Matching Hadronization and Perturbative Evolution: The Cluster Model in Light of Infrared Shower Cutoff Dependence

In the context of Monte Carlo (MC) generators with parton showers that have next-to-leading-logarithmic (NLL) precision, the cutoff $Q_0$ terminating the shower evolution should be viewed as an infrared factorization scale so that parameters or non-perturbative effects of the MC generator may have a field theoretic interpretation with a controllable scheme dependence. This implies that the generator's parton level should be carefully defined within QCD perturbation theory with subleading order precision. Furthermore, it entails that the shower cut $Q_0$ is not treated as one of the generator's tuning parameters, but that the tuning can be carried out reliably for a range of $Q_0$ values and that the hadron level description is $Q_0$-invariant. This in turn imposes non-trival constraints on the behavior of the generator's hadronization model, so that its parameters can adapt accordingly when the $Q_0$ value is changed. We investigate these features using the angular ordered parton shower and the cluster hadronization model implemented in the Herwig~7.2 MC generator focusing in particular on the $e^+e^-$ 2-jettiness distribution, where the shower is known to be NLL precise and where QCD factorization imposes stringent constraints on the hadronization corrections. We show that the Herwig default cluster hadronization model does not exhibit these features or consistency with QCD factorization with a satisfying precision. We design a modification of the cluster hadronization model, where some dynamical parton shower aspects are added that are missing in the default model. For this novel dynamical cluster hadronization model these features and consistency with QCD factorization are realized much more accurately.