Measurement of the total cross section and $\rho$-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, elastic scattering events were recorded at $\sqrt{s} = 13$ TeV with an integrated luminosity of $340~\mu \textrm{b}^{-1}$ using the ALFA sub-detector 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 $\sigma_{\textrm{tot}}$, parameters of the nuclear slope, and the $\rho$-parameter defined as the ratio of the real to imaginary part of the elastic scattering amplitude in the limit $t \rightarrow 0$. 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 $\sigma_{\textrm{tot}}$ 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 for $\sigma_{\textrm{tot}}$ is dominated by the luminosity measurement, while for $\rho$ by the knowledge of the detector alignment and the modelling of the nuclear amplitude.