Resummation of Singlet Parton Evolution at Small x

Abstract

We propose an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach. We obtain a stable expansion for the x-evolution function chi(M) near M=0 by including in it a sequence of terms derived from the one- and two-loop anomalous dimension gamma. The requirement of momentum conservation is always satisfied. The residual ambiguity on the splitting functions is effectively parameterized in terms of the value of lambda, which fixes the small x asymptotic behaviour x^-lambda of the singlet parton distributions. We derive from this improved evolution function an expansion of the splitting function which leads to good apparent convergence, and to a description of scaling violations valid both at large and small x.

16 pages, 6 figures, LaTeX with epsfig; final version, to be published in Nucl. Phys. B. A few typos corrected for the record

References in corpus (17)

• BFKL pomeron in the next-to-leading approximation
• A resummation of large sub-leading corrections at small x
• The Infrared Behavior of One-Loop Gluon Amplitudes at Next-to-Next-to-Leading Order
• The 3-loop QCD calculation of the moments of deep inelastic structure functions
• The QCD Pomeron with Optimal Renormalization
• The BFKL Equation at Next-to-Leading Order and Beyond
• Irreducible part of the next-to-leading BFKL kernel
• The Evolution of Unpolarized Singlet Structure Functions at Small x
• k-Factorization and Small-x Anomalous Dimensions
• NLO BFKL Equation, Running Coupling and Renormalization Scales
• Asymptotically Free Partons at High Energy
• Rapidity veto effects in the NLO BFKL equation
• Real next-to-leading corrections to the multigluon amplitudes in the helicity formalism
• Rapidity-Separation Dependence and the Large Next-to-Leading Corrections to the BFKL Equation
• Perturbative Evolution and Regge Behaviour
• Virtual Next-to-Leading Corrections to the Impact Factors in the High-Energy Limit
• Small x resummations confronted with F_2(x,Q^2) data

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