Scale dependence of the quark masses and mixings: leading order

Abstract

We consider the Renormalization Group Equations (RGE) for the couplings of the Standard Model and its extensions. Using the hierarchy of the quark masses and of the Cabibbo-Kobayashi-Maskawa (CKM) matrix our argument is that a consistent approximation for the RGE should be based on the parameter $\lambda =|{\hat{V}}_{ud}|\approx 0.22$. We consider the RGE in the approximation where we neglect all the relative terms of the order $\sim {\lambda }^4$ and higher. Within this approximation we find the exact solution of the evolution equations of the quark Yukawa couplings and of the vacuum expectation value of the Higgs field. Then we derive the evolution of the observables: quark masses, CKM matrix, Jarlskog invariant, Wolfenstein parameters of the CKM matrix and the unitarity triangle. We show that the angles of the unitarity triangle remain constant. This property may restrict the possibility of new symmetries or textures at the grand unification scale.

15 pages, 4 figures, author of one reference added

References in corpus (6)

• New Formulas and Predictions for Running Fermion Masses at Higher Scales in SM, 2HDM, and MSSM
• Gauge-Independent W-Boson Partial Decay Widths
• Theorems on the Renormalization Group Evolution of Quark Yukawa Couplings and CKM Matrix
• CP Violation for Leptons at Higher Energy Scales
• Evolution of the Yukawa coupling constants and seesaw operators in the universal seesaw model
• Effects of the Scale-dependent Vacuum Expectation Values in the Renormalization Group Analysis of Neutrino Masses

Cited by in corpus (15)

• High scale mixing unification and large neutrino mixing angles
• Assignments of Universal Texture Components for Quark and Lepton Mass Matrices
• Bottom-Up Discrete Symmetries for Cabibbo Mixing
• Tri-bimaximal Mixing and Cabibbo Angle in S4 Flavor Model with SUSY
• The Matrix of Unitarity Triangle Angles for Quarks
• Renormalization of the quark mass matrix
• Precise bounds on the Higgs boson mass
• Renormalization Group Equations for the CKM matrix
• Lowering the scale of Pati-Salam breaking through seesaw mixing
• Renormalization Invariants and Quark Flavor Mixings
• CKM substructure from the weak to the Planck scale
• CKM Substructure
• Gaugino Mediation Combined with the Bulk Matter Randall-Sundrum Model
• Renormalization Group Evolution of Flavour Invariants
• Observing Signals of the Bulk Matter RS Model through Rare Decays of SUSY Particles