Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics

TL;DR

This thesis advances the precision of Higgs boson amplitude calculations in QCD by deriving higher-order corrections with full quark mass dependence, including complex two-loop processes involving elliptic integrals.

Contribution

It introduces new methods to compute two-loop Higgs amplitudes with full quark mass dependence, including elliptic integral structures, and derives third-order corrections for Higgs-bottom quark interactions.

Findings

Derived third-order corrections to Higgs-bottom quark form factor.

Computed two-loop $H\to Z\gamma$ decay width with full quark mass dependence.

Developed a method for series expansions of elliptic Master Integrals.

Abstract

In this thesis, higher-order corrections to the perturbative expansions of scattering amplitudes involving the Higgs boson in the framework of Quantum Chromodynamics are evaluated, where we focus on processes that are mediated through heavy-quark loops. First, we derive the third-order corrections to the form factor describing the Yukawa coupling of a Higgs boson to a pair of bottom quarks. Furthermore, we compute the two-loop corrections to the $H\to Z\,\gamma$ decay width by retaining the full dependence on the internal quark mass. Finally, we describe the calculation of the planar Master Integrals relevant to the two-loop amplitude for Higgs-plus-jet production with full quark mass dependence. We accomplish this by establishing a method to derive series expansions from differential equations, since the set of Master Integrals involves elliptic structures.