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, 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_{$\text{tot}$}(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.