Flavors and Phases in Unparticle Physics

Inspired by the recent Georgi's unparticle proposal, we study the flavor structures of the standard model (SM) particles when they couple to unparticles. At a very high energy scale, we introduce \BZ charges for the SM particles, which are universal for each generation and allow \BZ fields to distinguish flavor generations. At the \Lambda_{\UP} scale, \BZ operators and charges are matched onto unparticle operators and charges, respectively. In this scenario, we find that tree flavor changing neutral currents (FCNCs) can be induced by the rediagonalizations of the SM fermions. As an illustration, we employ the Fritzsch ansatz to the SM fermion mass matrices and we find that the FCNC effects could be simplified to be associated with the mass ratios denoted by $\sqrt{m_{i}m_{j}/m^2_{3}}$, where $m_3$ is the mass of the heaviest particle in each type of fermion generations and $i, j$ are the flavor indices. In addition, we show that there is no new CP violating phase beside the unique one in the CKM matrix. We use $\bar B_{q}\to \ell^{+} \ell^{-}$ as examples to display the new FCNC effects. In particular, we demonstrate that the direct CP asymmetries in the decays can be $O(10$ due to the peculiar CP conserving phase in the unparticle propagator.Comment: 1+14 pages, 2 figures, version to appear in Phys. Lett.

Characterization for entropy of shifts of finite type on Cayley trees

The notion of tree-shifts constitutes an intermediate class in between one-sided shift spaces and multidimensional ones. This paper proposes an algorithm for computing of the entropy of a tree-shift of finite type. Meanwhile, the entropy of a tree-shift of finite type is $\dfrac{1}{p} \ln \lambda$ for some $p \in \mathbb{N}$, where $\lambda$ is a Perron number. This extends Lind's work on one-dimensional shifts of finite type. As an application, the entropy minimality problem is investigated, and we obtain the necessary and sufficient condition for a tree-shift of finite type being entropy minimal with some additional conditions