UC Irvine

In a special run of the LHC with β⋆=2.5$$\beta ^{\star } = 2.5$$ km, proton–proton elastic-scattering events were recorded at s=13$$\sqrt{s} = 13$$ TeV with an integrated luminosity of 340μb-1$$340~\upmu {\text {b}}^{-1}$$ 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$$-t = 2.5 \cdot 10^{-4}$$ GeV2$$^{2}$$ to -t=0.46$$-t = 0.46$$ GeV2$$^{2}$$ using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section σtot$$\sigma _{\text {tot}}$$, parameters of the nuclear slope, and the ρ$$\rho $$-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t→0$$t \rightarrow 0$$. 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 σtot$$\sigma _{\text {tot}}$$ and ρ$$\rho $$ are σtot(pp→X)=104.7±1.1mb,ρ=0.098±0.011.$$\begin{aligned} \sigma _{\text {tot}}(pp\rightarrow X) = 104.7 \pm 1.1 \; \text{ mb },\quad \rho = 0.098 \pm 0.011 . \end{aligned}$$The uncertainty in σtot$$\sigma _{\text {tot}}$$ is dominated by the luminosity measurement, and in ρ$$\rho $$ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.