QCD axion and quintessential axion

The axion solution of the strong CP problem is reviewed together with the other strong CP solutions. We also point out the quintessential axion(quintaxion) whose potential can be extremely flat due to the tiny ratio of the hidden sector quark mass and the intermediate hidden sector scale. The quintaxion candidates are supposed to be the string theory axions, the model independent or the model dependent axions.Comment: 15 pages. Talk presented at Castle Ringberg, June 9-14, 200

Study of Bc→ψ(2S)KB_{c} \rightarrow \psi(2S) K, ηc(2S)K\eta_{c}(2S)K, ψ(3770)K\psi(3770)K decays with perturbative QCD approach

We study the $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays with perturbative QCD approach (pQCD) based on $k_T$ factorization. The new orbitally excited charmonium distribution amplitudes $\psi(1^{3}D_{1})$ based on the Schr\"{o}dinger wave function of the $n=1$, $l=2$ state for the harmonic-oscillator potential are employed. By using the corresponding distribution amplitudes, we calculate the branching ratio of $B_{c}$$\rightarrow$$\psi(2S)$K, $\eta_{c}(2S)$K, $\psi(3770)$K decays and the form factors $A_{0,1,2}$ and $V$ for the transition $B_{c}$$\rightarrow$$\psi(1^{3}D_{1})$. We obtain the branching ratio of both $B_{c}$$\rightarrow$$\psi(2S)$K and $B_{c}$$\rightarrow$$\eta_{c}(2S)$K are at the order of $10^{-5}$. The effects of two sets of the S-D mixing angle $\theta=-12^{\circ}$ and $\theta=27^{\circ}$ for the decay $B_{c}$$\rightarrow$$\psi(3770)$K are studied firstly in this paper. Our calculations show that the branching ratio of the decay $B_{c}$$\rightarrow$$\psi(3770)$K can be raised from the order of $10^{-6}$ to the order of $10^{-5}$ at the mixing angle $\theta=-12^{\circ}$, which can be tested by the running LHC-b experiments.Comment: 12pages, 2 figure

Ferroelectricity in (K@C60_{60})n_n

A theoretical analysis of the ground state of long-chain (K@C$_{60}$)$_n$ is presented. Within mean field theory, a ferroelectric ground state is found to be stable because of the pseudo-Jahn-Teller mixing of the b$_{1u}$ and the b$_{2g}$ band with a zone-center optical phonon involving the displacement of the endohedral K^+ ions. A phase diagram for this model is derived in the narrow bandwidth regime.Comment: 6 pages, 4 figure

Self-Similar kk-Graph C*-Algebras

In this paper, we introduce a notion of a self-similar action of a group $G$ on a $k$-graph $\Lambda$, and associate it a universal C*-algebra \O_{G,\Lambda}. We prove that \O_{G,\Lambda} can be realized as the Cuntz-Pimsner algebra of a product system. If $G$ is amenable and the action is pseudo free, then \O_{G,\Lambda} is shown to be isomorphic to a "path-like" groupoid C*-algebra. This facilitates studying the properties of \O_{G,\Lambda}. We show that \O_{G,\Lambda} is always nuclear and satisfies the Universal Coefficient Theorem; we characterize the simplicity of \O_{G,\Lambda} in terms of the underlying action; and we prove that, whenever \O_{G,\Lambda} is simple, there is a dichotomy: it is either stably finite or purely infinite, depending on whether $\Lambda$ has nonzero graph traces or not. Our main results generalize the recent work of Exel and Pardo on self-similar graphs.Comment: 28 pages; minor change

K-theory for group C*-algebras

These notes are based on a lecture course given by the first author in the Sedano Winter School on K-theory held in Sedano, Spain, on January 22-27th of 2007. They aim at introducing K-theory of C*-algebras, equivariant K-homology and KK-theory in the context of the Baum-Connes conjectur