Both neutrons and muons decay via the weak force/a weak interaction, with the neutron having a mean lifetime of around 900 seconds, and the muon having a lifetime of around 2.2$\mu$s, i.e., a factor of roughly $4 \cdot10^8$ between their lifetimes. Their "mass difference factor" $m_n/m_\mu$, however, is only around 9 (approx. 900 MeV/$c^2$ vs 100 MeV/$c^2$).
I would think that their lifetimes somehow are linked to their mass (and charge?) and the mass of their decay product, i.e., a proton and electron, respectively. But somehow all these numbers don't add up to the massive difference in decay lifetime. What's the mechanism/formula describing this discrepancy?
The Wikipedia article on muons, specifically the section linked here to decay, mentions a theoretical description of the decay width via "Fermi's golden rule [which] follows Sargent's law of fifth-power dependence on $m_\mu$", but I do not really understand that section.