Building a consistent parton shower

Modern parton showers are built using one of two models: dipole showers or angular ordered showers. Both have distinct strengths and weaknesses. Dipole showers correctly account for wide-angle, soft gluon emissions and track the leading flows in QCD colour charge but they are known to mishandle partonic recoil. Angular ordered showers keep better track of partonic recoil and correctly include large amounts of wide-angle, soft physics but azimuthal averaging means they are known to mishandle some correlations. In this paper, we derive both approaches from the same starting point; linking our under- standing of the two showers. This insight allows us to construct a new dipole shower that has all the strengths of a standard dipole shower together with the collinear evolution of an angular-ordered shower. We show that this new approach corrects the next-to-leading- log errors previously observed in parton showers and improves their sub-leading-colour accuracy.