A new standard for the logarithmic accuracy of parton showers

TL;DR

This paper advances the precision of parton shower simulations to NNLL accuracy for event shapes, bridging analytic resummation and shower algorithms, with numerical validation and phenomenological relevance.

Contribution

It introduces a new standard for logarithmic accuracy in parton showers by establishing a relation between NNLL resummation and shower algorithms, validated through numerical tests.

Findings

Achieved NNLL accuracy for a wide class of event-shape observables.

Numerical tests confirm the logarithmic accuracy of three shower variants.

NNLL terms have significant phenomenological impact, aligning with experimental data.

Abstract

We report on a major milestone in the construction of logarithmically accurate final-state parton showers, achieving next-to-next-to-leading-logarithmic (NNLL) accuracy for the wide class of observables known as event shapes. The key to this advance lies in the identification of the relation between critical NNLL analytic resummation ingredients and their parton-shower counterparts. Our analytic discussion is supplemented with numerical tests of the logarithmic accuracy of three shower variants for more than a dozen distinct event-shape observables in $Z \to q \bar q$ and Higgs $\to gg$ decays. The NNLL terms are phenomenologically sizeable, as illustrated in comparisons to data.