arXiv:2607.06985·v1·High Energy Physics — Phenomenology

Perturbative determination of CP phase in CKM matrix using rephasing invariants of hierarchical mass matrices and their inverses

Abstract

In this paper, we derive approximate expressions for the CP phase $δ$ in the CKM matrix by a perturbative singular value decomposition for hierarchical quark mass matrices $m_{q}$ . The diagonalization is achieved through a seesaw-like procedure in which the heavier generations are successively integrated out, naturally leading to mixing matrices expressed in terms of the mass matrix and its inverse $m_{q}^{- 1}$ . As a result, in the basis where the up-type quark mass matrix is diagonal, $δ$ is reduced to the fourth-order invariant $δ ≃ ar g [- m_{d 12}^{- 1} m_{d 23} / m_{d 11}^{- 1} m_{d 13}]$ , constructed from the down-type mass matrix and its inverse. Furthermore, in the Kobayashi--Maskawa parametrization, the CP phase is likewise expressed in the same basis as the invariant $δ_{KM} ≃ ar g [m_{d 13}^{- 1} m_{d 33} / m_{d 11}^{- 1} m_{d 13}] ≃ π /2$ .

Comments: 9 pages