Measurement of theWWγ vertex through single photon production ate+e−colliders

We perform a detailed study of the process ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$→γ${\nu }_{\mathit{l}}$ν${\mathrm{¯}}_{\mathit{l}}$ and its sensitivity to anomalous gauge boson couplings of the γWW vertex. We concentrate on CERN LEP II energies, √s =200 GeV, and energies appropriate to the proposed Next Linear Collider (NLC), a high energy ${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$ collider, with center of mass energies √s =500 and 1 TeV. At 200 GeV, the process offers, at best, a consistency check of other processes being considered at LEP 200. At 500 GeV, the parameters ${\mathrm{\kappa }}_{\gamma }$ and ${\lambda }_{\gamma }$ can be measured to about ±0.05 and ±0.1, respectively, at 95% C.L. while at 1 TeV they can be measured to about ±0.02. At the high luminosities anticipated at high energy linear colliders precision measurements are likely to be limited by systematic rather than statistical errors.