Measurement of the $p\overline{p}\to W\gamma +X$ cross section at $\sqrt{s}=1.96$ TeV and $WW\gamma$ anomalous coupling limits

The $WW\gamma$ triple gauge boson coupling parameters are studied using $p\overline{p}\to \ell \nu \gamma +X(\ell =e,\mu )$ events at $\sqrt{s}=1.96$ TeV. The data were collected with the D0 detector from an integrated luminosity of $162{\mathrm{pb}}^{-1}$ delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for $p\overline{p}\to W(\gamma )+X\to \ell \nu \gamma +X$ with $E_T^{\gamma }>8$ GeV and $\Delta {\mathcal{R}}_{\ell \gamma }>$ 0.7 is $14.8\pm 1.6(\mathrm{stat})\pm 1.0(\mathrm{syst})\pm 1.0(\mathrm{lum})\mathrm{pb}$. The one-dimensional $95\%$ confidence level limits on anomalous couplings are $-0.88<\Delta {\kappa }_{\gamma }<0.96$ and $-0.20<{\lambda }_{\gamma }<0.20$.