Discrete Symmetry and CP Phase of the Quark Mixing Matrix

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.Comment: 9 pages, no figur

Exotic Fermions and Bosons in the Quartification Model

Exotic fermions of half-integral charges at the TeV energy scale are predicted by the quartification model of Babu, Ma, and Willenbrock. We add to these one copy of their scalar analogs and discuss the ensuing phenomenological implications, i.e. radiative contributions to lepton masses and flavor-changing leptonic decays.Comment: 7 pages, including 3 figure

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time, we find that when Nash equilibrium exists the pay off function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example where quantum game and classical game may differ. When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.Comment: 5 pages and 3 figure