  The stability of $O(n)$-symmetric fixed point regarding the presence of
vector-field term ($\sim h p_{\alpha}p_{\beta}$) in the $\varphi^4$ field
theory is analyzed. For this purpose, the four-loop renormalization group
expansions in $d=4-2\varepsilon$ within Minimal Subtraction (MS) scheme are
obtained. This frequently neglected term in the action requires a detailed and
accurate study on the issue of existing of new fixed points and their
stability, that can lead to the possible change of the corresponding
universality class. We found that within lower order of perturbation theory the
only $O(n)$-symmetric fixed point $(g_{\text{H}},h=0)$ exists but the
corresponding positive value of stability exponent $\omega_h$ is tiny. This led
us to analyze this constant in higher orders of perturbation theory by
calculating the 4-loop contributions to the $\varepsilon$ expansion for
$\omega_h$, that should be enough to infer positivity or negativity of this
exponent. The value turned out to be undoubtedly positive, although still small
even in higher loops: $0.0156(3)$. These results cause that the corresponding
vector term should be neglected in the action when analyzing the critical
behaviour of $O(n)$-symmetric model. At the same time, the small value of the
$\omega_h$ shows that the corresponding corrections to the critical scaling are
significant in a wide range.
