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

In a special run of the LHC with β = 2.5 β ⋆ = 2.5 km, proton–proton elastic-scattering events were recorded at √s = 13 s = 13 TeV with an integrated luminosity of 340~ b⁻¹ 340 μ 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 - t = 2.5 · 10 - 4 GeV ² 2 to $$-t = 0.46$$ - t = 0.46 GeV ² 2 using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section σ ₜₒₜ σ tot , parameters of the nuclear slope, and the ρ ρ -parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t → 0 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 σ tot and ρ ρ are aligned σ ₜₒₜ(pp→ X) = 104.7 ± 1.1 \; mb , ρ = 0.098 ± 0.011 . aligned σ tot ( p p → X ) = 104.7 ± 1.1 mb , ρ = 0.098 ± 0.011 . The uncertainty in σ ₜₒₜ σ tot is dominated by the luminosity measurement, and in ρ ρ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.