\midheading{$Z+$~jet production, processes 41--43}
\label{subsec:zjet}

These processes represent the production of a $Z$ boson and a single jet,
where the $Z$ subsequently
decays either into electrons ({\tt nproc=41}), neutrinos ({\tt nproc=42})
or bottom quarks ({\tt nproc=43}). Where appropriate, the effect of a virtual
photon is also included. The calculation may be performed at LO and NLO and NNLO\cite{Neumann:2022lft}
although the NLO, (NNLO) calculation of process {\tt 43} does not include radiation
from the bottom quarks.
The one-loop virtual amplitudes are taken from the appendix IV of ref.~\cite{Bern:1997sc}.

When {\tt removebr} is true in process {\tt 41}, the $Z$ boson does not decay.