Pad\'e approach to top-quark mass effects in gluon fusion amplitudes

TL;DR

This paper introduces a novel Padé approximant method utilizing conformal mapping to accurately reconstruct top-quark mass effects in gluon fusion amplitudes, improving computational efficiency for Higgs production processes.

Contribution

The paper presents a new approach combining conformal mapping and Padé approximants to model top-quark mass effects in gluon fusion amplitudes at higher loop orders.

Findings

Effective reconstruction of top-quark mass dependence at two- and three-loop levels.

Enhanced convergence and computational efficiency in gluon fusion amplitude calculations.

Applicability to single and double Higgs production processes.

Abstract

Gluon fusion processes like single and double Higgs production exhibit slow convergence and pose severe computational challenges. We show how the top-quark mass dependence of the virtual amplitudes can be reconstructed with a conformal mapping and Pad\'e approximants based on the expansion in the inverse top-quark mass and the non-analytic terms in the expansion around the top threshold. The method is then applied at two- and three-loop order.