̄ events to suppress background from other decays of the signal B candidate and light-quark pair production. We validate the measurement with an auxiliary analysis based on a conventional hadronic reconstruction of the accompanying B meson. For background suppression, we exploit distinct signal features using machine learning methods tuned with simulated data. The signal-reconstruction efficiency and background suppression are validated through various control channels. The branching fraction is extracted in a maximum likelihood fit. Our inclusive and hadronic analyses yield consistent results for the B+→K+νν ̄ branching fraction of [2.7±0.5(stat)±0.5(syst)]×10-5 and [1.1-0.8+0.9(stat)-0.5+0.8(syst)]×10-5, respectively. Combining the results, we determine the branching fraction of the decay B+→K+νν ̄ to be [2.3±0.5(stat)-0.4+0.5(syst)]×10-5, providing the first evidence for this decay at 3.5 standard deviations. The combined result is 2.7 standard deviations above the standard model expectation.
