Renormalization Group Equations for the CKM matrix

Abstract

We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa matrix for the Standard Model, its two Higgs extension and the minimal supersymmetric extension in a novel way. The derived equations depend only on a subset of the model parameters of the renormalization group equations for the quark Yukawa couplings so the CKM matrix evolution cannot fully test the renormalization group evolution of the quark Yukawa couplings. From the derived equations we obtain the invariant of the renormalization group evolution for three models which is the angle $\alpha$ of the unitarity triangle. For the special case of the Standard Model and its extensions with $v_1\approx v_2$ we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters $\bar{\rho }=(1-1/2{\lambda }^2)\rho$ and $\bar{\eta }=(1-1/2{\lambda }^2)\eta$ are conserved. The invariance of the angles of the unitarity triangle means that it is not possible to find a model in which the CKM matrix might have a simple, special form at asymptotic energies.

9 pages

References in corpus (6)

• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• Waiting for the Top Quark Mass, K^+ --> π^+ ν\barν, B_s^0-\bar{B}_s^0 Mixing and CP Asymmetries in B-Decays
• Mass and mixing angle patterns in the Standard Model and its Minimal Supersymmetric Extension
• Scale dependence of the quark masses and mixings: leading order
• Precise bounds on the Higgs boson mass
• Theorems on the Renormalization Group Evolution of Quark Yukawa Couplings and CKM Matrix

Cited by in corpus (6)

• Flavor structures of charged fermions and massive neutrinos
• Naturally small Yukawa couplings from trans-Planckian asymptotic safety
• Flavor anomalies from asymptotically safe gravity
• Constraints on $Z^{\prime }$ solutions to the flavor anomalies with trans-Planckian asymptotic safety
• Renormalization-Group Equations of Neutrino Masses and Flavor Mixing Parameters in Matter
• Mass Matrices and Their Renormalization