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 → b b ¯ , H → c c ¯ , and H → gg . We demonstrate how the matched NNLO+NNLL results clarify the relative contributions of key hadronic Higgs-decay channels ( H → b b ¯ , H → c c ¯ , H → 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.