Measurement of the total cross section from elastic scattering in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector

This paper presents a measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV. In a special run with high $\beta^\star$, beam optics, an integrated luminosity of $80$ $\mu$b$^{-1}$ was accumulated in order to measure the differential elastic cross section as a function of the Mandelstam momentum transfer variable $t$. The measurement is performed in the range from $-t=0.0025$ GeV$^2$ to $-t=0.38$ GeV$^2$, with the ALFA sub-detector of ATLAS. From the extrapolation of the elastic $t$-spectrum to $|t|\rightarrow 0$, the total cross section $\sigma_\mathrm{tot}(pp\rightarrow X)$ is measured using the optical theorem to be \begin{equation*} \sigma_\mathrm{tot}(pp\rightarrow X) = \mbox{95.35} \; \pm 0.38 \; ({\mbox{stat.}}) \pm 1.25 \; ({\mbox{exp.}}) \pm 0.37 \; (\mbox{extr.}) \; \mbox{mb} \; \; , \end{equation*} where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties on the extrapolation to $|t| \rightarrow 0$. In addition, the nuclear slope is determined to be $B = 19.73 \pm 0.14 \; ({\mbox{stat.}}) \pm 0.26 \; ({\mbox{syst.}}) \; $GeV$^{-2}$