Past exam of the particle physics course of the University of Oxford / 2021 / 5 / c

Use a clean Z boson sample with final-state radiation, $Z\to e^{+}{e}^{-}\gamma$, and independently calibrated electron four-momenta. For measured $P=p_{e^{+}}+p_{e^{-}}$ and measured photon direction ${\hat{n}}_{\gamma }$, write $p_{\gamma }=E_{\gamma }(1,{\hat{n}}_{\gamma })$. The known Z boson mass suppliesComparing the reconstructed photon energy with this prediction constrains its scale versus energy, detector position and conversion status. In practice fit the $e^{+}{e}^{-}\gamma$ invariant mass distribution, allowing for the physical Z boson decay width, detector response and backgrounds, instead of assigning every event exactly $M_Z$. Select final-state-radiation topologies: an initial-state-radiation photon is not part of the Z boson decay and generally does not satisfy the same mass constraint. The calibration applies over the populated photon energy range; extrapolation to still higher energies needs a validated response model.