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(a) Loop corrections to the $\phi$ boson mass
(b) Diagram of one-loop mixing of light and heavy scalars of
the model
FIG. 1: One-loop diagrams which become significant at low energies for some values of the model coupling.
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We found out that if $|g_{\phi}|$ and $|g_{\chi}|$ are small, then the loop corrections are negligible and the EL (2) is applicable for description of the scattering processes at low energies. For the values of $m_1$, $m_2$ and $\mu$ chosen in our research this takes place if $|g_{\phi}| < 0.4$ and $|g_{\chi}| < 0.4$.
If $|g_{\chi}|$ is big, then loop corrections to $\chi$ boson mass are considerable even at low energies. In our model, we have that if $|g_{\chi}| > 2.5$ then corrections displayed in Fig.(1a) have a magnitude of more than $10\,\%$ of the $\chi$ boson mass. These corrections suppress the contribution of the heavy scalar in a reaction cross-section. Hence, if $|g_{\chi}|$ is big, then (2) significantly overestimates $\chi$ boson contribution in a cross-section when $\chi$ decouples.
If $|g_{\phi}|$ is not small, then contribution of the scalar fields one-loop mixing is significant in both $s$- and $t$-channels. One-loop mixing of $\phi$ and $\chi$ is introduced by the diagram in Fig.(1b). In our model, we get that if $|g_{\phi}| > 1.5$, then modulus of the contribution of scalars one-loop mixing in the matrix elements of the considered reactions is bigger than $50\,\%$ of the four-fermion interaction term modulus at $s > \mu^2$ and $|t| > \mu^2$. This was observed in the limit when loop correction in Fig.(1a) is negligible.