First observations of the rare decays B⁺→ K⁺π⁺π⁻µ⁺µ⁻ and B⁺→ φK⁺µ⁺µ⁻

First observations of the rare decays B+→ K+π+π−µ+µ− and B+→ φK+µ+µ− are presented using data corresponding to an integrated luminosity of 3.0 fb−1, collected by the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The branching fractions of the decays are
B(B+→K+π+π−µ+µ−) =4.36 +0.29−0.27 (stat) ± 0.21 (syst) ±0.18(norm)×10−7
B(B+→φK+µ+µ−) =0.82 +0.19−0.17 (stat) +0.10−0.04 (syst)±0.27(norm)×10−7
where the uncertainties are statistical, systematic, and due to the uncertainty on the branching fractions of the normalisation modes. A measurement of the differential branching fraction in bins of the invariant mass squared of the dimuon system is also presented for the decay B+→ K+π+π−µ+µ