A numerical estimate of the small-kT region in the BFKL pomeron

Abstract

A computer study is performed to estimate the influence of the small-k T region in the BFKL evolution equation. We consider the small-x region of the deep inelastic structure function F 2 and show that the magnitude of the small-k T region depends on Q 2 and x B . We suggest that the width of the log k 2 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 2 . 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 F 2 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 Q 2 0 , 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, Q 2 ) ∼ (1/x) ω BFKL with ω BFKL = 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, Q 2 ) the observed power lies in the interval ω exp = 0.3...0.4 [4], and for F 2 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 k 2 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 *

The γ∗γ∗ total cross section and the BFKL Pomeron at e+e− colliders

“…In addition, the diffusion in log k 2 T always leads to a nonzero contribution of small transverse momenta where the use of the leading logarithmic approximation becomes doubtful. A numerical estimate shows that for the forward jets at HERA [3] the contribution from this dangerous infrared region is reasonably small, whereas in the case of F 2 [4] the situation is much less favorable. As to the experimental situation, a recent analysis of HERA data [5,6] on the production of forward jets shows a very encouraging agreement between data and the theoretical prediction.…”

Baryon stopping and valence quark distribution at small x

“…The problem with summing the ladder graphs is justifying a weak coupling expansion [32]. If the coupling is weak, then such diagrams indeed generate the leading order contribution.…”

Small-x one-particle-inclusive quantities in the CCFM approach

“…BFKL evolution is not ordered in transverse momentum, as a result of which diffusion in transverse momentum [11][12][13] leads to significant dependence on the infra-red region, where the perturbative series is irretrievably out of control.…”