Ultraviolet asymptotic behavior in the presence of non-Abelian gauge groups

A study is made of a class of theories of a Yang–Mills field interacting with scalar and spinor fields, including models with spontaneously broken symmetries. It is shown that all fairly simple models of such type, except for the massless Yang–Mills field interacting with only fermions, lead to theories that go beyond the framework of weak coupling with respect to at least one of the coupling constants. However, there exists a possibility under which in the ultraviolet limit the effective constant of the four-meson interaction tends to a finite value and the Yang–Mills constant tends to zero. Allowance for an additional Yukawa interaction does not qualitatively affect this picture.