# Measurement of the inelastic $pp$ cross-section at a centre-of-mass energy of 13 TeV

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## Abstract

The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13 TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum $p>2$ GeV/$c$ in the pseudorapidity range $2<\eta<5$ is determined to be $\sigma_{\rm acc}= 62.2 \pm 0.2 \pm 2.5$ mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section $\sigma_{\rm inel}= 75.4 \pm 3.0 \pm 4.5$ mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7 TeV is also reported.

## Figures and captions

 Overall fiducial cross-section (vertical line), compared to the averages of the individual results in different LHC fills. The error bars indicate the statistical uncertainties. The grey band indicates the systematic uncertainty on the overall average due to the unfolding parameter $\alpha$. The $\chi^2$-values for the averages inside a fill are calculated with only the statistical uncertainties and the number of degrees of freedom ($\rm ndf$) is one less than the number of individual results contributing to the average. Systematic uncertainties inferred from the observed spread between the fills are discussed in the text. Fig1.pdf [8 KiB] HiDef png [215 KiB] Thumbnail [70 KiB] *.C file Posterior densities of (left) the cross-section fractions $f_X$ for non-diffractive (ND) double-diffractive (DD) and single-diffractive (SD=SDA+SDB) contributions, and (right) of the extrapolation factor $F_{\rm T}$. Fig2.pdf [10 KiB] HiDef png [122 KiB] Thumbnail [31 KiB] *.C file Measurement of the total inelastic proton-proton cross-section at the LHC at centre-of-mass energies of 2.76, 7, 8 and 13 TeV. Results are shown from the ALICE [8], ATLAS [9,10,11,12] and TOTEM [16,17,18,19,20,21] collaborations. For better visibility, measurements at the same energy are drawn at slightly displaced locations. The error bars show the total uncertainties, with positive and negative uncertainties of the respective results independently added in quadrature. The line shows the result from a power-law fit. Fig3.pdf [7 KiB] HiDef png [65 KiB] Thumbnail [20 KiB] *.C file Animated gif made out of all figures. PAPER-2018-003.gif Thumbnail

## Tables and captions

 Summary of systematic uncertainties on the fiducial cross-section. For the contribution from the unfolding parameter $\alpha$ a breakdown into the individual components is given. Table_1.pdf [25 KiB] HiDef png [87 KiB] Thumbnail [13 KiB] tex code Properties of Pythia {} 8.230 proton-proton tunes. Mean values and standard deviations are given for the fractions $f_X$ of the inelastic cross-section, the fractions $v_X$ of interactions inside the acceptance and, for those interactions, the average numbers of long-lived prompt charged particles $n_{{\rm ch},X}$ inside the acceptance. Table_2.pdf [39 KiB] HiDef png [71 KiB] Thumbnail [10 KiB] tex code

## Supplementary Material [file]

 Supplementary material full pdf supple[..].pdf [954 KiB] SupplFig1.pdf [761 KiB] HiDef png [1 MiB] Thumbnail [107 KiB] *C file SupplFig2.pdf [22 KiB] HiDef png [181 KiB] Thumbnail [58 KiB] *C file SupplFig3.pdf [28 KiB] HiDef png [321 KiB] Thumbnail [106 KiB] *C file SupplFig4.pdf [35 KiB] HiDef png [328 KiB] Thumbnail [87 KiB] *C file SupplFig5.pdf [35 KiB] HiDef png [328 KiB] Thumbnail [87 KiB] *C file

Created on 16 February 2019.Citation count from INSPIRE on 16 February 2019.