Mass Dependence of Higgs Production at Large Transverse Momentum through a Bottom Quark Loop

TL;DR

This paper develops a factorization approach to simplify the calculation of Higgs production at large transverse momentum via a bottom-quark loop, isolating the dominant contributions and separating relevant scales.

Contribution

It introduces a factorization formula that isolates the large transverse momentum scale from the quark and Higgs masses, simplifying calculations of the bottom-quark-loop contribution.

Findings

The leading power of 1/P_T^2 can be factorized into separate components.

The dependence on m_b and m_H can be encapsulated in distribution amplitudes.

The approach reduces the calculation to at most two scales.

Abstract

In the production of the Higgs through a bottom-quark loop, the transverse momentum distribution of the Higgs at large $P_T$ is complicated by its dependence on two other important scales: the bottom quark mass $m_b$ 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 $m_b^2/P_T^2$. In this paper, we consider the bottom-quark-loop contribution to the parton process $q\bar{q}\to H+g$ 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 $m_b$ and $m_H$ can be factorized into a distribution amplitude for $b \bar b$ in the Higgs, a distribution amplitude for $b \bar b$ in a real gluon, and an endpoint contribution. The factorization formula can be used to organize the calculation of the leading terms in the expansion in $m_b^2/P_T^2$ so that every calculation involves at most two scales.