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Register a new userThe Next-to-Leading BFKL Pomeron with Optimal Renormalization
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Victor T. Kim
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The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at the CERN LEP2.
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The next-to-leading order (NLO) corrections to the BFKL equation in the BLM optimal scale setting are briefly discussed. A striking feature of the BLM approach is rather weak Q^2-dependence of the Pomeron intercept, which might indicate an approximate conformal symmetry of the equation. An application of the NLO BFKL resummation for the virtual gamma-gamma total cross section shows a good agreement with recent L3 data at CERN LEP2 energies.
We determine an approximate expression for the O(alpha_s^3) contribution chi_2 to the kernel of the BFKL equation, which includes all collinear and anticollinear singular contributions. This is derived using recent results on the relation between the GLAP and BFKL kernels (including running-coupling effects to all orders) and on small-x factorization schemes. We present the result in various schemes, relevant both for applications to the BFKL equation and to small-x evolution of parton distributions.
On the basis of previous work by Fadin, Lipatov, and collaborators, and of our group, we extract the irreducible part of the next-to-leading (NL) BFKL kernel, we compute its (IR finite) eigenvalue function, and we discuss its implications for small-x structure functions. We find consistent running coupling effects and sizable NL corrections to the Pomeron intercept and to the gluon anomalous dimension. The qualitative effect of such corrections is to smooth out the small-x rise of structure functions at low values of Q2. A more quantitative analysis will be possible after the extraction of some additional, energy-scale dependent contributions to the kernel, which are not treated here.
In this lecture the next-to-leading order (NLO) corrections to the QCD Pomeron intercept obtained from the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation are discussed. It is shown that the BFKL Pomeron intercept when evaluated in non-Abelian physical renormalization schemes with Brodsky-Lepage-Mackenzie (BLM) optimal scale setting does not exhibit the serious problems encountered in the modified minimal subtraction (bar{MS}) scheme. The results obtained provide an opportunity for applications of the NLO BFKL resummation to high-energy phenomenology. One of such applications for virtual gamma-gamma total cross section shows a good agreement with preliminary data at CERN LEP.
On the basis of a renormalization group analysis of the kernel and of the solutions of the BFKL equation with subleading corrections, we propose and calculate a novel expansion of a properly defined effective eigenvalue function. We argue that in this formulation the collinear properties of the kernel are taken into account to all orders, and that the ensuing next-to-leading truncation provides a much more stable estimate of hard Pomeron and of resummed anomalous dimensions.
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