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Sector Showers for Hadron Collisions

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.