On the 2nd Order Corrections to the Hard Pomeron and the Running Coupling Constant

Abstract

It is shown that solutions to the 2nd order BFKL eigenvalue equation exist for arbitrary large real values of the complex angular momentum $j$. This corresponds to a cut in the complex $j$ plane along the whole real axis, and it makes the use of the complex angular momentum variable for the calculation of the high-energy behavior somewhat questionable. The eigenfunctions contain non-perturbative pieces which behave as $\exp (-1/{\alpha }_{s}b)$ and have no counterpart in the leading-log BFKL equation. The high-energy behavior of the 2nd order BFKL Green function as found by other authors, is reproduced by excluding these non-perturbative pieces of the eigenfunctions.

19 pages, 2 figures

References in corpus (4)

• BFKL pomeron in the next-to-leading approximation
• The Effect of Higher Order Corrections to the BFKL Equation on the Perturbative Pomeron
• Model (In)dependent Features of the Hard Pomeron
• Limitations on using the operator product expansion at small values of x

Cited by in corpus (41)

• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• The Large Hadron-Electron Collider at the HL-LHC
• A New Odderon Solution in Perturbative QCD
• The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution
• Renormalisation group improved small-x Green's function
• Numerical analysis of the Balitsky-Kovchegov equation with running coupling: dependence of the saturation scale on nuclear size and rapidity
• Factorization and Resummation of Small x Scaling Violations with Running Coupling
• An anomalous dimension for small x evolution
• An "all-poles" approximation to collinear resummations in the Regge limit of perturbative QCD
• The quark part of the non-forward BFKL kernel and the ``bootstrap'' for the gluon Reggeization
• Heavy Quark Production at High Energy
• The Running Coupling BFKL Anomalous Dimensions and Splitting Functions
• The Gluon Impact Factors
• The Quark Impact Factors
• NLO BFKL Equation, Running Coupling and Renormalization Scales
• Extending QCD perturbation theory to higher energies
• Resummation of Hadroproduction Cross-sections at High Energy
• Rapidity-Separation Dependence and the Large Next-to-Leading Corrections to the BFKL Equation
• The Gluon Green's Function in the BFKL Approach at Next-to-Leading Logarithmic Accuracy
• Expanding running coupling effects in the hard Pomeron
• Electroproduction of two light vector mesons in next-to-leading BFKL: study of systematic effects
• Solving the BFKL Equation in the Next-to-Leading Approximation
• Tunneling transition to the Pomeron regime
• Collinear improvement of the BFKL kernel in the electroproduction of two light vector mesons
• Infrared safety of impact factors for colourless particle interactions
• One-loop Reggeon-Reggeon-gluon vertex at arbitrary space-time dimension
• Solution of the NLO BFKL Equation and a Strategy for Solving the All-Order BFKL Equation
• The Small x Behaviour of Altarelli-Parisi Splitting Functions
• A modified Balitsky-Kovchegov equation
• ${\gamma }^{\ast }{\gamma }^{\ast }$ Cross Section at NLO and Properties of the BFKL Evolution at Higher Orders
• Diffusion corrections to the hard pomeron
• The Gluon Green's Function in N=4 Supersymmetric Yang-Mills Theory
• Non-linear equation: energy conservation and impact parameter dependence
• The Challenge of Small x
• High energy amplitude as an admixture of "soft" and "hard" Pomerons
• Heavy quark impact factor in kT-factorization
• Non-Forward BFKL at Next-to-Leading Approximation
• Describing F_2 through a finite sum of gluon ladders
• Exploring the DGLAP resummation in the JIMWLK Hamiltonian
• Low x and diffraction: theory
• Properties of inclusive hadron production in Deep Inelastic Scattering on heavy nuclei at low x