Radiative and leptonic decays of the pseudoscalar charmonium state ηc\eta_c

The radiative and leptonic decays of $\eta_c\to \gamma\gamma$ and $\eta_c\to l^+l^-$ are studied. For $\eta_c\to \gamma\gamma$ decay, the second-order electromagnetic tree-level diagram gives the leading contribution. The decay rate of $\eta_c\to \gamma\gamma$ is calculated, the prediction is in good agreement with the experimental data. For \eta_c\to l^+\l^-, both the tree and loop diagrams are calculated. The analysis shows that the loop contribution dominates, the contribution of tree diagram with $Z^0$ intermediate state can only modifies the decay rate by less than 1%. The prediction of the branching ratios of $\eta_c\to e^+e^-$ and $\mu^+\mu^-$ are very tiny within the standard model. The smallness of these predictions within the standard model makes the leptonic decays of $\eta_c$ sensitive to physics beyond the standard model. Measurement of the leptonic decay may give information of new physics.Comment: 9 pages, 4 figures, RevTex, small change, version to appear in Phys. Rev.

Scalar Perturbations Through Cycles

We analytically and numerically investigate the evolutions of the scalar perturbations through the cycles with nonsingular bounce. It is found that the amplitude of the curvature perturbation on large scale will be amplified cycle by cycle, and the isocurvature perturbations also obtain an amplification, but the rate of its amplification is slower than that of curvature perturbation, unless its coupling to the metric perturbation is not negligible.Comment: 7 pages, 10 figure

Bell Inequalities Classifying Bi-separable Three-qubit States

We present a set of Bell inequalities that gives rise to a finer classification of the entanglement for tripartite systems. These inequalities distinguish three possible bi-separable entanglements for three-qubit states. The three Bell operators we employed constitute an external sphere of the separable cube.Comment: 8 page

The Multiphase Intracluster Medium in Galaxy Groups Probed by the Lyman Alpha Forest

The case is made that the intracluster medium (ICM) in spiral-rich galaxy groups today probably has undergone much slower evolution than that in elliptical-rich groups and clusters. The environments of proto-clusters and proto-groups at z > 2 are likely similar to spiral-rich group environments at lower redshift. Therefore, like the ICM in spiral-rich groups today, the ICM in proto-groups and proto-clusters at z > 2 is predicted to be significantly multiphased. The QSO Lyman alpha forest in the vicinity of galaxies is an effective probe of the ICM at a wide range of redshift. Two recent observations of Lyman alpha absorption around galaxies by Adelberger et al. and by Pascarelle et al are reconciled, and it is shown that observations support the multiphase ICM scenario. Galaxy redshifts must be very accurate for such studies to succeed. This scenario can also explain the lower metallicity and lower hot gas fraction in groups.Comment: 4 pages, 1 figure, replaced with the version after proo

Multifractal detrending moving average cross-correlation analysis

There are a number of situations in which several signals are simultaneously recorded in complex systems, which exhibit long-term power-law cross-correlations. The multifractal detrended cross-correlation analysis (MF-DCCA) approaches can be used to quantify such cross-correlations, such as the MF-DCCA based on detrended fluctuation analysis (MF-X-DFA) method. We develop in this work a class of MF-DCCA algorithms based on the detrending moving average analysis, called MF-X-DMA. The performances of the MF-X-DMA algorithms are compared with the MF-X-DFA method by extensive numerical experiments on pairs of time series generated from bivariate fractional Brownian motions, two-component autoregressive fractionally integrated moving average processes and binomial measures, which have theoretical expressions of the multifractal nature. In all cases, the scaling exponents $h_{xy}$ extracted from the MF-X-DMA and MF-X-DFA algorithms are very close to the theoretical values. For bivariate fractional Brownian motions, the scaling exponent of the cross-correlation is independent of the cross-correlation coefficient between two time series and the MF-X-DFA and centered MF-X-DMA algorithms have comparative performance, which outperform the forward and backward MF-X-DMA algorithms. We apply these algorithms to the return time series of two stock market indexes and to their volatilities. For the returns, the centered MF-X-DMA algorithm gives the best estimates of $h_{xy}(q)$ since its $h_{xy}(2)$ is closest to 0.5 as expected, and the MF-X-DFA algorithm has the second best performance. For the volatilities, the forward and backward MF-X-DMA algorithms give similar results, while the centered MF-X-DMA and the MF-X-DFA algorithms fails to extract rational multifractal nature.Comment: 15 pages, 4 figures, 2 matlab codes for MF-X-DMA and MF-X-DF

A Note on Normal Forms of Quantum States and Separability

We study the normal form of multipartite density matrices. It is shown that the correlation matrix (CM) separability criterion can be improved from the normal form we obtained under filtering transformations. Based on CM criterion the entanglement witness is further constructed in terms of local orthogonal observables for both bipartite and multipartite systems.Comment: 8 page

Radio Supernova SN 1998bw and Its Relation to GRB 980425

SN 1998bw is an unusual Type Ic supernova that may be associated with the $\gamma$-ray burst GRB 980425. We use a synchrotron self-absorption model for its radio emission to deduce that the synchrotron-emitting gas is expanding into a circumstellar medium of approximately $r^{-2}$ density profile, at a speed comparable to the speed of light. We assume that the efficiencies of production of relativistic electrons and magnetic field are constant through the evolution. The circumstellar density is consistent with that expected around the massive star core thought to be the progenitor of SN 1998bw. The explosion energy in material moving with velocity $>0.5c$ is $\sim 10^{49}- 3\times 10^{50}$ ergs, with some preference for the high values. The rise in the radio light curves observed at days 20-40 is inferred to be the result of a rise in the energy of the blast wave by a factor $\sim 2.5$. Interaction with a jump in the ambient density is not consistent with the observed evolution. We infer that the boost in energy is from a shell of matter from the explosion that catches up with the decelerating shock front. Both the high explosion energy and the nature of the energy input to the blast wave are difficult to reconcile with energy input from the shock-accelerated high velocity ejecta from a supernova. The implication is that there is irregular energy input from a central engine, which is the type of model invoked for normal $\gamma$-ray bursts. The link between SN 1998bw and GRB 980425 is thus strengthened.Comment: 21 pages, 9 figures, revised version to appear in Ap

Resonances from meson-meson scattering in U(3) CHPT

In this work, the complete one loop calculation of meson-meson scattering amplitudes within U(3)\otimes U(3) chiral perturbation theory with explicit resonance states is carried out for the first time. Partial waves are unitarized from the perturbative calculation employing a non-perturbative approach based on the N/D method. Once experimental data are reproduced in a satisfactory way we then study the resonance properties, such as the pole positions, corresponding residues and their N_C behaviors. The resulting N_C dependence is the first one in the literature that takes into account the fact that the \eta_1 becomes the ninth Goldstone boson in the chiral limit for large N_C. Within this scheme the vector resonances studied, \rho(770), K^*(892) and \phi(1020), follow an N_C trajectory in agreement with their standard \bar{q}q interpretation. The scalars f_0(1370), a_0(1450) and K^*(1430) also have for large N_C a \bar{q}q pole position trajectory and all of them tend to a bare octet of scalar resonances around 1.4 GeV. The f_0(980) tends asymptotically to the bare pole position of a singlet scalar resonance around 1 GeV. The \sigma, \kappa and a_0(980) scalar resonances have a very different N_C behavior. The case of the \sigma resonance is analyzed with special detail.Comment: 50 pages, 15 figures, 1 table. Enlarged version with more detail comparisons with previous results in the literature. To match with accepted version for publicatio