Past exam of the particle physics course of the University of Oxford / 2021 / 6 / b

Count a reference process whose fiducial cross section is accurately calculable. At an electron-positron collider, small-angle Bhabha scattering, dominated by $t$-channel photon exchange, is abundant and provides a standard choice. Require coincident high-energy electron and Positron deposits on opposite sides of the interaction point, with consistent back-to-back directions, and impose precisely specified angular and energy cuts. ThenThe theoretical prediction must include radiation and other relevant electroweak effects under the same event definition. Finite angular resolution, alignment, beam position, live time, trigger efficiency and background contamination enter the uncertainty budget. For small scattering angle $\theta$, $t\simeq -s{\theta }^2/4$ and the leading differential scattering cross-section behaves approximately as $d\sigma /d\theta \propto {\theta }^{-3}$; the inner fiducial angle must therefore be particularly accurately known. Binning these counts in time can also measure the instantaneous collider luminosity.