We complete the calculation of the next-to-leading kernel of the BFKL equation by disentangling its energy-scale dependent part from the impact factor corrections in largek dijet production. Using the irreducible part previously obtained, we derive the final form of the kernel eigenvalue and of the hard Pomeron shift for various scales. We also discuss the scale changes, the physical equivalence of a class of scales, and how to use the collinear safe ones. PACS 12.38.Cy 1 Work supported in part by EU Network contract FMRX-CT98-0194 and by M.U.R.S.T. (Italy) 1The theoretical effort devoted in the past few years [1-10] to the next-to-leading (NL) corrections to the BFKL equation [1], is now approaching its final steps [11,12].After the calculation of the relevant high-energy vertices [2][3][4][5][6][7] by Fadin, Lipatov and other authors, and of the qq part of the kernel [8,10] by the present authors, we computed the eigenvalue of the "irreducible" part of the gluonic kernel [9], by pointing out that the left-over "leading terms", after subtraction of a common scale, would lead to an additional contribution to the kernel, yet to be determined.The purpose of this note is to complete the calculation above with its missing part, and to discuss the energy-scale dependence of the kernel. Our results, which refer to large-k dijet production, are based on the separation of the NL kernel from the one-loop partonic impact factors, recently determined by one of us [11], and depending on some input scale s 0 . For the case s 0 = k 1 k 2 (where the k's are the transverse momenta of the jets), the full kernel derived here agrees with the one recently proposed by Fadin and Lipatov [12], who do not discuss the impact factors' contribution.

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We discuss the small-x behaviour of the next-to-leading BFKL equation, depending on various smoothing out procedures of the running coupling constant at low momenta. While scaling violations (with resummed and calculable anomalous dimensions) turn out to be always consistent with the renormalization group, we argue that the nature and the location of the so-called hard Pomeron are dependent on the smoothing out procedure, and thus really on soft hadronic interactions.PACS 12.38.Cy

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We investigate the consistency requirements of the next-to leading BFKL equation with the renormalization group, with particular emphasis on running coupling effects and NL anomalous dimensions. We show that, despite some model dependence of the bare hard Pomeron, such consistency holds at leading twist level, provided the effective variable α s (t) log(1/x) is not too large. We give a unified view of resummation formulas for coefficient functions and anomalous dimensions in the Q 0 -scheme and we discuss in detail the new one for the qq contributions to the gluon channel.