On Third-Order Timelike Splitting Functions and Top-Mediated Higgs Decay into Hadrons

TL;DR

This paper calculates third-order timelike splitting functions in QCD and confirms the N^3LO Higgs decay rate into hadrons, advancing precision in perturbative predictions for high-energy processes.

Contribution

It introduces NNLO timelike splitting functions for quark and gluon evolution and confirms the N^3LO Higgs decay rate, linking spacelike and timelike processes in QCD.

Findings

Computed NNLO timelike splitting functions for quark and gluon channels.

Confirmed N^3LO Higgs decay rate into hadrons.

Analyzed the end-point behavior and numerical size of corrections.

Abstract

We employ relations between spacelike and timelike deep-inelastic processes in perturbative QCD to calculate the next-to-next-to-leading order (NNLO) contributions to the timelike quark-quark and gluon-gluon splitting functions for the evolution of flavour-singlet fragmentation distributions. We briefly address the end-point behaviour and the numerical size of these third-order corrections, and write down the second moments of all four timelike splitting functions. In the same manner we re-derive the NNLO result for the Higgs-boson decay rate into hadrons in the limit of a heavy top quark and five massless flavours, and confirm the recent N^3LO computation of this quantity.