A closer look at the beam-beam processes at ILC and CLIC
  The strength of the electromagnetic fields in the bunch collision at a linear collider will have a significant effect, yielding large numbers of beamstrahlung photons and associated coherent pair production. These effects are limited in the proposed ILC beam parameters which limit the strength of the bunch field to $\Upsilon_{\text{ave}}=0.27$. The CLIC 3 Tev design by comparison has a $\Upsilon_{\text{ave}}=3.34$ yielding huge number of coherent pairs. In terms of the precision physics programs of these proposed colliders there is an imperative to investigate the effect of the strong bunch fields on higher order processes. From the exact wavefunctions used in the calculation of transition rates within the Furry interaction picture, and using appropriate simplifications, a multiplicative factor to the coupling constants was obtained. This indicates a significant variation to the transition rate near threshold energies. Further studies are in progress to calculate the exact effect on expected observables. 
Anthony Hartin
physics.acc-ph