Non-global and clustering effects for groomed multi-prong jet shapes

We present a resummation of the non-global and clustering effects in groomed (with modified mass drop tagger) multi-pronged observables, valid to next-to leading logarithmic accuracy in the D₂ distribution (all single logarithmic terms), focusing on the non-global and clustering effects which cannot be removed by normalizing the cross-section. These effects are universal in the sense that they depend only on the flavor structure of the 1 → 2 splitting forming the multi-pronged subjets and the opening angle of the splitting, being insensitive to the underlying hard process or underlying event. The differential spectra with and without the non-global and clustering effects are presented, and the change in the spectra is found to be small.