Eur. Phys. J. C (2007) 52: 591-595
https://doi.org/10.1140/epjc/s10052-007-0399-z

Regular Article - Theoretical Physics

Quark mixing in the standard model and space rotations

¹ Gruppo Fisica Teorica e Matematica Applicata Unita Tecnico Scientifica Tecnologie Fisiche Avanzante (FIS-MAT), ENEA – Centro Richerche Frascati, Via Enrico Fermi 45, 00044, Frascati, Rome, Italy
² Dept. of Optics and Spectroscopy, Faculty of Physics, M.V. Lomonosov Moscow State University, 119991, Vorobyovy Gory, Moscow, Russia

^* e-mail: zhukovsk@phys.msu.ru

Received: 30 April 2007
Revised: 13 July 2007
Published online: 13 September 2007

Abstract

The rotation matrix and the Cabibbo–Kobayashi–Maskawa (CKM) matrix are discussed. The CKM matrix is viewed as the rotation matrix in Euler angles with pitch–roll–yaw convention for the angles and as the angle–axis representation of the rotation matrix. A comparison of the exponential parameterisation of the CKM matrix with the matrix exponent generator of the space rotations is made. How to account for the CP violating phase in CKM and the O(3) rotation matrix in the angle–axis form is discussed in the context of such a view of the mixing matrix. The generation of the new parameterisations of the CKM matrix in an exponential form with distinguished CP violating part is demonstrated.