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The $B^{\pm}$ meson production asymmetry in $pp$ collisions is measured using$B^+ \to \bar{D}^0 \pi^+$ decays. The data were recorded by the LHCb experimentduring Run 1 of the LHC at centre-of-mass energies of $\sqrt{s}=$ 7 and 8 TeV.The production asymmetries, integrated over transverse momenta in the range $2< p_{\rm T} < 30$ GeV/$c$, and rapidities in the range $2.1 < y < 4.5$, aremeasured to be  \begin{align*} \mathcal{A}_{\rm prod}(B^+,\sqrt{s}=7~{\rm TeV}) &= (-0.41 \pm0.49 \pm 0.10) \times 10^{-2},\\ \mathcal{A}_{\rm prod}(B^+,\sqrt{s}=8~{\rmTeV}) &= (-0.53 \pm 0.31 \pm 0.10) \times 10^{-2},  \end{align*} where the first uncertainties are statistical and the second aresystematic. These production asymmetries are used to correct the rawasymmetries of $B^{+} \to J/\psi K^{+}$ decays, thus allowing a measurement ofthe $CP$ asymmetry, \begin{equation*}  \mathcal{A}_{CP} = (0.09 \pm 0.27 \pm 0.07) \times 10^{-2}.  \end{equation*}

Measurement of the $B^{\pm}$ production asymmetry and the $CP$ asymmetry in $B^{\pm} \to J/\psi K^{\pm}$ decays