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 β* = 2.5 km, proton–proton elastic-scattering events were recorded at $\sqrt{s}=13$ TeV with an integrated luminosity of $340$ μb -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 σ tot , parameters of the nuclear slope, and the p -parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t → 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 σ tot and p are σ tot (pp → X) = 104.7 ± 1.1 mb, p = 0.098 ± 0.011. The uncertainty in σ tot is dominated by the luminosity measurement, and in p by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.