= Solution
An extra active generation with the same <weak neutral current> couplings would increase the <Z boson> <total decay width> if any new particle–antiparticle pair were light enough. A simple sufficient kinematic condition for closing each such two-body channel is
$$
\boxed{m_T,m_B,m_\sigma,m_N\gtrsim\frac{m_Z}{2}\simeq45.6\ \mathrm{GeV}/c^2.}
$$
The corresponding within-generation <W boson> channels close when
$$
\boxed{m_T+m_B\gtrsim m_W,\qquad m_\sigma+m_N\gtrsim m_W,\qquad
m_W\simeq80.4\ \mathrm{GeV}/c^2.}
$$
If both members of each doublet already exceed $m_Z/2$, these two sum constraints follow automatically. Mixing with lighter generations can also open charged-current channels involving one heavy and one light particle, depending on the mixing amplitudes; that information is not specified.
These are threshold estimates, not precise confidence limits. Close to threshold, <two-body decay phase space> suppresses a new <partial decay width>, and a quantitative lower mass bound requires the experimental width uncertainties and the fermion's couplings. The given observations yield no upper mass bound. A sterile <neutrino> with no standard active coupling would not obey the stated $Z$-width inference, whereas the question specifies the same quantum numbers as the existing generations.
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