Measurement of the ratio of branching fractions and difference in CP asymmetries of the decays $B^+$ → $J/ψπ^+$ and $B^+$ → $J/ψK^+$
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 B ( B + →<!-- → --> J / ψ<!-- ψ --> π<!-- π --> + ) B ( B + →<!-- → --> J / ψ<!-- ψ --> K + ) = ( 3.83 ±<!-- ± --> 0.03 ±<!-- ± --> 0.03 ) ×<!-- × --> 10 −<!-- - --> 2 , A C P ( B + →<!-- → --> J / ψ<!-- ψ --> π<!-- π --> + ) −<!-- - --> A C P ( B + →<!-- → --> J / ψ<!-- ψ --> K + ) = ( 1.82 ±<!-- ± --> 0.86 ±<!-- ± --> 0.14 ) ×<!-- × --> 10 −<!-- - --> 2 , where the first uncertainties are statistical and the second are systematic. Combining this result with a recent LHCb measurement of $A^{CP}$ ($B^+$ → $J/ ψK^+$) provides the most precise estimate to date of $CP$ violation in the decay $B^+$ → $J/ψπ^+$, A C P ( B + →<!-- → --> J / ψ<!-- ψ --> π<!-- π --> + ) = ( 1.91 ±<!-- ± --> 0.89 ±<!-- ± --> 0.16 ) ×<!-- × --> 1 0 −<!-- - --> 2 .