# Threshold Resummation at NNLL for Single-particle Production in Hadronic Collisions

## TL;DR

This paper develops a high-precision threshold resummation method at NNLL accuracy for single-particle production in hadronic collisions, including full two-loop matching and detailed soft function calculations.

## Contribution

It introduces a comprehensive NNLL threshold resummation framework with complete two-loop hard and soft function calculations for all partonic channels.

## Key findings

- NLO expansions match exact NLO results very well.
- Two-loop corrections significantly impact many kinematic configurations.
- Explicit Mellin space results facilitate resummation implementation.

## Abstract

We develop threshold resummation for single-particle inclusive cross sections in hadron-hadron collisions to the level of next-to-next-to-leading logarithm, up to full matching with two-loop hard functions. We define and calculate all one-loop soft functions for all partonic channels. This enables us to separate the hard and soft functions at one loop. Along with these results, the one-loop finite parts of jet functions are used to check that the full soft, collinear and virtual corrections are reproduced to one loop for all partonic reactions. We exhibit these NLO results explicitly. NLO expansions of the resummed cross section match the exact NLO results extremely well numerically, and two loop expansions result in substantial corrections over many kinematic configurations. Explicit results are given in Mellin moment space, and a number of options for generating resummed cross sections are discussed.