Beam-size or MD-effect at colliders and correlations of particles in a beam

Abstract

For several processes at colliding beams, macroscopically large impact parameters give an essential contribution to the standard cross section. These impact parameters may be much larger than the transverse sizes of the colliding bunches. In that case, the standard calculations have to be essentially modify. The corresponding formulae for such a beam-size effect were given twenty years ago without taking into account correlations of particle coordinates in the beams. In the present paper we derive formulae which necessary to take into account quantitatively the effect of particle correlations in the spectrum of bremsstrahlung as well as in pair production. Besides, we consider critically recent papers of Baier and Katkov [Phys. Rev. D {\bf 66}, 053009 (2002) and hep-ph/0305304] in which it was calculated a new additional ``subtraction term'' related to the coherent contribution into beam-size effect. We show that this result is groundless and point out the origin of the mistake.