Top quark ($t$)

The top quark is the up-type member of the third quark generation. Its mass exceeds the W boson mass, so a real W boson cannot decay into an on-shell top quark. A massless approximation for accessible decay products must not silently remove this channel threshold.

Here $x=m_W^2/m_t^2$, and the tree-level decay width neglects the bottom quark mass. The open two-body W channel gives a top quark lifetime of a few $10^{-25}\mathrm{s}$, shorter than the hadronization time. A fifth-power Sargent's rule extrapolation misses this physical regime.^[ref]

Here $x=m_W^2/m_t^2$, the bottom quark mass is neglected, and the W boson is on shell. The weak charged current gives the spin-averaged squared scattering amplitude $g_W^2|V_{tb}{|}^2(m_t^2-m_W^2)(m_t^2+2m_W^2)/(4m_W^2)$. The two-body Lorentz-invariant phase space has $p^{\ast }=(m_t^2-m_W^2)/(2m_t)$; multiplying by $p^{\ast }/(8\pi m_t^2)$ gives the displayed decay width. Its longitudinal-vector contribution explains the large-$m_t$ cubic growth, and its threshold factor makes the width vanish as $m_t\downarrow m_W$. The formula requires $m_t>m_W$ and receives finite-mass and radiative corrections.