Tree amplitudes and color decomposition in broken SU(2)

TL;DR

This paper introduces a color decomposition method for tree-level scattering amplitudes in a spontaneously broken SU(2) gauge theory, enabling efficient calculations involving gauge bosons and the Higgs boson.

Contribution

It presents a novel color decomposition framework in broken SU(2) gauge theory with explicit gauge-invariant primitive amplitudes and efficient recursive computation methods.

Findings

Primitive amplitudes are gauge-invariant and maintain unitarity.

The method efficiently computes multi-W-boson scattering amplitudes.

Demonstrated calculations include five, six, and nine W-boson scattering processes.

Abstract

We propose a color decomposition for general tree amplitudes in a SU(2) gauge theory which is spontaneously broken via the Higgs mechanism. Working in the unitary gauge, we construct color-ordered amplitudes by explicitly presenting a set of color-ordered Feynman rules. Those primitive amplitudes are gauge-invariant, and they preserve perturbative unitarity in the high-energy limit. Serving as building blocks of color-dressed tree amplitudes, they allow for efficient evaluation of tree-level scattering amplitudes involving gauge bosons and the Higgs boson via the Berends-Giele recursion relations for color-ordered currents. We demonstrate the efficiency of this computational scheme by calculating on-shell amplitudes for scattering of five, six and nine W-bosons in the limit of vanishing Weinberg angle.