Measurement of the branching fractions of the decays D ⁺ → K ⁻ K ⁺ K ⁺ , D ⁺ → π ⁻ π ⁺ K ⁺ and D _s ⁺ → π ⁻ K ⁺ K ⁺

The branching fractions of the doubly Cabibbo-suppressed decays D ⁺ → K ⁻ K ⁺ K ⁺ , D ⁺ → π ⁻ π ⁺ K ⁺ and D _s ⁺ → π ⁻ K ⁺ K ⁺ are measured using the decays D ⁺ → K ⁻ π ⁺ π ⁺ and D _s ⁺ → K ⁻ K ⁺ π ⁺ as normalisation channels. The measurements are performed using proton-proton collision data collected with the LHCb detector at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 2.0 fb ⁻¹ . The results areℬ(D+→K−K+K+)ℬ(D+→K−π+π+)=(6.541±0.025±0.042)×10−4,ℬ(D+→π−π+K+)ℬ(D+→K−π+π+)=(5.231±0.009±0.023)×10−3,ℬ(Ds+→π−K+K+)ℬ(Ds+→K−K+π+),=(2.372±0.024±0.025)×10−3, where the uncertainties are statistical and systematic, respectively. These are the most precise measurements up to date.[Figure not available: see fulltext.].