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

The ratio of branching fractions and the difference in $CP$ asymmetries of the decays $B^+to J/psi pi^+$ and $B^+to J/psi K^+$ are measured using a data sample of $pp$ collisions collected by the LHCb experiment, corresponding to an integrated luminosity of $3~{{,mbox{fb}^{-1}}}$ at centre-of-mass energies of 7 and $8~mathrm{,Tekern -0.1em V}$. The results are begin{equation*} {mathcal{B}(B^+to J/psi pi^+)overmathcal{B}(B^+to J/psi K^+)}=(3.83pm0.03pm0.03)times10^{-2},, end{equation*} begin{equation*} mathcal{A}^{CP}(B^+to J/psi pi^+)-mathcal{A}^{CP}(B^+to J/psi K^+)=(1.82pm0.86pm0.14)times10^{-2}, end{equation*} where the first uncertainties are statistical and the second are systematic. Combining this result with a recent LHCb measurement of $mathcal{A}^{CP}(B^+to J/psi K^+)$ provides the most precise estimate to date of $CP$ violation in the decay $B^+to J/psi pi^+$, begin{equation*} mathcal{A}^{CP}(B^+to J/psi pi^+) =(1.91pm0.89pm0.16)times10^{-2}. end{equation*}