Solution (source code)

= Solution

In the stronger limit $m_H\ll m_W$, both intermediate <W bosons> must be virtual. Their heavy propagators suppress the four-fermion <decay amplitude>, while the small available <phase space> suppresses its rate further. At energies small compared with $m_W$, integrating out the two vectors gives a local interaction proportional to $G_FH J_\mu^+J^{-\mu}/v$. Its dimension-seven coefficient implies a rate of order $G_F^3m_H^7$ when all four final <fermions> can be treated as massless, with channel-dependent constants. This is a low-energy scaling statement, not the on-shell longitudinal-width formula. Other accessible <Higgs boson> decay channels, such as a pair of <fermions> or loop-induced two-<photon> decay, must then be compared using their actual masses and couplings.