Measurement of the Inelastic Cross Section in Proton-Lead Collisions at $\sqrt{s_{_\mathrm{NN}}}=$ 5.02 TeV

The inelastic hadronic cross section in proton-lead collisions at a centre-of-mass energy pernucleon pair of 5.02 TeV is measured with the CMS detector at the LHC. The data sample,corresponding to an integrated luminosity of $ \mathcal{L} =12.6 \pm 0.4\, \mathrm{nb}^{-1}$, has been collected with an unbiased trigger for inclusive particle production. The cross section is obtained from the measured number of proton-lead collisions with hadronic activity produced in the pseudo rapidity $ \eta $ ranges between 3 and 5 and/or $ -5 $ and $ -3 $, corrected for photon-induced contributions, experimental acceptance,and other instrumental effects. The inelastic cross section is measured to be $\sigma_{\text{inel}} (\text{pPb}) = 2061 \pm 3\, (\mathrm{stat}) \pm 34\, (\mathrm{syst}) \pm 72\, (\mathrm{lumi})\, \mathrm{mb}$. Various Monte Carlo generators, commonly used in heavy ion and cosmic ray physics, are found to reproduce the data within uncertainties. The value of $ \sigma_{\text{inel}} (\text{pPb}) $ is compatible with that expected from the proton-proton cross section at 5.02 TeV scaled up within a simple Glauber approach to account for multiple scatterings in the lead nucleus, indicating that further net nuclear corrections are small