Non-resonant diagrams in radiative four-fermion processes
  The complete tree level cross section for $e^+e^- \to e^- \bar\nu_e u \bar{d} \gamma$ is computed and discussed in comparison with the cross sections for $e^+e^- \to e^- \bar\nu_e u \bar{d} $ and $e^+e^- \to \bar{u} d u \bar{d}$. Event generators based on the GRACE package for the non-radiative and radiative case are presented. Special interest is brought to the effect of the non-resonant diagrams overlooked so far in other studies. Their contribution to the total cross section is presented for the LEP II energy range and for future linear colliders ($\sqrt s$ =500 GeV). Effects, at the W pair threshold, of order 3\% ($e^- \bar\nu_e u \bar{d}$) and 27\% ($\bar{u} d u \bar{d}$) are reported. Similar behaviour for the radiative case is shown. At $\sqrt s$ = 500 GeV, the relative contribution of the non-resonant diagrams for the radiative channel reaches 42.5\%. 
J. Fujimoto, T. Ishikawa, S. Kawabata, Y. Kurihara, Y. Shimizu D.   Perret-Gallix