NNLO+NNLL Predictions for Heavy-Jet Mass and C-parameter in Higgs Decays to Quarks and Gluons

We consider the resummation of large logarithmic corrections arising in the two-particle limit at next-to-next-to-leading logarithmic (NNLL) accuracy for the heavy-jet mass and $C$-parameter distributions in the decay of a Higgs boson to quarks and gluons: $H\to b\bar{b}$, $H\to c\bar{c}$, and $H\to gg$. We demonstrate how the matched NNLO+NNLL results clarify the relative contributions of key hadronic Higgs-decay channels ($H\to b\bar{b}$, $H\to c\bar{c}$, $H\to gg$) yielding reduced uncertainties for both event-shape observables – especially for heavy-jet mass – while revealing substantial effects that shift the $C$-parameter peak in gluonic decays.