Abstract
We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2 → 5 amplitude in planar mathcal{N}=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N -particle MHV amplitude in this region to a function, we specialize to N = 7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.
Highlights
Where the limit corresponds to a center-of-mass energy squared s being much larger than the momentum transfer |t|, the necessity for the respective amplitude to behave as
We will give a brief overview of the main aspects of a convolution-based method to compute amplitudes in Multi-Regge kinematics (MRK), introduced in [69], and how it can be adapted for computations beyond leading logarithmic approximation (LLA)
Focusing on the 2 → 5 amplitude, we first succeeded in describing it in this limit in terms of the all-loop dispersion integral (3.37)–(3.38), or equivalently (3.51), which has a well-defined weak-coupling expansion, overcoming regularization issues that arose in previous attempts beyond LLA
Summary
Let us start by recalling the precise definition of the limit and the kinematic region we will be considering, mostly following the conventions of [69]. ABNDS denotes the tree-level amplitude of the given helicity, times the same scalar factor that is present in the BDS amplitude for the MHV case, encoding the universal infrared-divergent structure of amplitudes in N = 4 super Yang-Mills theory Due to their equivalence to bosonic Wilson loops, the MHV and MHV ratios are equal to each other, and are alternatively described by their logarithm, the remainder function, R+ . In this paper we will be focusing on the regions where all produced particles have their energy components flip sign under analytic continuation, which amounts [74, 77] to transforming a single cross-ratio as follows, u ≡ U2,N−1 → e−2πiU2,N−1.
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