Efficiencies for different particle species in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the simulated sample generated with the magnetic field pointing upwards. The product of the efficiency and the particle charge in units of the elementary charge is shown to separate values for oppositely charged particles. The light-grey areas indicate the limit of the kinematic acceptance.

Efficiency corrections, $R_\varepsilon $, for positively and negatively charged particles in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the simulated sample generated with the magnetic field pointing upwards. The bands indicate the systematic uncertainty. The light-grey areas represent the limit of the kinematic acceptance. The gap between this limit and the correction is due to the tighter requirement of ${ p > 5\text{ Ge V /}c }$ applied to the control measurements on which this correction is based.

Origins of the candidate tracks in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the simulated sample generated with the magnetic field pointing upwards. The prompt category refers to the signal tracks, while the other categories correspond to non-prompt tracks originating from the listed parent particles and include both decays and material interactions. Fake tracks are indicated by the white areas above the stacked histograms. The light-grey areas represent the limit of the kinematic acceptance.

Distributions of $P_\mathrm{fake}$ in a kinematic interval (left) at low $ p_{\mathrm{T}}$ and (right) at high $ p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing upwards and the simulated sample with the same magnetic-field configuration. The statistical uncertainty of the data is indicated by error bars, but they are not visible on these scales. The purity of the proxy is shown in the lower panels, where light-grey boxes represent the $P_\mathrm{fake}$ interval selected to determine the proxy. Vertical lines indicate the threshold ${P_\mathrm{fake} < 0.3}$ for candidate tracks. The normalisation of the simulated sample is described in Sect. 3.

Ratio of the proxies for fake tracks in data and simulation in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing upwards and the simulated sample with the same magnetic-field configuration. The error bars indicate the statistical uncertainty, and the boxes indicate the systematic uncertainty. The light-grey areas represent the limit of the kinematic acceptance.

Ratio of the proxies for material interactions in data and simulation and purity of the proxy in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing upwards and the simulated sample with the same magnetic-field configuration. The quantities are shown separately for positively and negatively charged particles. The error bars indicate the statistical uncertainty, and the boxes indicate the systematic uncertainty. The points are slightly displaced horizontally within the $ p_{\mathrm{T}}$ intervals to increase the visibility. The dashed grey lines represent the purity threshold. The larger points indicate the median value computed from the intervals above the threshold. The light-grey areas represent the limit of the kinematic acceptance.

Mass distributions of (left) $ K ^0_{\mathrm{S}}$ and (right) $\Lambda$ candidates in one kinematic interval for (top) the LHC fill recorded with the magnetic field pointing upwards and (bottom) the simulated sample with the same magnetic-field configuration. Solid lines indicate the total fit and dotted lines the background. In the case of simulation, the signal and background contributions are shown for illustration, but this information is not used in the analysis.

Ratio of the proxies for strange-hadron decays in data and simulation in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing upwards and the simulated sample with the same magnetic-field configuration. The $\mathit{ V^0 }$ model lines indicate the interpolated $ K ^0_{\mathrm{S}}$ , $\Lambda$ and $\overline{ \Lambda}$ yield ratios, with support points indicated by black dots. The lines labelled as products represent the proxy ratio of the decay products, with the bands representing the propagated systematic uncertainty. The light-grey areas indicate the limit of the kinematic acceptance.

Leading sources of relative uncertainties of the number of prompt long-lived charged particles in intervals of $\eta$ and as a function of $ p_{\mathrm{T}}$ for the LHC fill recorded with the magnetic field pointing upwards. The total uncertainty, represented by the grey envelopes, excludes the uncertainty of the integrated luminosity of $2.0 \%$. The light-grey areas indicate the limit of the kinematic acceptance.

Differential cross-section of inclusive production of prompt long-lived charged particles in intervals of pseudorapidity, $\eta$, and as a function of transverse momentum, $ p_{\mathrm{T}}$ . The error bars indicate the total uncertainty. The ratios of the model predictions and this measurement are shown in the lower panels. The lines labelled as Pythia 8.1 LHCb correspond to the occupancy-weighted simulated samples of this analysis.

Ratios of the differential cross-sections of inclusive production of prompt long-lived positively and negatively charged particles as a function of transverse momentum and pseudorapidity for the data and the models shown in Fig. 10.

Correlation matrix for the uncertainties of the differential cross-section of prompt inclusive production of long-lived charged particles. The four large quadrants correspond to the correlations between negatively and positively charged particles. The 36 cells within each quadrant correspond to the $\eta$ intervals. In each cell, the correlations of the $ p_{\mathrm{T}}$ intervals are shown from low to high $ p_{\mathrm{T}}$ in logarithmic intervals.

Animated gif made out of all figures.

Statistical and systematic uncertainties affecting the measured differential cross-section.

Inelastic cross-sections used in the models of which the predictions are compared with this measurement and values from recent measurements at the LHC .