# Triple collinear emissions in parton showers

## TL;DR

This paper introduces a framework for incorporating triple collinear splitting functions into parton showers, demonstrating its implementation with flavor-changing NLO kernels and validating through numerical simulations in Pythia and Sherpa.

## Contribution

It presents a novel method to include triple collinear emissions and NLO splitting kernels in parton shower algorithms, bridging Monte Carlo and analytic approaches.

## Key findings

- Successful implementation in Pythia and Sherpa
- Explicit correspondence between Monte Carlo and analytic NLO kernels
- Numerical results demonstrating the new algorithm's effectiveness

## Abstract

A framework to include triple collinear splitting functions into parton showers is presented, and the implementation of flavor-changing NLO splitting kernels is discussed as a first application. The correspondence between the Monte-Carlo integration and the analytic computation of NLO DGLAP evolution kernels is made explicit for both timelike and spacelike parton evolution. Numerical simulation results are obtained with two independent implementations of the new algorithm, using the two independent event generation frameworks Pythia and Sherpa.