Differential luminosity under 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+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. In this paper the authors derive an analytic formula for such a differential luminosity, which agrees very well with computer simulations. A major characteristic of this formula is discussed