Measurement of the total cross section and $\rho$-parameter from elastic scattering in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Abstract

In a special run of the LHC with ${\beta }^{\star }=2.5$km, proton-proton elastic-scattering events were recorded at $\sqrt{s}=13$TeV with an integrated luminosity of $340\mu {\text{b}}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam $t$ variable in the range from $-t=2.5\cdot 10^{-4}$GeV${}^2$ to $-t=0.46$GeV${}^2$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section ${\sigma }_{\text{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit $t\to 0$. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the $t$-dependence. The results for ${\sigma }_{\text{tot}}$ and $\rho$ are \begin{equation*} σ_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \pm 1.1 \; \mbox{mb} , \; \; \; ρ= \mbox{0.098} \pm 0.011 . \end{equation*} The uncertainty in ${\sigma }_{\text{tot}}$ is dominated by the luminosity measurement, and in $\rho$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.

55 pages in total, 26 figures, 13 tables, submitted to EPJC. All figures including auxiliary figures are available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2018-08/

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• Results on Elastic Cross Sections in Proton-Proton Collisions at $\sqrt{s}=510$ GeV with the STAR Detector at RHIC
• Geometric scaling of elastic $pp$ cross section at the LHC
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