An analytic result for the $0 \to ggHHH$ amplitude

TL;DR

This paper derives a fully analytic, efficient formula for the one-loop amplitude of triple Higgs production via gluon fusion, crucial for probing Higgs self-couplings at colliders.

Contribution

It provides the first complete analytic expression for the $gg o HHH$ amplitude with full heavy quark mass dependence, improving computational speed significantly.

Findings

Amplitude expressed in compact form using advanced analytic techniques.

Evaluation speed increased by over an order of magnitude compared to previous methods.

Enables more precise and efficient studies of Higgs self-couplings at colliders.

Abstract

We present a fully analytic calculation of the leading-order one-loop amplitude for triple Higgs production via gluon fusion, $gg \to HHH$, retaining full dependence on the mass of the heavy quark circulating in the loop. This amplitude provides a direct probe of the triple and quartic Higgs self-couplings, the measurement of which is a central goal of current and future colliders. The amplitude can be presented in compact form thanks to the use of analytic reconstruction techniques, based on finite-field and $p$-adic evaluations, partial fraction decompositions, and primary decompositions to identify common numerator factors. Our results provide a compact and efficient representation of the matrix element for this process, enabling evaluations that are more than an order of magnitude faster than existing numerical alternatives.