DIFFERENTIAL LUMINOSITY UNDER MULTIPHOTON BEAMSTRAHLUNG

For the next generation of e+e- linear colliders in the TeV range, the energy loss due to beam-strahlung during the collision of the e+e- beams 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-gamma-gamma-luminosity. In this paper, we derive analytic formulas for the e+e- and gamma-energy spectra under multiple beam-strahlung process, and the e+e- and gamma-gamma-differential luminosities. Major characteristics of these formulas are discussed.