# Two-loop amplitudes for Higgs plus jet production involving a modified trilinear Higgs coupling

## TL;DR

This paper computes two-loop scattering amplitudes involving a modified Higgs trilinear coupling, providing analytic expressions crucial for understanding Higgs production dynamics at colliders.

## Contribution

It presents the first analytic calculation of two-loop amplitudes with a modified Higgs trilinear coupling using an asymptotic expansion near a heavy top quark limit.

## Key findings

- Analytic expressions for two-loop amplitudes involving modified Higgs coupling.
- Insights into the impact of ${
m O}( ext{lambda})$ corrections on Higgs transverse momentum distributions.
- Facilitates more accurate predictions for Higgs production at colliders.

## Abstract

We calculate the contributions to the two-loop scattering amplitudes $h \to gg$, $h \to ggg$ and $h \to q \bar q g$ that arise from a modified trilinear Higgs coupling $\lambda$. Analytic expressions are obtained by performing an asymptotic expansion near the limit of infinitely heavy top quark. The calculated amplitudes are necessary to study the impact of the ${\cal O} (\lambda)$ corrections to the transverse momentum distributions ($p_{T,h}$) in single-Higgs production at hadron colliders for low and moderate values of $p_{T,h}$.