Elementary and composite particles in asymptotically free gauge theories

We demonstrate that in asymptotically free gauge theories the wave-function renormalization constants for spin-1/2 fields do not vanish. (The scalar fields, if incorporated, also have this property.) However, there exists a subclass of such theories where the $Z\text{'}\mathrm{s}$ for the gauge fields themselves tend to zero in the limit of infinite cutoff. These features are shown to be gauge-independent. This suggests the potentiality of constructing asymptotically free strong-interaction theories in which the only elementary fields are "quarks" and all other hadrons are bound states.