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

Tag an energetic initial-state radiation photon in $e^{+}{e}^{-}\to \gamma Z^{(\ast )}\to \gamma +\text{invisible}$, observing a single-photon signature with missing energy and missing momentum. At known squared center-of-mass energy $s$, the leading single-photon recoil invariant mass isAbove the Z boson mass, radiative-return events cluster at $m_{\mathrm{recoil}}\simeq M_Z$. At or near the pole the full off-shell recoil spectrum is fitted instead. Folding the Breit-Wigner resonance cross section with the calculable QED radiation kernel gives a predicted tagged rate proportional to ${\Gamma }_e{\Gamma }_{\mathrm{inv}}$ for fixed total decay width. A fit with the known luminosity and visible line-shape parameters therefore determines ${\Gamma }_{\mathrm{inv}}$ directly from invisible events, rather than subtracting visible widths. Comparing identically selected radiative-return events with visible Z boson decays can instead constrain ${\Gamma }_{\mathrm{inv}}/{\Gamma }_{\mathrm{vis}}$ while cancelling much of the luminosity normalization.

The detector needs efficient single-photon triggering, good photon energy and angular resolution, reliable timing, and nearly hermetic charged-particle and particle calorimeter coverage. Forward vetoes reject radiative Bhabha scattering with escaped electrons; additional-photon vetoes reject $\gamma \gamma$ events with a lost photon. Require sufficient transverse photon momentum that a recoiling visible system could not all disappear down a beam hole. Timing rejects cosmic rays and beam backgrounds. Detector inefficiencies and beam holes must be measured, since visible final states with lost particles imitate the signal. The irreducible $e^{+}{e}^{-}\to {\nu }_e{\bar{\nu }}_e\gamma$ contribution from $t$-channel W boson exchange and its interference must be included when isolating the Z boson invisible decay width.