TY - JOUR
T1 - Theorems on the renormalization group evolution of quark Yukawa couplings and CKM matrix
AU - Kielanowski, P.
AU - Juárez W, S. R.
AU - Mora H, J. G.
N1 - Funding Information:
This paper is partially supported by the CoNaCyT (Mexico) project 3512P-E9608. S.R.J.W. gratefully acknowledges partial support by Comisión de Operación y Fomento de Actividades Académicas - COFAA (Instituto Politécnico Nacional). J.G. Mora H. thanks dr. A. Odzijewicz for the hospitality in the Institute of Theoretical Physics of the Białystok University (Poland) during the preparation of the paper.
PY - 2000/4/20
Y1 - 2000/4/20
N2 - We analyze the two loop renormalization group equations in the standard model and its extensions for the coupling constants and the quark Yukawa couplings. The key point of our analysis is the observed hierarchy of the quark masses and the CKM matrix. For the one loop evolution we find the explicit solution for the evolution of the Yukawa couplings and show the following: 1. the CKM matrix depends on the energy on only one function of energy; 2. the ratios of the down quark masses depend on the energy through the same function as the CKM matrix; 3. the diagonalizing matrices of the biunitary transformation of the up quarks are energy independent. Next we give the explicit form of the two loop corrections to the evolution of the quark Yukawa couplings and show that the relative corrections are of the order λ4 for the quark Yukawa couplings and of the order λ5 for the CKM matrix. Finally we give the equations of the one loop evolution of the squares of the matrix elements of the CKM matrix and their explicit solution. (C) 2000 Elsevier Science B.V.
AB - We analyze the two loop renormalization group equations in the standard model and its extensions for the coupling constants and the quark Yukawa couplings. The key point of our analysis is the observed hierarchy of the quark masses and the CKM matrix. For the one loop evolution we find the explicit solution for the evolution of the Yukawa couplings and show the following: 1. the CKM matrix depends on the energy on only one function of energy; 2. the ratios of the down quark masses depend on the energy through the same function as the CKM matrix; 3. the diagonalizing matrices of the biunitary transformation of the up quarks are energy independent. Next we give the explicit form of the two loop corrections to the evolution of the quark Yukawa couplings and show that the relative corrections are of the order λ4 for the quark Yukawa couplings and of the order λ5 for the CKM matrix. Finally we give the equations of the one loop evolution of the squares of the matrix elements of the CKM matrix and their explicit solution. (C) 2000 Elsevier Science B.V.
UR - http://www.scopus.com/inward/record.url?scp=0034689965&partnerID=8YFLogxK
U2 - 10.1016/S0370-2693(00)00295-1
DO - 10.1016/S0370-2693(00)00295-1
M3 - Artículo
SN - 0370-2693
VL - 479
SP - 181
EP - 189
JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
IS - 1-3
ER -