Higgs branching-fraction normalization from mass-weighted channels ($B_f=B_{\mathcal{S}}{N}_c^f{m}_f^2/{\sum }_{j\in \mathcal{S}}{N}_c^j{m}_j^2$)

At leading order, neglecting phase-space suppression and radiative corrections, Higgs decay to a fermion pair has partial decay width proportional to $N_c^f{m}_f^2$, with $N_c=3$ for a quark and one for a lepton. A known sum of branching fractions therefore fixes the proportionality between these weights and individual branching fractions without requiring the Higgs vacuum expectation value. The same normalization estimates a small additional fermionic channel if its weight is not included in the known sum.