Abstract
We study the solutions to the scattering equations in various quasi-multi-Regge regimes where the produced particles are ordered in rapidity. We observe that in all cases the solutions to the scattering equations admit the same hierarchy as the rapidity ordering, and we conjecture that this behaviour holds independently of the number of external particles. In multi-Regge limit, where the produced particles are strongly ordered in rapidity, we determine exactly all solutions to the scattering equations that contribute to the Cachazo-He-Yuan (CHY) formula for gluon scattering in this limit. When the CHY formula is localised on these solutions, it reproduces the expected factorisation of tree-level amplitudes in terms of impact factors and Lipatov vertices. We also investigate amplitudes in various quasi-MRK. While in these cases we cannot determine the solutions to the scattering equations exactly, we show that again our conjecture combined with the CHY formula implies the factorisation of the amplitude into universal buildings blocks for which we obtain a CHY-type representation.
Highlights
Over the last couple of years several new techniques to compute tree-level scattering amplitudes have been introduced
The aim of this paper is to show that the CHY formalism presents a very natural framework to study other kinematical limits of tree-level amplitudes in gauge theory, namely the so-called Regge limits of a 2-to-(n−2) scattering where the produced particles are ordered in rapidity
In this paper we have initiated the study of Regge kinematics through the lens of the scattering equations and the CHY formula
Summary
Our main objects of interest are tree-level scattering amplitudes for massless particles in an SU(N ) gauge theory. The functional form of the colour-ordered amplitudes is determined by the helicities of the gluons. The arguments of the δ-functions are the scattering equations, which establish a map from a configuration of n massless momenta to the moduli space M0,n fa b=a ka · kb σa−σb. Equation (2.1) is valid for scattering amplitudes in any space-time dimension. We refer to eq (2.4) as the four-dimensional scattering equations They were originally derived from the four-dimensional ambitwistor string model in ref. The tree-level amplitude for n-gluon scattering takes the form [28], n. (2.1) and (2.5) for tree-level amplitudes as CachazoHe-Yuan (CHY) formulas, even though eq (2.5) was originally derived from ambitwistor string theory by Geyer, Lipstein and Mason. Here we always use the convention where {1, 2} ⊆ N
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