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

In this project, we aim for a full control of quark-mass effects in Higgs production through gluon fusion at higher orders in perturbation theory. This includes the calculation of the top- and bottom-quark mass effects for the total and differential cross section at 4th order in the strong coupling and their implementation in Monte-Carlo programs. In parallel to the exact evaluation of these quantities, we will also approach the problem through approximations by evaluating and combining amplitudes in characteristic kinematical limits. The developed methods will also allow us to consider effects from potential physics beyond the Standard Model.

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