CMS luminosity measurement using 2016 proton-nucleus collisions at nucleon-nucleon center-of-mass energy of 8.16 TeV

The calibration of the integrated luminosity delivered to the CMS experiment during the 2016 lead-proton (Pbp) and proton-lead (pPb) periods at $\sqrt{s_{\rm{NN}}}=8.16\ {\rm TeV}$ is presented. Three different subdetectors are used: the forward hadronic calorimeter, the pixel luminosity telescope, and the silicon tracker. Visible cross sections are obtained using the van der Meer procedure for integrating the luminometer rate as a function of beam separation. After taking into account the effects due to horizontal-vertical beam correlations, bunch-to-bunch and scan-to-scan variations, spurious charges, adjustments of the length scale measurements provided by LHC magnet currents, and beam-beam effects, an overall uncertainty of 3.2 (3.7)$\%$ is assessed for the Pbp (pPb) period. The total uncertainty is obtained from the combination of the visible cross sections in the two periods and is found to be 3.5$\%$. Time stability of these calibrations is considered and included in the final systematic uncertainty.