Measurement of the branching fractions of the decays D⁺ → K ⁻ K⁺ K ⁺ , D⁺ → π ⁻ π ⁺ K⁺ + and Dₛ ⁺ → π⁻ K⁺ K ⁺ [Measurement of the branching fractions of the decays D+ -> K-K+K+, D+ -> pi-pi(+) K+ and D-s(+) -> pi-K+K+]

The branching fractions of the doubly Cabibbo-suppressed decays D + \u2192 K 12 K + K + , D + \u2192 \u3c0 12 \u3c0 + K + and D s+ \u2192 \u3c0 12 K + K + are measured using the decays D + \u2192 K 12 \u3c0 + \u3c0 + and D s+ \u2192 K 12 K + \u3c0 + 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 121 . The results are\u212c(D+\u2192K 12K+K+)\u212c(D+\u2192K 12\u3c0+\u3c0+)=(6.541\ub10.025\ub10.042) 710 124,\u212c(D+\u2192\u3c0 12\u3c0+K+)\u212c(D+\u2192K 12\u3c0+\u3c0+)=(5.231\ub10.009\ub10.023) 710 123,\u212c(Ds+\u2192\u3c0 12K+K+)\u212c(Ds+\u2192K 12K+\u3c0+),=(2.372\ub10.024\ub10.025) 710 123, where the uncertainties are statistical and systematic, respectively. These are the most precise measurements up to date.[Figure not available: see fulltext.]