A Numerical Estimate of the Small-kT Region in the BFKL Pomeron

A computer study is performed to estimate the influence of the small-kT region in the BFKL evolution equation. We consider the small-x region of the deep inelastic structure function F2 and show that the magnitude of the small-kT region depends on Q 2 and xB. We suggest that the width of the log k T -distribution in the final state may serve as an additional footprint of BFKL–dynamics. For diffractive dissociation it is shown that the contribution of the infrared region is large even for large Q. This contribution becomes smaller only if restrictions on the final state are imposed. 1.) Deep inelastic electron proton scattering at HERA has put strong emphasis on small-x physics. Both the observed rise of F2 at small x and the discovery of the large rapidity gap events have raised the question of how to connect these observations with the perturbative Balitskii, Fadin, Kuraev, Lipatov (BFKL) Pomeron [1] and the (nonperturbative) soft Pomeron [2] seen in hadron hadron scattering at high energies. In the context of the deep inelastic structure functions the BFKL Pomeron suggests the possibility of calculating, for a not too small momentum scale Q0, the x-dependence of the input gluon distribution which then enters the DGLAP [3] evolution equations. The main result is the powerlike increase xg(x,Q2) ∼ (1/x)BFKL with ωBFKL = Ncαs π 4 log 2 ≈ 0.5. Such an increase is consistent with the data, but the preferred power is slightly smaller: for the gluon distribution xg(x,Q2) the observed power lies in the interval ωexp = 0.3...0.4 [4], and for F2 one finds a power in the range 0.2...0.4. A recent analysis [4] leads to the conclusion that the experimental results are compatible with the BFKL interpretation, but the evidence is not yet compelling. Unfortunately, numerical predictions based upon the BFKL approximation have several principal uncertainties. Most important is the observation that, as a result of the diffusion of log k2 T , the internal transverse momenta of the BFKL ladders may become arbitrarily small, and the contribution from this region of phase space cannot be extracted reliably within the leading logarithmic approximation. One expects that in this region higher order corrections will be very important, and ∗Supported by Bundesministerium für Forschung und Technologie, Bonn, Germany under Contract 05 6HH93P(5) and EEC Program ”Human Capital and Mobility” through Network ”Physics at High Energy Colliders” under Contract CHRX-CT93-0357 (DG12 COMA)