Multi-channel phase space with Feynman-diagram-gauge amplitudes

Abstract

Multi-channel phase space with a single Feynman diagram enhancement is a powerful tool for high-energy physics event generation if a diagram with a singular propagator dominates the total scattering amplitude at the corresponding singular kinematical region, and when the interference among amplitudes is not larger than the square of each amplitude. These conditions are satisfied in the Feynman-diagram-gauge amplitudes for both unbroken (QED and QCD) and broken (EW) gauge theories. We illustrate the usefulness of this method in lepton collider processes that are challenging to accurately simulate at very high energies, i.e., $ l\bar{l} \to \nu_l \bar{\nu}_l t\bar{t} H $, $ l \bar{\nu}_l t\bar{b} H $, and $ l \bar{l} t\bar{t} H $, in the SMEFT with a complex top-Yukawa coupling. The total cross sections of the latter two processes contain lepton-mass singularities arising from $t$-channel photon-exchange diagrams. To address this issue, we develop a phase-space parametrization that accurately generates the distributions of forward-emitted charged leptons. We modify the \HELAS\ library to evaluate helicity amplitudes in the singular region so that vertices at very small invariant momentum square of order $m_e^2$ can be accurately evaluated even at multi-TeV energies.