Running coupling and BFKL pomeron

PACS numbers: 12.38 Cy One of the major issues in the high energy limit of QCD is the problem of interplay between the perturbative and non-perturbative regimes. The BFKL Pomeron in the leading logarithmic approximation [1] results in the equation which exhibits the characteristic diffusion pattern [2]. In the process with two, comparable hard scales (for example γ−γ, or forward jet/π0 in DIS) the distribution of the transverse scales of the gluons broadens with increasing rapidity, with the width ∆t ≃ √ αsY where t = ln k 2/Λ2 with k2 being the transverse momentum of the gluon and Λ being a QCD parameter. Thus, for sufficiently high energies the distribution of the gluon momenta will always reach non-perturbative regime. This picture of diffusion is well rooted in the case of the fixed αs coupling. The effect of subleading corrections [3] is, among other, the running of the QCD coupling. In this case one would expect small modification of the diffusion picture, namely that the distribution of the momenta will develop an asymmetry towards lower scales. The exponent of the cross section gains additional term bαsY 3 apart from the usual leading αsY term, where Y is the rapidity of the process. This picture holds however for rapidities which are not too large. In [4] it has been pointed out that the transition to the non-perturbative regime can occur as a sudden tunneling effect rather than a gradual diffusion process. Instead of slow increase of the width of the distribution of the momenta, one observes a sudden transition from the perturbative scales t ≃ t = lnQ2/Λ2