Measurement of the ratio of branching fractions and difference in $CP$ asymmetries of the decays $B^+\to J/\psi\pi^+$ and $B^+\to J/\psi K^+$

The ratio of branching fractions and the difference in CP asymmetries of the decays B$^{+}$ → J/ψπ$^{+}$ and B$^{+}$ → J/ψK$^{+}$ are measured using a data sample of pp collisions collected by the LHCb experiment, corresponding to an integrated luminosity of 3 fb$^{−1}$ at centre-of-mass energies of 7 and 8 TeV. The results are $ \frac{\mathrm{\mathcal{B}}\left({B}^{+}\to J/\psi {\pi}^{+}\right)}{\mathrm{\mathcal{B}}\left({B}^{+}\to J/\psi {K}^{+}\right)}=\left(3.83\pm 0.03\pm 0.03\right)\times {10}^{-2}, $ $ {\mathcal{A}}^{\mathrm{CP}}\left({B}^{+}\to J/\psi {\pi}^{+}\right)-{\mathcal{A}}^{\mathrm{CP}}\left({B}^{+}\to J/\psi {K}^{+}\right)=\left(1.82\pm 0.86\pm 0.14\right)\times {10}^{-2}, $ where the first uncertainties are statistical and the second are systematic. Combining this result with a recent LHCb measurement of $ {\mathcal{A}}^{\mathrm{CP}}\left({B}^{+}\to J/{\psi K}^{+}\right) $ provides the most precise estimate to date of CP violation in the decay B$^{+}$ → J/ψπ$^{+}$, $ {\mathcal{A}}^{\mathrm{CP}}\left({B}^{+}\to J/{\psi \pi}^{+}\right)=\left(1.91\pm 0.89\pm 0.16\right)\times 1{0}^{-2}. $