$D$-Dimensional Modular Assembly of Higher-Derivative Four-Point Contact Amplitudes Involving Fermions

TL;DR

This paper introduces a systematic, modular framework for constructing D-dimensional four-point higher-derivative contact amplitudes involving fermions, compatible with gauge invariance, symmetries, and the double-copy program.

Contribution

The authors develop a novel modular approach that simplifies the construction of higher-derivative amplitudes directly in D dimensions, incorporating evanescent operators and avoiding combinatorial complexity.

Findings

Framework operates entirely in D dimensions, including evanescent operators.

Constructs amplitudes from gauge-invariant blocks, color factors, and Mandelstam polynomials.

Compatible with double-copy, enabling systematic generation of operator towers.

Abstract

We present a novel robust framework for systematically constructing $D$-dimensional four-point higher-derivative contact amplitudes. Our modular block ("LEGO"-like) approach builds amplitudes directly from manifestly gauge-invariant kinematic blocks, color-weight factors, and scalar Mandelstam polynomials. Symmetries (Bose/Fermi) are imposed algebraically, acting as filters on combinations of compatible pieces. This framework operates entirely in $D$ dimensions, naturally incorporating evanescent operators crucial for loop-level consistency. Scaling to arbitrary mass dimension is achieved in a highly controlled manner using permutation-invariant scalar polynomials, avoiding combinatorial explosion. A key feature is its manifest compatibility with the double-copy program, allowing the systematic generation of operator towers not only for gauge theories but also for gravity and other theories within the double-copy web.