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

A measurement of the total $pp$ cross section at the LHC at $\sqrt{s}=7$ TeV is presented. 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 with the ALFA sub-detector of ATLAS. Using a fit to the differential elastic cross section in the $\mathrm{\mid }t\mathrm{\mid }$ range from 0.01 GeV${}^2$ to 0.1 GeV${}^2$ to extrapolate to $\mathrm{\mid }t\mathrm{\mid }\to 0$, the total cross section, ${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}(pp\to X)$, is measured via the optical theorem to be: $${\sigma }_{\mathrm{t}\mathrm{o}\mathrm{t}}(pp\to X)=95.35\pm 0.38(stat\mathrm{.})\pm 1.25(exp\mathrm{.})\pm 0.37(extr\mathrm{.})mb,$$ where the first error is statistical, the second accounts for all experimental systematic uncertainties and the last is related to uncertainties in the extrapolation to $\mathrm{\mid }t\mathrm{\mid }\to 0$. In addition, the slope of the elastic cross section at small $\mathrm{\mid }t\mathrm{\mid }$ is determined to be $B = 19.73 \pm 0.14 ; ({\mbox{stat.}}) \pm 0.26 ; ({\mbox{syst.}}) ; \mbox{GeV}^{-2}$.