Analytic structure of the $n = 7$ scattering amplitude in $\mathcal{N}=4$ SYM theory in multi-Regge kinematics: Conformal Regge cut contribution

TL;DR

The work provides a complete weak-coupling construction of the analytic structure for the $n=7$ scattering amplitude in planar $\mathcal{N}=4$ SYM under multi-Regge kinematics. It develops a systematic Regge-pole plus Regge-cut framework, deriving the trigonometric coefficients and employing energy-discontinuity unitarity to obtain conformally invariant Regge-cut amplitudes $f_{\omega_2}$, $f_{\omega_3}$ and $f_{\omega_2\omega_3}$. By analyzing all Mandelstam regions, the authors show that Regge cuts are essential to cancel unphysical singularities and yield IR-finite, conformal remainder functions $R_{7;\tau_i\tau_j...}$ in every region. The results bridge weak- and strong-coupling analyses and lay groundwork for extending the calculation to NLO while maintaining conformal invariance.

Abstract

In this second part of our investigation of the analytic structure of the $2\to5$ scattering amplitude in the planar limit of $\mathcal{N}=4$ SYM in multi-Regge kinematics we compute, in all kinematic regions, the Regge cut contributions in leading order. The results are infrared finite and conformally invariant.

Figures (14)

• Figure 1: Terms without Regge cuts. For the produced particles we also use the labels $a,b,c$.
• Figure 2: Terms which contain Regge cut contributions: two doublets (a) and (b)
• Figure 3: Terms which contain Regge cut contributions: two triplets (c) and (d)
• Figure 4: Mandelstam criterion for the Regge cut in the $2\to4$ scattering amplitude (wavy lines denote reggeons, straight lines scalar particles). (a) the simplest diagram illustrating the Mandelstam criterion (b) a generalization (enhanced diagram) in which the propagators $a$ and $a'$ are replaced by sets of ladder diagrams (reggeons).
• Figure 5: The RPRR production vertex