# Loops with heavy particles in multi Higgs production amplitudes

## TL;DR

This paper analyzes loop corrections from heavy particles in multi-Higgs production amplitudes, revealing that these corrections break known scaling laws and are numerically significant, especially from top quark loops.

## Contribution

It provides explicit calculations of loop corrections from heavy fermions and scalars, showing their impact on multi-Higgs production amplitudes and scaling behavior.

## Key findings

- Heavy particle loops break the known scaling dependence on n and self-coupling.
- Top quark loop corrections are numerically large and dominant at lower n.
- Loop corrections significantly affect multi-Higgs production amplitudes.

## Abstract

In view of a recently renewed interest to production of multiple Higgs bosons the amplitude for such process at the threshold of $n$ particles is considered. An explicit calculation is done for the loop corrections to the amplitude arising from interaction with a heavy fermion (e.g. top quark) and also with a heavy scalar. It is shown that such corrections generally break the scaling dependence on the number $n$ and the Higgs self coupling, which dependence is known from the past studies of models with one field. The correction due to the top quark loop is also found to be numerically large and exceeding that from the self coupling until very high $n$.