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 $340\phantom{\rule{3.33333pt}{0ex}}\mu {\text{b}}^{-1}$ using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from $-t=2.5·{10}^{-4}$ 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 $\begin{array}{c}{\sigma }_{\text{tot}}\left(pp\to X\right)=104.7±1.1\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.333333em}{0ex}}\text{mb}\phantom{\rule{0.333333em}{0ex}},\phantom{\rule{1em}{0ex}}\rho =0.098±0.011.\end{array}$ 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.