Forward-Backward Asymmetry in $pp\rightarrow Z/\gamma^* X\rightarrow e^+e^- X$ Events

This paper describes a study on the measurement of the forward-backward asymmetry in $pp\rightarrow Z/\gamma^* X\rightarrow e^+e^- X$ events with the ATLAS detector for an integrated luminosity of 100 fb$^{-1}$. Such a measurement can be used to determine the effective weak mixing angle, $\sin^{2}\theta^{lept}_{eff}$. We will demonstrate that a very high accuracy on the weak mixing angle, $\delta\sin^{2}\theta^{^{lept}}_{eff}= (1.5(\rm{stat}) \pm 0.3(\rm{exp}) \pm 2.4(\rm{PDF}))\times10^{-4}$, can be reached. This is possible due to the large cross-section for the production of $Z$ bosons at the LHC and by using electron reconstruction in the forward calorimeters of ATLAS (2.5 $< |\eta| <$ 4.9).