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

The ratio of branching fractions and the difference in $CP$ asymmetries of the decays $B^{+}\to J\mathrm{/}\psi {\pi }^{+}$ and $B^{+}\to J\mathrm{/}\psi K^{+}$ are measured using a data sample of $pp$ collisions collected by the LHCb experiment, corresponding to an integrated luminosity of $3f{b}^{-1}$ at centre-of-mass energies of 7 and $8\mathrm{T}\mathrm{e}\mathrm{V}$. The results are \begin{equation*} {$\mathcal{B}$(B^+\to J/\psi \pi^+)\over$\mathcal{B}$(B^+\to J/\psi K^+)}=(3.83\pm0.03\pm0.03)\times10^{-2},, \end{equation*} \begin{equation*} $\mathcal{A}$^{CP}(B^+\to J/\psi \pi^+)-$\mathcal{A}$^{CP}(B^+\to J/\psi K^+)=(1.82\pm0.86\pm0.14)\times10^{-2}, \end{equation*} where the first uncertainties are statistical and the second are systematic. Combining this result with a recent LHCb measurement of ${\mathcal{A}}^{CP}(B^{+}\to J\mathrm{/}\psi K^{+})$ provides the most precise estimate to date of $CP$ violation in the decay $B^{+}\to J\mathrm{/}\psi {\pi }^{+}$, \begin{equation*} $\mathcal{A}$^{CP}(B^+\to J/\psi \pi^+) =(1.91\pm0.89\pm0.16)\times10^{-2}. \end{equation*}