Subleading Regge limit from a soft anomalous dimension

TL;DR

The paper investigates subleading corrections to the Regge limit of a massive four-point amplitude in planar ${ m N}=4$ SYM on the Coulomb branch. By leveraging dual conformal symmetry and existing three-loop analytic results, the authors show that the leading Regge exponent is governed by the angle-dependent cusp anomalous dimension, and remarkably, the first subleading exponent also exponentiates, suggesting a simple dynamical structure. They propose and test a precise dictionary identifying the subleading Regge trajectory with the scaling dimension of a cusped Wilson loop containing a scalar insertion, providing one- and two-loop perturbative evidence and connecting to the Bremsstrahlung function for high-energy cross-sections. The work offers a pathway to a systematic Regge expansion via Wilson-line/soft-current methods and lays groundwork for further integrability-based and AdS/CFT analyses at higher orders and strong coupling, with potential implications for multi-scale scattering in other theories.

Abstract

Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop with a scalar inserted at the cusp, and we provide perturbative evidence for this proposal. We also analyze other limits of the amplitude and conjecture an exact formula for a total cross-section at high energies.

Figures (12)

• Figure 1: The scattering amplitude $A(s,t,m^2)$ has various physically interesting and overlapping limits. In many of the latter, exact results are known or conjectured (e.g. high-energy limit), while other limits are known to be governed by integrability.
• Figure 2: The amplitude on the left, with four massive $W$ bosons (thick lines) running outside the loop, is equivalent, through eq. (\ref{['cross ratios']}), to an amplitude with unequal-mass bosons. In a limit equivalent to the Regge limit, one of the masses go to zero, revealing infrared divergences within the associated cusp.
• Figure 3: Wilson line with two straight line segments forming a cusp.
• Figure 4: Sample diagrams for the correlator $\langle 0| \, W_{\textrm{cusp},\Phi} | \Phi(p_3) \rangle$. Double, curly and dashed lines represent Wilson lines, gluons and scalars, respectively
• Figure 5: Sample diagrams for the correlator $\langle 0| \, \partial{W}_{\rm cusp} | \Phi(p_3) \rangle$. Double, curly and dashed lines represent Wilson lines, gluons and scalars, respectively