before us [@Buttazzo:2013uya; @Espinosa:2015kwx]. For completeness here we revisit this analysis. This serves us to calibrate our Renormalization Group (RG) analysis against known results. Although for the [[Standard Model ]{}]{}case there are some partial 3-loop results in dedicated studies[@Buttazzo:2013uya] here we perform the RG analysis at the two-loop level. We perform our analysis in the $\overline{MS}$ scheme, taking the parameter values at low scale as the input values [@Tanabashi:2018oca]. In particular, the Higgs pole mass is taken as the current best fit value of $m_H = 125.18\pm 0.16$ GeV, the pole mass of top quark is taken as $m_t = 173\pm 0.4$ GeV and the strong coupling constant $\alpha_{s}(M_{Z})=0.1184\pm 0.0007$. Using these experimental values, we adopt the “On-Shell” renormalization scheme (OS) to directly express the renormalized parameters in terms of the physical observables and then relate the OS parameters to the $\overline{MS}$ parameters in a way similar to [@Buttazzo:2013uya]. In Table. \[input parameter\] we list the $\overline{MS}$ input values of the relevant parameters at the top mass $m_t$ scale.

                 $g_{1}$    $g_{2}$    $g_{3}$   $y_{t}$   $\lambda$
  ------------- ---------- ---------- --------- --------- -----------
   $\mu (m_t)$   0.462607   0.647737   1.16541   0.93519   0.126115

Taking the initial $\overline{MS}$ values of Table. \[input parameter\] as input values, we 