BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes (0802.2065v5)

Abstract: After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are investigated, in order to verify their self-consistency. It is found that, for the number of external particles being larger than five, these amplitudes, beyond one loop, are not in agreement with the BFKL approach which predicts the existence of Regge cuts in some physical channels.

• The paper refines the BFKL framework by calculating NNLO corrections and detailing Reggeized gluon interactions in QCD and supersymmetric models.
• It employs an effective action approach to probe the geometric properties of high-energy MHV scattering and the limitations of the BDS ansatz.
• The findings elucidate anomalous dimensions and integrability in N=4 super Yang-Mills theory, providing insights for enhanced scattering predictions.

Analysis of the BFKL Pomeron in Supersymmetric Gauge Theories and High Energy Scattering Amplitudes

The paper by Bartels et al. offers a comprehensive examination of Regge theory processes within the framework of Quantum Chromodynamics (QCD) and supersymmetric (SUSY) gauge theories, with a specific focus on the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron and the interactions of Reggeized gluons. A robust strategy is proposed for calculating the next-to-next-to-leading order (NNLO) corrections to the BFKL kernel. The authors leverage the effective action approach for high-energy scattering and investigate the intricate geometric properties of scattering amplitudes, notably the Bern-Dixon-Smirnov (BDS) ansatz employed in maximal helicity violations (MHV).

Key Components of the Paper

• BFKL Approach: The paper revisits the BFKL methodology, examining the elastic scattering amplitude in QCD at high energies in the leading logarithmic approximation (LLA). It meticulously addresses the Regge form and gluon Regge trajectory.
• Reggeized Gluon Interactions: Various cross-sections for the interactions of Reggeized gluons are derived, forming a pivotal part of understanding higher-order corrections to the BFKL kernel. Multi-Regge kinematics and factorization properties become central themes as the paper explores MHV amplitudes in this regime.
• Anomalous Dimensions and Integrability: The authors explore the integrability of supersymmetric models, presenting the anomalous dimension calculations for twist-2 operators and emphasizing the integrability reflected in Heisenberg spin models.
• Bern-Dixon-Smirnov Ansatz: The investigation centers on the BDS ansatz for scattering amplitudes in $N=4$ super Yang-Mills theory, assessing its analytic properties at high energies and validating self-consistency. It discusses the limitations of these amplitudes with external particles numbering beyond five, where discrepancies with BFKL predictions about Regge cuts arise.

Numerical Results and Methodological Insights

The authors provide a meticulous comparison of numerical results derived from the BDS amplitude with known high-energy limits of QCD scattering amplitudes. Key findings indicate that while the BDS formula agrees with the one-loop approximation, it fails to encapsulate certain contributions beyond this level due to missing Regge cut elements in specific high-energy kinematic regions.

Theoretical Implications and Future Directions

This paper's implications are numerous, contributing pivotally to the theoretical understanding of high-energy scattering in supersymmetric gauge theories. These include:

• Refinement of BFKL Calculations: The approach developed here can potentially refine the NNLO corrections to the BFKL equations impacting phenomenological predictions.
• Analyzing Regge Cuts: Understanding Regge cuts in amplitudes offers a deeper insight into scattering theories beyond simple reggeization models, aligning unitarity sums with realistic atomic collision models.
• Supersymmetry and Analytic Structure: The breakdown of factorization within the BDS ansatz signals susceptibilities in supersymmetric calculations, indicating further improvements are needed in predicting scattering processes involving numerous external particles.

Practical Impact on AI and Computational Models

For AI and computational theoretical physics, these findings hold potential for enhancing algorithmic complexity modeling within high-energy physics simulations and refining computation strategies based on gauge invariance and reggeization principles.

In conclusion, Bartels et al.'s extensive paper provides foundational tools and stratagems to explore multi-particle scattering at high energies, particularly within the context of $N=4$ SUSY, highlighting significant discrepancies within BDS amplitudes and paving paths for future explorations into the richly complex domain of quantum field theory.