Jantzen coefficients and simplicity of generalized Verma modules

The main purpose of the paper is to establish new tools in the study of $\mathcal{O}^\mathfrak{p}$. We introduce the Jantzen coefficients of generalized Verma modules. It comes from the Jantzen's simplicity criteria for generalized Verma modules and has a deep relation with the structure of $\mathcal{O}^\mathfrak{p}$. We develop a reduction process to compute those coefficients. For which we need to consider generalized Verma modules induced from maximal parabolic subalgebras having maximal nontrivial singularity, so called basic generalized Verma modules. The classification of such modules is obtained in this paper. As the first application of our results, we give a refinement of Jantzen's simplicity criteria.Comment: 43 pages, 4 figure

Analysis of Exotic Hybrid eta pion, eta-prime pion Decays

Investigations of the mass and decays of the exotic hybrid are reviewed, including calculation of the pion1 to eta pion, eta-prime pion decay widths within the QCD sum rules technique. In this calculation, the recently-proposed eta, eta-prime quark mixing scheme is employed. The results indicate that the decay width Gamma(pion1 to eta pion) around 250 MeV is large compared with the decay width Gamma(pion1 to eta-prime pion) around 20 MeV. Inspired by these results, some phenomenological approaches are suggested to gain an understanding of the underlying mechanism of eta pion and eta-prime pion hybrid decays.Comment: 4 pages, talk presented at the 10th International Symposium on Meson-Nucleon Physics and the Structure of the Nucleon(MENU2004), Beijing, China, August 29 to September 4, 200

Possible 2S and 1D charmed and charmed-strange mesons

Possible $2S$ and $1D$ excited $D$ and $D_s$ states are studied, the charmed states $D(2550)^0$, $D^\ast(2600)$, $D(2750)^0$ and $D^\ast(2760)$ newly observed by the BaBar Collaboration are analyzed. The masses of these states are explored within the Regge trajectory phenomenology, and the strong decay widths are computed through the method proposed by Eichten {\it et al.}\cite{Eichten}. Both the mass and the decay width indicate that $D(2550)^0$ is a good candidate of $2^1S_0$. $D^\ast(2600)$ and $D_{s1}^\ast(2700)^\pm$ are very possible the admixtures of $2^3S_1$ and $1^3D_1$ with $J^P=1^-$ and a mixing angle $\phi\approx 19^0$. $D^\ast(2760)$ and $D_{sJ}^\ast(2860)^\pm$ are possible the $1^3D_3$ $D$ and $D_s$, respectively. $D(2750)^0$ and $D^\ast(2760)$ seem two different states, and $D(2750)^0$ is very possible the $1D(2^-, \frac{5}{2})$ though the possibility of $1D(2^-, \frac{3}{2})$ has not been excluded. There may exist an unobserved meson $D_{sJ}(2850)^\pm$ corresponding to $D^\ast_{sJ}(2860)^\pm$.Comment: 6 pages, 5 tables, 4 figures, RevTe

Light Four-quark States and New Observations by BES

Four-quark states are discussed within the constituent quark model. Incompleteness of existed studies of four-quark state with QCD sum rule is analyzed. The masses of diquark cluster were determined by QCD sum rules, and light four-quark states masses were obtained in terms of the diquark. The four-quark state possibility of the newly observed near-threshold p\bar p enhancement, X(1835), X(1812) and X(1576) by BES is discussed.Comment: 4pages, no figure, PTPTEX, talk at the Yukawa International Seminar (YKIS2006), "New frontiers in QCD", Kyoto, Japa

The spectrum and strong couplings of heavy-light hybrids

The spectrum of the $0^{++}$, $0^{--}$, $1^{-+}$ and $1^{+-}$ heavy-light hybrids have been calculated in HQET. The interpolated current of the hybrid is chosen as $g\bar q\gamma_{\alpha}G_{\alpha\mu}^aT^ah_{\it v}(x)$, $g\bar q\gamma_{\alpha}\gamma_{5}G_{\alpha\mu}^aT^ah_{\it v}(x)$ and $g\bar q\sigma_{\mu\alpha}G_{\alpha\mu}^aT^ah_{\it v}(x)$. Some strong couplings and decay widths of the heavy-light hybrids to $B(D)\pi$ are calculated by using the QCD sum rules. The mass of $0^{++}$ hybrid with gluon in TM($1^{--}$) or TE($1^{+-}$) mode is found similar, while their decay widths are different. A two-point correlation function between the pion and vacuum is employed and the leading order of $1/M_Q$ expansion is kept in our calculation.Comment: 12 pages, 5 ps figures, Latex fil