The light quark sector, CP violation, and the unitarity triangle

Abstract

In view of the observed strong hierarchy of quark masses, we propose a new description of flavor mixing which is particularly suited for models of quark mass matrices based on flavor symmetries. The necessary and sufficient conditions for CP violation are clarified. The emergence of CP violation is primarily linked to a large phase difference (near 90 • ) in the light quark sector. The unitarity triangle is determined by the mass ratios of the light quarks. We conclude that the unitarity triangle should be close or identical to a rectangular triangle, and CP violation is maximal in this sense. Instructive predictions for flavor mixing angles and CP -violating parameters, which can directly be confronted with the forthcoming data from B-meson factories, are obtained from a specific texture of quark mass matrices.

Quark flavor mixings from hierarchical mass matrices

“…As a consequence of texture zeros [32][33][34][35][36][37][38][39][40][41][42], a few simple but instructive relations among flavor mixing angles and quark mass ratios can be established [34,36,[43][44][45][46][47][48][49] and tested in experiments. Unfortunately, the Fritzsch ansatz failed to reconcile a large top-quark mass with the observed value of |V cb | [50,51].…”

Quark mixing sum rules and the right unitarity triangle

“…We are left with little alternative but to follow an ad hoc approach pioneered some time ago by Fritzsch [13,14] and currently represented by the myriads of proposed effective Yukawa textures (see e.g. [13][14][15][16][17][18]) whose starting assumption is that (in some basis) the Yukawa matrices exhibit certain nice features such as symmetries or zeros in specific elements which have become known as "texture zeros." For example, in his classic paper, Fritzsch pioneered the idea of having six texture zeros in the 1-1, 2-2, 1-3 entries of the Hermitian up and down quark Yukawa (or mass) matrices [13].…”

“…However, four-zero textures featuring zeros in the 1-1 and 1-3 entries of both up and down Hermitian mass matrices may also lead to the bad prediction |V ub |/|V cb | ∼ m u /m c unless |V cb | results from the cancellation of quite sizeable up-and down-type quark 2-3 mixing angles, leading to non-negligible induced 1-3 up-and downtype quark mixing [18]. Another possibility is to give up on the 1-3 texture zeros, as well as the 2-2 texture zeros, retaining only two texture zeros in the 1-1 entries of the up and down quark matrices [16].…”

“…Fritzsch and Xing have previously emphasized how their four-zero scheme with 1-1 and 1-3 texture zeros in the Hermitian up and down mass matrices can be used to accommodate right unitarity triangles [18], but since their scheme involves large 2-3 and non-negligible 1-3 up and down quark mixing, our sum rules are not applicable to their case. Therefore, the textures in Refs.…”

Hierarchy and up-down parallelism of quark mass matrices

“…Without loss of generality, one may arrange M U and M D to be Hermitian in the framework of the standard model or its extensions which have no flavor-changing right-handed currents [5]. There exist two reciprocal ways to explore possible relations between the hierarchy of V and that of M U and M D :…”