Two-loop renormalization-group calculations in theories with scalar quarks

We discuss the problem of estimating values of the effective scales of strong interactions in the channels of hypothetical scalar-containing mesons which might exist in models with scalar quarks. The two-loop strong interaction corrections to the anomalous dimensions and coefficient functions of two-point correlators of operators $\varphi^+\varphi$ and $\varphi^+ q$ with quantum numbers of hadrons with spin 0 and spin 1/2 are calculated. Values of effective scale parameters of strong interactions in the channels of $\pi_s$ and $\chi_s$ hadrons are determined. It is pointed out that the results obtained $\Lambda_{\pi_s}=5,81\Lambda_{\overline{MS}}$ and $\Lambda_{\chi_s}=12,78\Lambda_{\overline{MS}}$ can be interpreted as a one more argument in favour of the statement that the mass scale of the scalar-containing mesons can be large.