Differential luminosity under multiphoton beamstrahlung.

+ For the next generation of e e linear colliders in the TeV range, the energy loss due to beamstrahlung during the collision of the e+ebeams is expected to be substantial. One consequence is that the center-of-mass energy between the colliding particles can be largely degraded from the designed value. The knowledge on the differential luminosity as a function of the center-of-mass energy is essential for particle physics analysis on the interesting events. On the other hand, the beamstrahlung photon spectrum provides useful information on the low energy backgrounds and high energy yy luminosity. In this paper, we derive analytic formulas for the e+eand y energy spectra under multiple beamstrahlung process, and the e’eand yy differential luminosities. Major characteristics of these formulas are discussed. Submitted to Physical Review D1. * Work supported by Department of Energy contra.ct DE-AC03-76SF00515. . .