  In conventional parton showers (including ones based on dipoles/antennae), a
given $(\mathrm{Born}+m)$-parton configuration can typically be reached via
${\mathcal O}(m!)$ different "shower histories". In the context of
matrix-element-correction and merging procedures, accounting for these
histories mandates fairly complex and resource-intensive algorithms. A so far
little-explored alternative in the shower context is to divide the branching
phase spaces into distinct "sectors", each of which only receives contributions
from a single branching kernel. This has a number of consequences including
making the shower operator bijective; i.e., each parton configuration now has a
single unique "inverse". As a first step towards developing a full-fledged
matrix-element-correction and merging procedure based on such showers, we here
extend the sector approach for antenna showers to hadron-hadron collisions,
including mass and helicity dependence.
