# Combining states without scale hierarchies with ordered parton showers

## TL;DR

This paper introduces a parameter-free method to combine fixed-order multi-jet calculations with parton-shower evolution, achieving accurate jet cross sections without arbitrary ordering constraints or merging scales.

## Contribution

The authors develop a novel, scale-setting scheme and matrix-element correction for unordered phase-space points, enabling seamless combination of fixed-order results with parton showers.

## Key findings

- Achieves leading-order accuracy across complete phase space.
- Resums large logarithms effectively.
- Matches well with LHC data.

## Abstract

We present a parameter-free scheme to combine fixed-order multi-jet results with parton-shower evolution. The scheme produces jet cross sections with leading-order accuracy in the complete phase space of multiple emissions, resumming large logarithms when appropriate, while not arbitrarily enforcing ordering on momentum configurations beyond the reach of the parton-shower evolution equation. This requires the development of a matrix-element correction scheme for complex phase-spaces including ordering conditions as well as a systematic scale-setting procedure for unordered phase-space points. The resulting algorithm does not require a merging-scale parameter. We implement the new method in the Vincia framework and compare to LHC data.