Renormalization group: new relations between the parameters of the Standard Model

Abstract

We analyze the renormalization group equations for the Standard Model at the one and two loops levels. At one loop level we find an exact constant of evolution built from the product of the quark masses and the gauge couplings $g_{1}$ and $ g_{3}$ of the $U(1)$ and $SU(3)$ groups. For leptons at one loop level we find that the ratio of the charged lepton mass and the power of $g_{1}$ varies $\simeq 4\times 10^{-5}$ in the whole energy range. At the two loop level we have found two relations between the quark masses and the gauge couplings that vary $\simeq 4\%$ and $\simeq 1\%$, respectively. For leptons at the two loop level we have derived a relation between the charged lepton mass and the gauge couplings $g_ {1}$ and $g_{2}$ that varies $\simeq 0.1\%$. This analysis significantly simplifies the picture of the renormalization group evolution of the Standard Model and establishes new important relations between its parameters.