\midheading{$H+$~jet production, $m_t=$~finite, process 200}
\label{subsec:hjetma}
This process represents the production of a Higgs boson in association
with a single jet based on
refs.~\cite{Neumann:2016dny,Neumann:2018bsx,Ellis:1987xu,Baur:1989cm,Ellis:2018hst,Budge:2020oyl}.
Decay modes are currently unsupported/untested. The top-quark mass is taken
into account exactly for the Born and real-emission parts, as well as for the singular part of the virtual corrections.
The real emission calculation is based on the one-loop, Higgs boson + 4 parton calculations
with full quark masss effects of ref.\cite{Ellis:2018hst,Budge:2020oyl}.

The finite part of the two-loop virtual corrections can be computed in
different ways by setting the input file parameter {\tt mtex}.
\begin{itemize}
    \item In a low energy asymptotic expansion in $1/m_t^k$ up to
    order $k=2,4$ by setting {\tt mtex} to $2$ or $4$ in the input
    file. This is recommended for transverse momenta up to $\simeq
    225$~GeV.

\item In a high energy expansion by setting {\tt mtex}=100 in the input
    file. This is recommended for transverse momenta beyond $450$~GeV.

\item In a rescaling approach where the finite part of the two-loop virtual
     amplitude in the effective field theory
    ($m_t=\infty$) is rescaled pointwise by the ratio of the one-loop
    amplitude computed with full $m_t$ dependence to the one-loop
    amplitude for $m_t=\infty$. This mode is the default mode and
    enabled with {\tt mtex}=0 in the input file.  This is the
    recommended approach for the intermediate energy region and for
    estimating top-mass uncertainties in the transition regions
    between these approaches.

\end{itemize}

This process is therefore calculable at leading LO and at
next-to-leading order NLO (using an approximation for the two loop
matrix element). Full NLO calculations (with the exact two-loop matrix
element) have been performed in refs.~\cite{Jones:2018hbb,Chen:2021azt,Bonciani:2022jmb}.