# A1a Quark-mass effects in Higgs-boson production in gluon fusion

Principal investigators
Prof. Michal Czakon RWTH Aachen University
Prof. Robert Harlander RWTH Aachen University

### Subject

Gluon fusion is the dominant Higgs-boson production mode at the LHC. Its theoretical understanding directly impacts the extraction of the Higgs-boson couplings from experimental measurements. In this project, we aim for a full control of quark-mass effects in gluon fusion, both at the inclusive and at the differential level. This includes the calculation of the top- and bottom-quark mass effects for the inclusive total cross section at NNLO QCD, i.e. ${\cal O}(\alpha_s^4)$, but also the differential partonic cross section at NLO QCD, which also corresponds to ${\cal O}(\alpha_s^4)$. In parallel to the exact evaluation of these quantities, we will also approach the problem through approximations by evaluating and combining the amplitudes in characteristic kinematical limits. The complementarity of these two approaches will provide us with deeper insights into the structure of the dominant corrections, and possible ways to go beyond the fixed-order results.

### Topics

1. Gluon fusion cross section: exact evaluation of top- and bottom-quark mass effects; total and differential cross section at $\mathcal{O}(\alpha_s^4)$
2. Kinematical limits: expansions around threshold, high energy, large and small quark mass; interpolations among these limits, reconstruction of full mass dependence; resummation in kinematically and parametrically enhanced regions;
3. Multi-scale integrals: efficient multi-loop amplitude reduction to master integrals using algebraic geometry and finite field methods; numerical differential equations for asymptotic expansions
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