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

In a special run of the LHC with $\beta^\star = 2.5~$km, proton-protonelastic-scattering events were recorded at $\sqrt{s} = 13~$TeV with anintegrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA subdetectorof ATLAS in 2016. The elastic cross section was measured differentially in theMandelstam $t$ 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. Thispaper presents measurements of the total cross section $\sigma_{\textrm{tot}}$,parameters of the nuclear slope, and the $\rho$-parameter defined as the ratioof the real part to the imaginary part of the elastic-scattering amplitude inthe limit $t \rightarrow 0$. These parameters are determined from a fit to thedifferential elastic cross section using the optical theorem and differentparameterizations of the $t$-dependence. The results for$\sigma_{\textrm{tot}}$ and $\rho$ are \begin{equation*}\sigma_{\textrm{tot}}(pp\rightarrow X) = \mbox{104.7} \pm 1.1 \; \mbox{mb} , \;\; \; \rho = \mbox{0.098} \pm 0.011 . \end{equation*} The uncertainty in$\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, and in$\rho$ by imperfect knowledge of the detector alignment and by modelling of thenuclear amplitude.