Beam-size 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 modified. The corresponding formulas for such a beam-size effect were given 20 years ago without taking into account correlations of particle coordinates in the beams. In the present paper we derive formulas necessary to take into account quantitatively the effect of particle correlations in the spectrum of bremsstrahlung as well as in pair production. Our results are quite different from those obtained in recent papers [V. N. Baier and V. M. Katkov, Phys. Rev. D 66, 053009 (2002)PRVDAQ0556-282110.1103/PhysRevD.66.053009; V. N. Baier and V. M. Katkov, hep-ph/0305304.]. We point out the origin of this difference.