Towards understanding bb¯ production in γγ collisions

The data on the total cross section σₜₒₜ(e⁺e^-→e⁺e^-bb̄) measured at LEP2 represent a serious challenge for perturbative QCD. In order to understand the origin of the excess of data over QCD calculations, we investigate the dependence of the four contributions to this cross section on γγ collision energy. As the reliability of the existing calculations of σₜₒₜ(e⁺e^-→e⁺e^-bb̄) depends, among other things, on the stability of the calculations of the cross section σₜₒₜ(γγ→bb̄) with respect to variations of the renormalization and factorization scales, we investigate this aspect in detail. We show that in most of the region relevant for the LEP2 data the existing QCD calculations of the cross section σₜₒₜ(γγ→bb̄) do not exhibit a region of local stability. A possible source of this instability is suggested.