Initial-Final and Initial-Initial antenna functions for real radiation at next-to-leading order

TL;DR

This paper extends an algorithm for constructing antenna functions to include initial-state partons, explicitly builds all NLO QCD antenna functions, and validates their integration, resulting in more compact and applicable functions for higher-order calculations.

Contribution

It introduces an extended algorithm for initial-state antenna functions, constructs all NLO QCD antennae, and validates their integration, improving applicability for advanced calculations.

Findings

Constructed all NLO QCD antenna functions involving initial states.

Validated antenna functions through integration matching previous methods.

Produced more compact and reduced sets of antenna functions for practical use.

Abstract

The antenna subtraction method has achieved remarkable success in various processes relevant to the Large Hadron Collider. In Reference [1], an algorithm was proposed for constructing real-radiation antenna functions for electron-positron annihilation, directly from specified unresolved limits, accommodating any number of real emissions. Here, we extend this algorithm to build antennae involving partons in the initial state, specifically the initial-final and initial-initial antennae. Using this extended algorithm, we explicitly construct all NLO QCD antenna functions and compare them with previously extracted antenna functions derived from matrix elements. Additionally, we rigorously match the integration of the antenna functions over the initial-final and initial-initial unresolved phase space with the previous approach, providing an independent validation of our results. The improved antenna functions are more compact and reduced in number, making them more readily applicable for higher-order calculations.