QCD resummation for groomed jet observables at NNLL+NLO

We use a direct QCD approach to carry out the next-to-next-to-leading logarithmic (NNLL) resummation for observables groomed with the modified mass-drop tagger (Soft Drop $\beta=0$). We focus on observables which are additive given an arbitrary number of soft-collinear emissions. For this class of observables, we arrange the structure of the NNLL terms into two distinct categories. The first defines a simplified inclusive tagger, whereby the NNLL collinear structure is directly related to ungroomed observables. The second defines a clustering correction which takes a particularly simple form when the Cambridge-Aachen (C/A) algorithm is used to cluster the jets. We provide, in addition to the QCD resummation of groomed jet mass, the first NNLL resummed predictions, matched to NLO, for a range of groomed jet angularities with mMDT grooming. Moreover, we also include for the first time in the same calculation, finite $z_{\mathrm{cut}}$ effects computed at NLL level alongside the small $z_{\mathrm{cut}}$ NNLL results which simultaneously improves upon both of the calculations used for groomed jet mass phenomenological studies to date. While for simplicity we focus on $e^{+}e^{-}$ collisions, the essential NNLL resummation we develop is process independent and hence with the appropriate NLO matching our results are also applicable for hadron collider phenomenology.