Towards tree Yang-Mills and Yang-Mills-scalar amplitudes with higher-derivative interactions

TL;DR

This paper extends a soft behavior-based approach to construct tree-level Yang-Mills and Yang-Mills-scalar amplitudes with higher-derivative interactions, proposing a universal expansion and a conjectured general formula.

Contribution

It introduces a new method for constructing higher-derivative Yang-Mills amplitudes and proposes a conjecture for a compact general formula for these amplitudes.

Findings

Constructed tree YM and YMS amplitudes with $F^3$ and $F^4$ operators.

Represented results as universal expansions in an appropriate basis.

Proposed a conjecture for a compact formula generating higher-mass-dimension YM amplitudes.

Abstract

In our recent works, a new approach for constructing tree amplitudes, based on exploiting soft behaviors, was proposed. In this paper, we extend this approach to effective theories for gluons which incorporate higher-derivative interactions. By applying our method, we construct tree Yang-Mills (YM) and Yang-Mills-scalar (YMS) amplitudes with the single insertion of $F^3$ local operator, as well as the YM amplitudes those receive contributions from both $F^3$ and $F^4$ operators. All results are represented as universal expansions to appropriate basis. We also conjecture a compact general formula for tree YM amplitudes with higher mass dimension, which allows us to generate them from ordinary YM amplitudes, and discuss the consistent factorizations of the conjectured formula.