Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills

L. N. Lipatov, A. Prygarin

TL;DR

The paper analyzes the planar N=4 SYM six-point MHV amplitude in Regge kinematics via its remainder function, performing an analytic continuation of the two-loop result to the Mandelstam region. It derives the NLO BFKL octet impact factors and computes the three-loop remainder in both leading (LLA) and next-to-leading (NLLA) logarithmic accuracy, expressing results through complex variables and dual cross-ratios. The work demonstrates consistency between the BFKL framework and the Wilson-loop/scattering-amplitude duality at LL A, while providing new NLLA information and NLO impact factors that enhance the understanding of high-energy behavior in this theory. These findings yield explicit, symmetry-respecting higher-order structures with potential implications for precision tests of the amplitude/Wilson loop duality and high-energy QCD-inspired approaches in supersymmetric settings.

Abstract

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2 -> 4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops.

BFKL approach and six-particle MHV amplitude in N=4 super Yang-Mills

TL;DR

The paper analyzes the planar N=4 SYM six-point MHV amplitude in Regge kinematics via its remainder function, performing an analytic continuation of the two-loop result to the Mandelstam region. It derives the NLO BFKL octet impact factors and computes the three-loop remainder in both leading (LLA) and next-to-leading (NLLA) logarithmic accuracy, expressing results through complex variables and dual cross-ratios. The work demonstrates consistency between the BFKL framework and the Wilson-loop/scattering-amplitude duality at LL A, while providing new NLLA information and NLO impact factors that enhance the understanding of high-energy behavior in this theory. These findings yield explicit, symmetry-respecting higher-order structures with potential implications for precision tests of the amplitude/Wilson loop duality and high-energy QCD-inspired approaches in supersymmetric settings.

Abstract

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2 -> 4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops.

Paper Structure

This paper contains 20 sections, 168 equations, 6 figures.

Table of Contents

  1. Introduction
  2. BFKL approach
  3. Analytic continuation
  4. NLO impact factor
  5. Three loops in LLA and NLLA
  6. Conclusion
  7. Acknowledgments
  8. Polylogarithms of $u_i$
  9. Polylogarithms of $x^\pm$ and $x_i^\pm$
  10. Logarithms of $x_i^{+}x_i^{-}$
  11. Polylogarithms of $x_1^{\pm}$
  12. Polylogarithms of $x_2^{\pm}$
  13. Polylogarithms of $x_3^{\pm}$
  14. Continuation of $J$
  15. Leading Logarithmic Approximation (LLA)
  16. ...and 5 more sections

Figures (6)

  • Figure 1: The BDS violating contribution appears in the region $s,s_2>0;\,s_1,s_3<0$.
  • Figure 2: The "unitarity" triangle.
  • Figure 3: The dual coordinates of the transverse momenta.
  • Figure 4: The region of the reduced cross ratios where the analytic continuation is performed.
  • Figure 5: The surface $\Delta =0$ is the boundary of the physical values of cross ratios.
  • ...and 1 more figures