g^2 + 3 {g^\prime}^2 \right)
\left(\lambda_4 + \lambda_3 + \lambda_1 \right)
+ \tfrac{1}{4} \left( 9 g^4 + 6 g^2 {g^\prime}^2 + 3{g^\prime}^4 \right).
\label{D_MSSM}\end{aligned}$$ The first equation vanishes if $\lambda_4 = \lambda_1 - \lambda_3$; the second does not vanish if $\lambda_4 = - \lambda_1 - \lambda_3$. That is, the condition $\lambda_4 = \lambda_1 - \lambda_3$ is renormalization group invariant, whereas the condition $\lambda_4 = - \lambda_1 - \lambda_3$ is not. Note that we have not yet imposed the specific relations between the $\lambda_i$ and the gauge couplings required by the MSSM. If we impose the MSSM constraints specified by Eqs. (\[MSSM\_L1\_L2\])–(\[MSSM\_L4\]) on the right hand side of , we obtain \[RGINV\] [D]{} (\_4 + \_3 + \_1 ) = 3 g\^4 + 2 g\^2 [g\^]{}\^2 + [g\^]{}\^4, i.e., $\lambda_1 = - \lambda_3 - \lambda_4$ is still not RGE invariant.

The latter result is not unexpected. After all, the gauge boson–Higgs boson sector considered by itself can never be supersymmetric, as the corresponding superpartners are not included. Consequently, the SUSY limit of the gauge boson–Higgs boson sector can only be defined in a manner invariant under Higgs basis changes if the corresponding gaugino and higgsino superpartners are taken into account. The 