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The branching fraction and direct asymmetry of the decay are measured using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7 and 8 TeV, corresponding to a total integrated luminosity of 3. The following results are obtained: \begin{align} (B^{+}\rightarrow J/\psi \rho^{+}) &= (3.81 ^{+0.25}{-0.24} \pm 0.35) \times 10^{-5}, \nonumber \ ^{C!P} (B^{+}\rightarrow J/\psi \rho^{+}) &= -0.045^{+0.056}{-0.057} \pm 0.008, \nonumber \end{align} where the first uncertainties are statistical and the second systematic. Both measurements are the most precise to date.

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