# Mass Dependence of Higgs Production at Large Transverse Momentum

## TL;DR

This paper develops a factorization approach to simplify the calculation of the Higgs boson transverse momentum distribution at large $P_T$, accounting for mass effects and enabling more precise predictions.

## Contribution

It introduces a factorization formula that separates large scale $P_T$ from mass scales, simplifying calculations of Higgs production at high transverse momentum.

## Key findings

- Factorization formula separates $P_T$ from mass effects.
- Leading power in $1/P_T^2$ expressed with distribution amplitudes.
- Method enables next-to-leading order calculations in $ ext{alpha}_s$.

## Abstract

The transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on three important energy scales: $P_T$, the top quark mass $m_t$, and the Higgs mass $m_H$. A strategy for simplifying the calculation of the cross section at large $P_T$ is to calculate only the leading terms in its expansion in $m_t^2/P_T^2$ and/or $m_H^2/P_T^2$. The expansion of the cross section in inverse powers of $P_T$ is complicated by logarithms of $P_T$ and by mass singularities. In this paper, we consider the top-quark loop contribution to the subprocess $q\bar{q}\to H+g$ at leading order in $\alpha_s$. We show that the leading power of $1/P_T^2$ can be expressed in the form of a factorization formula that separates the large scale $P_T$ from the scale of the masses. All the dependence on $m_t$ and $m_H$ can be factorized into a distribution amplitude for $t \bar t$ in the Higgs, a distribution amplitude for $t \bar t$ in a real gluon, and an endpoint contribution. The factorization formula can be used to simplify calculations of the $P_T$ distribution at large $P_T$ to next-to-leading order in $\alpha_s$.