  The implementation of a new final-state parton-shower algorithm in the Pythia
event generator is described. The shower algorithm, dubbed Apollo, combines
central aspects of the Vincia antenna shower with the global transverse-recoil
scheme of the Alaric framework in order to achieve formal consistency with
next-to-leading logarithmic (NLL) resummation. The shower algorithm is
constructed in such a way that it facilitates a straightforward combination
with fixed-order calculations. As an explicit proof of concept, a general
scheme for matrix-element corrections (MECs) and two separate multiplicative
next-to-leading order (NLO) matching schemes are outlined. It is argued that
both matching schemes retain the logarithmic accuracy of the shower. The
improved modelling of radiation is examined by contrasting the new algorithm
with existing leading-logarithmic parton showers in Pythia.
