Search for the decays B⁺(c) → μ⁺ ν_μγ

A search for the radiative leptonic decays B⁺→μ⁺ν_μγ and B⁺c→μ⁺ν_μγ is performed using proton-proton collision data collected with the LHCb experiment at a center-of-mass energy of 13~ TeV, corresponding to an integrated luminosity of 5.4~ fb⁻¹. No evidence for an excess of events over background is observed for either signal decay. Upper limits at 90% confidence level are set on the branching fractions: {align} {{B}}(B^+→μ^+ν_μγ)E_γ^ > 1\,GeV &< 4.0 × 10⁻⁶,\\ {{B}}(B_c^+→μ^+ν_μγ)E_γ^ > 1\,GeV &< 1.6 × 10⁻³, {align} where the photon energy in the B-meson rest frame, E_γ^, is required to be greater than 1~ GeV. This constitutes the first search for these decays at a hadron collider and the first experimental investigation of the Bc⁺→μ⁺ν_μγ decay to date.