General expressions for extra-dimensional tree amplitudes and all-plus 1-loop integrands in Q-cut representaion

TL;DR

This paper derives compact expressions for a special class of Yang-Mills tree amplitudes involving extra-dimensional momenta and positive helicity gluons, and constructs the 1-loop all-plus integrand in Q-cut form.

Contribution

It provides the first general formulas for these specific tree amplitudes and their use in forming the complete 1-loop all-plus integrand in Q-cut representation.

Findings

Derived compact spinor helicity expressions for special tree amplitudes.

Used BCFW recursion to prove the formulas.

Constructed the 1-loop all-plus integrand in Q-cut form.

Abstract

In this paper, we give the general expressions for a special series of tree amplitudes of the Yang-Mills theory. This series of amplitudes have two adjacent massless spin-1 particles with extra-dimensional momenta and any number of positive helicity gluons. With special helicity choices, we use the spinor helicity formalism to express these n-point amplitudes in compact forms, and find a clever way to use the BCFW recursion relations to prove the results. Then these amplitudes are used to form the complete 1-loop all-plus integrand with any number of gluons, expressed in the Q-cut representation.