All-loop renormalization group invariants for MSSM

Abstract: For MSSM from the gauge couplings, Yukawa couplings, and the coefficient $\mu$ in the part of superpotential quadratic in the Higgs superfields we construct combinations which (for certain renormalization prescriptions) do not depend on the renormalization point in all loops. In other words, these combinations are the renormalization group invariants. Similar invariants are also constructed for NMSSM. The derivation is based on the nonrenormalization of the superpotential and the NSVZ equations. We argue that the scale invariance of the considered combinations takes place in the class of the HD+MSL schemes. This fact has been verified in the lowest orders, up to and including the one in which the dependence on the renormalization prescription becomes essential. It is also demonstrated that in the $\overline{\mbox{DR}}$ scheme the renormalization group invariance does not take place starting from the approximation, where the scheme dependence manifests itself.