Measurement of the relative branching fractions of $B^+ to h^+h^{prime +}h^{prime -}$ decays

The relative branching fractions of $B^+ to h^+h^{prime +}h^{prime -}$ decays, where $h^{(prime)}$ is a pion or kaon, are measured. The analysis is performed with a data sample, collected with the LHCb detector, corresponding to an integrated luminosity of $3.0 {rm fb}^{-1}$ of $pp$ collisions. The results obtained improve significantly on previous measurements of these quantities, and are important for the interpretation of Dalitz plot analyses of three-body charmless hadronic decays of $B^+$ mesons.