Measurement of the instrumental asymmetry for $K^{-}\pi^{+}$-pairs at LHCb in Run 2

The instrumental asymmetry between $K^- \pi^+$ and $K^+ \pi^-$-pairs at the LHCb detector is evaluated using data collected in proton-proton collisions at the LHC at a centre-of-mass energy of $13\mathrm{\,Te\kern -0.1em V}$ in 2015 and 2016. To measure this asymmetry, Cabibbo-favoured $D^+ \to {\kern 0.2em\overline{\kern -0.2em K}{}}{}^0 \pi^+$ and $D^+\to K^- \pi^+\pi^+$ decays are used. The efficiency of recording these decay modes has increased with the start of Run-2 data taking. With these improvements the phase-space-integrated $K^- \pi^+$ asymmetry is measured with below-permille statistical precision: \begin{align*} A^{\mathrm{det}}(K^{-}\pi^+) = (-0.89 \pm 0.15 \mathrm{\,(stat)} \pm 0.06 \mathrm{\,(syst)})\% \ \rm{in} \ 2015, \\ A^{\mathrm{det}}(K^{-}\pi^+) = (-1.03 \pm 0.06 \mathrm{\,(stat)} \pm 0.06 \mathrm{\,(syst)})\% \ \rm{in} \ 2016. \end{align*}The dependence of $A^{\mathrm{det}}(K^{-}\pi^+)$ on the kaon momentum is evaluated, along with its sensitivity to the LHCb magnet configuration. Finally, the results are compared with the expected asymmetry determined from the known differences in cross sections of kaons with the detector material. This measurement forms the most precise data-driven determination of the charge bias in the detection of particles at LHCb.