# Parton branching at amplitude level

## TL;DR

This paper introduces a novel algorithm for evolving hard processes at the amplitude level, incorporating collinear, soft, and Coulomb/Glauber exchanges, with potential to surpass leading logarithmic accuracy.

## Contribution

It presents a comprehensive amplitude-level evolution algorithm that includes all orders in color, spin dependence, and kinematic recoils, advancing beyond existing methods.

## Key findings

- Derived DGLAP evolution using the algorithm
- Computed resummed thrust and jet mass distributions
- Demonstrated the handling of Coulomb exchanges in factorisation

## Abstract

We present an algorithm that evolves hard processes at the amplitude level by dressing them iteratively with (massless) quarks and gluons. The algorithm interleaves collinear emissions with soft emissions and includes Coulomb/Glauber exchanges. It includes all orders in $N_{\mathrm{c}}$, is spin dependent and is able to accommodate kinematic recoils. Although it is specified at leading logarithmic accuracy, the framework should be sufficient to go beyond. Coulomb exchanges make the factorisation of collinear and soft emissions highly non-trivial. In the absence of Coulomb exchanges, we show how factorisation works out and how a partial factorisation is manifest in the presence of Coulomb exchanges. Finally, we illustrate the use of the algorithm by deriving DGLAP evolution and computing the resummed thrust, hemisphere jet mass and gaps-between-jets distributions in $e^+ e^-$.