\midheading{$Z$-boson production, processes 31--33}
\label{subsec:zboson}

These processes represent the production of a $Z$ boson which subsequently
decays either into electrons ({\tt nproc=31}), neutrinos ({\tt nproc=32})
or bottom quarks ({\tt nproc=33}). Where appropriate, the effect of a virtual
photon is also included. As noted above, for {\tt nproc=31} and {\tt nproc=33} the constraint
{\tt m34min > 0} is obligatory. The calculation may be performed at LO, NLO
and NNLO~\cite{Boughezal:2016wmq,Campbell:2022gdq}
although the NLO and NNLO calculation of process {\tt 33} does not include radiation
from the bottom quarks (i.e.\ radiation occurs in the initial state only).

This process can be calculated at LO, NLO, and NNLO. NLO calculations
can be performed by subtraction, zero-jettiness slicing and
$q_T$-slicing. NNLO calculations can be performed by zero-jettiness
slicing and $q_T$-slicing.

To calculate the total cross section to on-shell $Z$ bosons, we take 
process ({\tt nproc=32}), (no $\gamma^{*}$ contribution) and 
set (zerowidth=.true.) and (removebr =.true.).
When {\tt removebr} is true in process {\tt 31}, the $Z$ boson does not decay.