The Instantaneous Bethe-Salpeter Equation and Its Analog: the Breit-like Equation

We take ($\mu^\pm e^\mp$) systems and consider the states with quantum number $J^P=0^-$ as examples, to explore the different contents of the instantaneous Bethe-Salpeter (BS) equation and its analog, Breit equation, by solving them exactly. The results show that the two equations are not equivalent, although they are analogous. Furthermore, we point out that the Breit equation contains extra un-physical solutions, so it should be abandoned if one wishes to have an accurate description of the bound states for the instantaneous interacting binding systems.Comment: 5 pages, no figur

On the Role of Surface Friction in Tropical Intraseasonal Oscillation

The Madden-Julian oscillation (MJO), or the tropical intraseasonal oscillation, has attracted much attention, ever since its discovery in the early seventies for reasons of both scientific understanding and practical forecasts. Among the theoretical interpretations of the MJO, the wave-CISK (conditional instability of the second kind) mechanism is the most popular. The basic idea of the wave-CISK interpretation is that the cooperation between the low-level convergence associated with the eastward moving Kelvin wave and the cumulus convection generates an eastward moving Kelvin-wave-like mode. Later it was recognized that the MJO has an important Rossby-wave-like component. However linear analysis and numerical simulations based on it (even when conditional heating is used) have revealed two problems with the wave-CISK interpretation; i.e., excessive speed and the most preferred scale being zero or grid scale. Chao (1995) presented a discussion of these problems and attributed these problems to the particular type of expression for the cumulus heating used in the linear analyses and numerical studies (i.e., the convective heating is proportional to low-level convergence and a fixed vertical heating profile). It should be pointed out that in the relatively successful simulation of MJO with general circulation models the problem of grid scale being the most preferred scale does not appear and die problem of excessive speed is not as severe as in the linear analysis

The meson BcB_c annihilation to leptons and inclusive light hadrons

The annihilation of the $B_c$ meson to leptons and inclusive light hadrons is analyzed in the framework of nonrelativistic QCD (NRQCD) factorization. We find that the decay mode, which escapes from the helicity suppression, contributes a sizable fraction width. According to the analysis, the branching ratio due to the contribution from the color-singlet component of the meson $B_c$ can be of order (10^{-2}). We also estimate the contributions from the color-octet components. With the velocity scaling rule of NRQCD, we find that the color-octet contributions are sizable too, especially, in certain phase space of the annihilation they are greater than (or comparative to) the color-singlet component. A few observables relevant to the spectrum of charged lepton are suggested, that may be used as measurements on the color-octet and color-singlet components in the future $B_c$ experiments. A typical long distance contribution in the annihilation is estimated too.Comment: 26 pages, 5 figures (6 eps-files), submitted to Phys. Rev.