Energy Spectrum of Electron-Positron Pairs Produced via the Trident Process, with Application to Linear Colliders in the Deep Quantum Regime

Explicit expressions for the energy spectrum of e+/- pairs produced via the trident process are derived using the quasi-classical approach of Baier, Katkov, and Strakhovenko (BKS). We examine the relevance of the trident process to the design of very high energy (Ecm several TeV) linear colliders having high (Upsilon ~ 100 to several thousand). We use our calculation of the energy spectrum of the pairs to estimate the maximum expected deflection of pair-produced particles having the same sign as the oncoming bunch in a linear collider. We also compare our results for the total pair production probability with the results obtained using formulas for very high Upsilon used previously in the literature on linear colliders. The agreement is very good at extremely high Upsilon, but in the range of Upsilon noted above, our result for the total trident pair production rate is about a factor of two lower than the corresponding approximate result in the literature.