The Effect of Higher Order Corrections to the BFKL Equation on the Perturbative Pomeron

We discuss the significance of the next-to-leading order term in the BFKL equation on the energy dependence of diffractive processes controlled by the perturbative QCD pomeron. It is shown that whereas the large negative corrections do indeed reduce the rate of growth of diffractive amplitudes with increasing energy, this reduction is considerably less than previously expected. SHEP-98/06 April 1998 In a recent paper Fadin and Lipatov [1] have presented, in compact form, the results of the higher order corrections to the BFKL [2, 4] equation. The solution to this equation is the amplitude, f(s, t,k, k), for the scattering of two gluons with transverse momenta k and k respectively, centre-of-mass energy √ s and square momentum transfer t, in the ‘diffractive region’ where s ≫ |t|. It may be written ∂ ∂ ln s f(s, t,k, k′) = ∫ dlK(t,k, l)f(s, t, l, k′). (1) We are interested here in the forward scattering amplitude required for total cross-sections or deep-inelastic structure functions and so we henceforth set t = 0 and suppress it. The solutions to Eq.(1) are found through the identification of a complete set of eigenfunctions, φν(k), of the kernel K and their corresponding eigenvalues, ω(ν)