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The normalized $\xi$ distributions for $E_{\mathrm{HF}} > 4$ and $E_{\mathrm{HF}} > 5$\GeV from MC simulation of inelastic pp collisions using (a) \PYTHIA6, (c) \PYTHIA8, and (e) \textsc{ Phojet}, are shown for the full range of $\xi$. The corresponding efficiencies are shown in (b), (d), and (f), respectively. The cut value of $\xi$ used in this analysis of $5\times10^{-6}$ is shown on the plots as a dashed vertical line.

The normalized $\xi$ distributions for $E_{\mathrm{HF}} > 4$ and $E_{\mathrm{HF}} > 5$\GeV from MC simulation of inelastic pp collisions using (a) \PYTHIA6, (c) \PYTHIA8, and (e) \textsc{ Phojet}, are shown for the full range of $\xi$. The corresponding efficiencies are shown in (b), (d), and (f), respectively. The cut value of $\xi$ used in this analysis of $5\times10^{-6}$ is shown on the plots as a dashed vertical line.

The normalized $\xi$ distributions for $E_{\mathrm{HF}} > 4$ and $E_{\mathrm{HF}} > 5$\GeV from MC simulation of inelastic pp collisions using (a) \PYTHIA6, (c) \PYTHIA8, and (e) \textsc{ Phojet}, are shown for the full range of $\xi$. The corresponding efficiencies are shown in (b), (d), and (f), respectively. The cut value of $\xi$ used in this analysis of $5\times10^{-6}$ is shown on the plots as a dashed vertical line.

The normalized $\xi$ distributions for $E_{\mathrm{HF}} > 4$ and $E_{\mathrm{HF}} > 5$\GeV from MC simulation of inelastic pp collisions using (a) \PYTHIA6, (c) \PYTHIA8, and (e) \textsc{ Phojet}, are shown for the full range of $\xi$. The corresponding efficiencies are shown in (b), (d), and (f), respectively. The cut value of $\xi$ used in this analysis of $5\times10^{-6}$ is shown on the plots as a dashed vertical line.

The normalized $\xi$ distributions for $E_{\mathrm{HF}} > 4$ and $E_{\mathrm{HF}} > 5$\GeV from MC simulation of inelastic pp collisions using (a) \PYTHIA6, (c) \PYTHIA8, and (e) \textsc{ Phojet}, are shown for the full range of $\xi$. The corresponding efficiencies are shown in (b), (d), and (f), respectively. The cut value of $\xi$ used in this analysis of $5\times10^{-6}$ is shown on the plots as a dashed vertical line.

The normalized $\xi$ distributions for $E_{\mathrm{HF}} > 4$ and $E_{\mathrm{HF}} > 5$\GeV from MC simulation of inelastic pp collisions using (a) \PYTHIA6, (c) \PYTHIA8, and (e) \textsc{ Phojet}, are shown for the full range of $\xi$. The corresponding efficiencies are shown in (b), (d), and (f), respectively. The cut value of $\xi$ used in this analysis of $5\times10^{-6}$ is shown on the plots as a dashed vertical line.

Fraction of reconstructed events with more than one track, corrected for efficiency, measured as a function of the number of vertices, in data (dots) and in Monte Carlo (histogram), for instantaneous bunch-crossing luminosities between $0.05\times 10^{30}$ and $0.7\times 10^{30}\percms$.

Fraction of pp events with $n$ pileup vertices, for $n = 0$ to 8, containing more than one charged particle, as a function of instantaneous bunch-crossing luminosity. The dashed lines are the fits described in the text. The data points are plotted at the mean of the differential distribution in each bin.

(a) Values of the inelastic pp cross section $\sigma_\text{inel}$ and (b) their associated goodness of fit $\chi^2/\mathrm{NDOF}$, obtained for each of the fits in Fig.~\ref{fig:final}, as a function of the number of pileup vertices, in interactions with $>1$ track with $\pt > 200$\MeVc and $|\eta| < 2.4$. The line in (a) is the result of a fit to the 9 individual values of $\sigma_\text{inel}$, while the dashed line in (b) indicates $\chi^2/\mathrm{NDOF} = 1$.

The two types of CMS measurements of the inelastic pp cross section (red filled circle and squares) compared to predictions from several Monte Carlo models for different criteria, as labelled below the abscissa axis. The MC predictions have an uncertainty of 1\unit{mb} (not shown). The label \PYTHIA6 (tunes D6T, Z1\_LEP, AMBT1, DW-Pro, and Pro-PT0) and \PYTHIA8 (versions 8.127--8.139, Tunes 2C 8.140 Cor10a, Tune 2M 8.140 Cor10a, and Tune 4C 8.145 Cor10a) indicates several versions that give equivalent results. Other LHC experimental results are also included for comparison.

Comparison of the measured inelastic pp cross sections with predictions of several Monte Carlo models, for different criteria, normalized to the value obtained for $>$3 tracks.