Energy dependence of the quark masses and mixings

Details Energy dependence of the quark masses and mixings Energy dependence of the quark masses and mixings

2000-09-13

arxiv.org/abs/hep-ph/0009148v1

AIPConf.Proc.562:303-308,2001

Physics

High Energy Physics

High Energy Physics - Phenomenology

Talk presented at the IX Mexican School on Particles and Fields, August 9-19, Metepec, Pue., Mexico. To be published in the AI

Scientific paper

10.1063/1.1374869

The one loop Renormalization Group Equations for the Yukawa couplings of quarks are solved. From the solution we find the explicit energy dependence on $t=\ln E/\mu $ of the evolution of the {\em down} quark masses $q=d,s,b$ from the grand unification scale down to the top quark mass $m_{t}$. These results together with the earlier published evolution of the {\em up} quark masses completes the pattern of the evolution of the quark masses. We also find the energy dependence of the absolute values of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $|V_{ij}|$. The interesting property of the evolution of the CKM matrix and the ratios of the quark masses: $m_{u,c}/m_{t}$ and $m_{d,s}/m_{b}$ is that they all depend on $t$ through only one function of energy $h(t)$.

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