It is also shown that both scenarios can not be ruled out by what are considered standard tests of QCD like R-parameter, g-2 for muons or deep inelastic phenomena. It is shown that asymptotic freedom is obtained without requiring that all additional couplings keep fixed ratios with each other. We consider two distinct scenarios, one in which the additional scalars are light and another in which they are heavier than half the Z-boson mass. In this paper we construct non-Abelian gauge theories with fermions and scalars that nevertheless possess asymptotic freedom.The scalars are taken to be in a chiral multiplet transforming as (2, 2) under SU(2) L ⊗ SU(2) R and transforming as singlets under the colour SU(3) group.
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