Renormalization invariants and the CKM matrix

Luxin Liu, Purdue University

Abstract

In this research work, we introduce a rephrasing invariant parameterization of the CKM matrix, which is parameterized in terms of six manifestly rephrasing invariant parameters, and they exhibit explicitly hierarchies in power of λ 2, from zero order toλ8, and correlations amongst the VCKM parameters are exhibited by these hierarchical structures as well. Among them, we identified a set of four rephasing invariant parameters of the CKM matrix. They are found to exhibit hierarchies in powers of λ2, from λ2 toλ 8, in contrast to the familiar CKM hierarchies ranging fromλ 2 to λ6. It is shown that, at the present level of accuracy, only the first three parameters are needed to fit all available data on flavor physics. In addition, we also obtain explicitly the renormalization group equations for the quark mass matrices in terms of these rephasing invariant parameters. It turns out that the RGE are simpler than earlier ones, and we are able to draw some general conclusions from them. We also further explore relations between the quark mixings and quark mass ratios in terms of these renormalization group equations. We find that a set of renormalization invariants can be constructed using approximate, two-flavor, analytic solutions for RGEs. These invariants exhibit explicitly the correlation between quark flavor mixings and mass ratios in the context of the SM, DHM and MSSM of electroweak interaction. The well known empirical relations &thetas; 23∝ m s/mb, &thetas;13 ∝ m d/mb can thus be understood as the result of renormalization evolution toward the infrared point. The validity of this approximation is evaluated by comparing the numerical solutions with the analytical approach. It is found that the scale dependence of these quantities for general three flavoring mixing follows closely these invariants up to the GUT scale.

Degree

Ph.D.

Advisors

Kuo, Purdue University.

Subject Area

Particle physics

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