BFKL approach and 2->5 MHV amplitude

TL;DR

The paper addresses high-energy behavior of MHV amplitudes in N=4 SYM using the BFKL framework to compute Mandelstam-cut corrections to the BDS remainder function. It derives a closed integral form for the all-loop leading-logarithmic remainder of the 2→5 amplitude, and provides an analytic two-loop result showing the remainder as a sum of two 2→4 remainders, enabled by recursive impact-factor structure. The authors generalize this iterative structure to 2→2+(n−4) amplitudes, expressing the two-loop remainder in Mandelstam regions where all produced gluons are flipped as a sum over n−5 six-point functions f6, with no BKP-state contributions in these regions. They also discuss other Mandelstam regions and note that the approach extends to N^kMHV amplitudes, while recognizing that the simple two-loop iteration may not persist at higher orders.

Abstract

We study MHV amplitude for the 2 -> 5 scattering in the multi-Regge kinematics. The Mandelstam cut correction to the BDS amplitude is calculated in the leading logarithmic approximation (LLA) and the corresponding remainder function is given to any loop order in a closed integral form. We show that the LLA remainder function at two loops for 2 -> 5 amplitude can be written as a sum of two 2 -> 4 remainder functions due to recursive properties of the leading order impact factors. We also make some generalizations for the MHV amplitudes with more external particles. The results of the present study are in agreement with all leg two loop symbol derived by Caron-Huot as shown in a parallel paper of one of the authors with collaborators.

Figures (17)

• Figure 1: The $2 \to 5$ amplitude. The produced particles $k_i$ are strongly ordered in rapidity in the multi-Regge kinematics.
• Figure 2: Mandelstam region of the $2 \to 5$ amplitude with a non-vanishing contribution of the discontinuities in $s$ and $s_{123}$ to the remainder function.
• Figure 3: The $2 \to 5$ amplitude factorized into blocks. $\Phi_i$ represent impact factors, $G_{BFKL}$ illustrates propagation of the BFKL state and $C$ denotes the central emission block. The dashed line stands for the discontinuity in $s_{123}$.
• Figure 4: The impact factor $\Phi_2$ in Fig. \ref{['fig:impact7']}.
• Figure 5: Decomposition of $2 \to 5$ amplitude into two impact factors and a central emission block. The dashed lines denote insertions of the BFKL eigenvalue.