Discrete Symmetry and CP Phase of the Quark Mixing Matrix

Abstract

A simple specific pattern of the two 3 X 3 quark mass matrices is proposed, resulting in a prediction of the CP phase of the charged-current mixing matrix V_CKM, i.e. sin 2 phi_1 (beta) = 0.733, which is in remarkable agreement with data, i.e. sin 2 phi_1 = 0.728 +/- 0.056 +/- 0.023 from Belle and sin 2 beta = 0.722 +/- 0.040 +/- 0.023 from Babar. This pattern can be maintained by a discrete family symmetry, an example of which is D_7, the symmetry group of the heptagon.