Matching Z $\to$ Hadrons at NNLO with Sector Showers

TL;DR

This paper develops a detailed method for matching NNLO calculations with sectorized parton showers in Z-boson decays, improving the accuracy of jet rate predictions through advanced subtraction techniques.

Contribution

It introduces a full subtraction-based calculation of the matching coefficient at NNLO for sector showers, optimizing numerical evaluation and including interference effects.

Findings

Accurate NNLO matching conditions derived for sector showers.

Optimized subtraction method improves numerical stability.

Inclusion of interference effects enhances prediction precision.

Abstract

We present a detailed technical derivation of matching conditions at next-to-next-to-leading order in the sectorised VINCIA parton shower, by considering leading-colour 2-, 3- and 4-jet rates in hadronic Z-boson decays. In particular, we introduce a full subtraction-based calculation of the matching coefficient required to obtain the NLO 3-jet rate. This is achieved through a judicious choice of the counter-terms, which optimises the numerical evaluation of the subtracted double-real matrix element. We additionally give a consistent prescription for incorporating interference effects due to higher-order mixing between Born states with different flavour contents. Finally, we briefly comment on higher-order uncertainty estimates.