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At an electron-positron collider tuned to the charmonium resonance, select the mixed leptonic tau lepton decaysand their charge conjugates. Require exactly two well-reconstructed oppositely charged tracks, one identified electron and one identified muon, little extra visible activity, visible energy below the beam total, and significant missing momentum pointing into the instrumented region. The multiple neutrinos prevent full reconstruction of each tau lepton, but the known initial four-momentum, lepton spectra and missing energy support a statistical signal extraction. Off-resonance data constrain nonresonant electron-positron annihilation into a tau lepton pair; that continuum is present at both beam energies.^[ref]

A resonant muon pair is one possible detector background: one muon can be misidentified as an electron, while radiation escaping along the beam or a badly measured track produces apparent missing energy. Particle-identification requirements and rejection of almost back-to-back tracks near the beam momentum suppress it. This background needs detector mismeasurement; an ideal measurement would distinguish it.

Above the open-charm threshold, $\psi (3770)\to D\bar{D}$ supplies an additional resonant background. Semileptonic decays of the two D mesons can give an electron, a muon and neutrinos; unreconstructed hadrons let some events pass the selection. This on-shell D meson-pair background is kinematically forbidden at $\psi (3686)$.

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.