TY - JOUR
T1 - Renormalization group equations for the CKM matrix
AU - Kielanowski, P.
AU - Juárez, W. S.R.
AU - Montes De Oca, Y. J.H.
PY - 2008/12/1
Y1 - 2008/12/1
N2 - We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa (CKM) 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 2 of the unitarity triangle. For the special case of the standard model and its extensions with v1 ≈ v2 we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters ρ̄ and η̄ 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.
AB - We derive the one loop renormalization group equations for the Cabibbo-Kobayashi-Maskawa (CKM) 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 2 of the unitarity triangle. For the special case of the standard model and its extensions with v1 ≈ v2 we demonstrate that also the shape of the unitarity triangle and the Buras-Wolfenstein parameters ρ̄ and η̄ 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.
UR - http://www.scopus.com/inward/record.url?scp=58149271073&partnerID=8YFLogxK
U2 - 10.1103/PhysRevD.78.116010
DO - 10.1103/PhysRevD.78.116010
M3 - Artículo
SN - 1550-7998
VL - 78
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
IS - 11
M1 - 116010
ER -