Eur. Phys. J. C (2007) 50: 817-821
https://doi.org/10.1140/epjc/s10052-007-0263-1

Regular Article - Theoretical Physics

Quark flavour mixing and the exponential form of the Kobayashi–Maskawa matrix

¹ Gruppo Fisica Teorica e Matematica Applicata, Unita Tecnico Scientifica Tecnologie Fisiche Avanzante (FIS-MAT), ENEA – Centro Ricerche Frascati, Via Enrico Fermi 45, 00044, Frascati, Rome, Italy
² Dept. of Optics and Spectroscopy, Faculty of Physics, M.V. Lomonosov Moscow State University, Vorobjovy Gory, Moscow, 119899, Russia

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

Received: 14 November 2006
Revised: 13 January 2007
Published online: 5 April 2007

Abstract

The form of the mixing matrix of quarks is discussed. The exponential parameterisation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix is identified as the most general form of the mixing matrix. Its properties are reviewed in the context of the unitarity requirement. A recurrence series representation of the exponential form of the mixing matrix that is easy to handle is obtained, allowing for a direct and simple method of calculation of the CKM matrix. The generation of the new parameterisations of the CKM matrix by the exponential form is demonstrated.