Describing relativistic fermions with two-component field

With a non-unitary transformation, the Lagrangian of a Dirac fermion is decomposed into two decoupled sectors. We propose to describe massive relativistic fermions in gauge theories in a two-component form. All relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the gamma-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. The advantages of the two-component form make it very useful in practical applications.Comment: 9 page

Solving the rho - pi puzzle by higher charmonium Fock states

A new explanation for the longstanding puzzle of the tiny branching fraction of psi' --> rho pi relative to that for J/psi --> rho pi was proposed. In the case of J/psi, we argue that this decay is dominated by a higher Fock state in which the c cbar pair is in a color-octet ^3S_1 state and annihilates via the process c cbar --> q qbar. In the case of the psi', we argue that the probability for the c cbar c pair in this higher Fock state to be close enough to annihilate is suppressed by a dynamical effect related to the small energy gap between the mass of the psi' and the D Dbar threshold.Comment: 11 pages, Talk given at 3rd Workshop on Continuous Advances in QCD (QCD 98), Minneapolis, MN, 16-19 Apr 199

Renormalons in Electromagnetic Annihilation Decays of Quarkonium

We study the large-order asymptotic behavior of the perturbation series for short-distance coefficients in the NRQCD factorization formulas for the decays J/psi --> e^+e^- and eta_c --> gamma gamma. The short-distance coefficients of the leading matrix elements are calculated to all orders in the large-N_f limit. We find that there is a universal Borel resummable renormalon associated with the cancellation of the Coulomb singularity in the short-distance coefficients. We verify that the ambiguities in the short-distance coefficients from the first infrared renormalon are canceled by ambiguities in the nonperturbative NRQCD matrix elements that contribute through relative order v^2. Our results are used to estimate the coefficients of higher order radiative corrections in the decay rates for J/psi --> e^+ e^-, eta_c --> gamma gamma, and J/\psi --> gamma gamma gamma.Comment: The revised version changed the error of the renormalization of the Borel transform

Positronium decay in a circular polarized laser field

We calculate the lifetime of both the o-Ps and the p-Ps positronium annihilation decay $Ps\to\gamma\gamma$ in the strong circular polarized laser field. We take a strategy of the factorization to separate the effects caused by the Coulomb interaction and the strong laser field interaction. It is factorized in the time direction but not in the space direction. Our results show that in the laser with long wavelength and high intensity, the lifetimes of those Ps states are dramatically increased. For $\rm CO_2$ laser with $10\, \mu m$ wavelength and $10^{13} W/cm^2$ intensity, lifetime of the spin-single positronium is increased by $10^8$ times. Our result is consistent with those obtained by solving the Sch{\"{o}}dinger equation. This effect may be useful for the high harmonic generation(HHG) effects provided with the Ps\cite{keitel2004}.Comment: submitted to Communications in Theoretical Physic

Stationary patterns and their selection mechanism of Urban crime models with heterogeneous near-repeat victimization effect

In this paper, we study two PDEs that generalize the urban crime model proposed by Short \emph{et al}. [Math. Models Methods Appl. Sci., 18 (2008), pp. 1249-1267]. Our modifications are made under assumption of the spatial heterogeneity of both the near-repeat victimization effect and the dispersal strategy of criminal agents. We investigate pattern formations in the reaction-advection-diffusion systems with nonlinear diffusion over multi-dimensional bounded domains subject to homogeneous Neumann boundary conditions. It is shown that the positive homogeneous steady state loses its stability as the intrinsic near-repeat victimization rate $\epsilon$ decreases and spatially nonconstant solutions emerge through bifurcation. Moreover, we find the wavemode selection mechanism through rigorous stability analysis of these nontrivial patterns, which shows that the only stable pattern must have wavenumber that maximizes the bifurcation value. Based on this wavemode selection mechanism, we will be able to precisely predict the formation of stable aggregates of the house attractiveness and criminal population density, at least when the diffusion rate $\epsilon$ is around the principal bifurcation value. Our theoretical results also suggest that large domains support more stable aggregates than small domains. Finally, we perform extensive numerical simulations over 1D intervals and 2D squares to illustrate and verify our theoretical findings. Our numerics also include some interesting phenomena such as the merging of two interior spikes and the emerging of new spikes, etc. These nontrivial solutions can model the well observed aggregation phenomenon in urban criminal activities

Global well-posedness of advective Lotka-Volterra competition systems with nonlinear diffusion

This paper investigates the global well-posedness of a class of reaction-advection-diffusion models with nonlinear diffusion and Lotka-Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the fully parabolic systems under certain growth conditions on the diffusion and sensitivity functions. Global existence and uniform boundedness of the corresponding parabolic-elliptic system are also obtained. Our results suggest that attraction (positive taxis) inhibits blowups in Lotka-Volterra competition systems

Anomalous gauge couplings of the Higgs boson at the LHC II: Study of additional backgrounds in semileptonic mode of WW scatterings

Searching for the Higgs boson is of first priority in LHC experiments. Once a Higgs candidate is found, we then need to know whether it is the standard model (SM) Higgs boson or a Higgs boson in new physics beyond the SM. So far we do not know what model of new physics will actually reflect the property of the nature. A model-independent way of measuring the anomalous couplings of the Higgs boson will provide a no-lose study, i.e., if we find nonvanishing anomalous couplings (deviation from the SM couplings), we can conclude that it is a new physics effect. In a previous paper \cite{QKLZ09}, we gave a hadron level study of a model-independent test of the anomalous gauge couplings of the Higgs boson at the 14 TeV LHC via the semileptonic mode of weak-boson scatterings $pp\to W^+W^\pm j^f_1 j^f_2\to l^+\nu^{}_lj^{}_1j^{}_2j^f_1j^f_2$, and the conclusion is that, with certain kinematical cuts imposed, the measurement can start for an integrated luminosity of 50 fb$^{-1}$. For higher integrated luminosity, say 100 fb$^{-1}$, the two main anomalous coupling constants $f^{}_{WW}/\Lambda^2$ and $f^{}_W/\Lambda^2$ can be determined separately which may provide a clue for figuring out the underlying theory of new physics.Comment: 4 pages RevTex4 file with 6 eps files for the figures. Format improve

Masses of doubly heavy baryons in the Bethe-Salpeter equation approach

A doubly heavy baryon can be regarded as composed of a heavy diquark and a light quark. In this picture, we study the masses of the doubly heavy diquarkes in the Bethe-Salpeter (BS) formalism first, which are then used as one of the inputs in studying the masses of the doubly heavy baryons in the quark-diquark model. We establish the BS equations for both the heavy diquarks and the heavy baryons with and without taking the heavy quark limit, respectively. These equations are solved numerically with the kernel containing the scalar confinement and one-gluon-exchange terms. The mass of the doubly charmed baryon $\Xi_{cc}^{(\ast)}$ is obtained in both approaches, $3.60\sim3.65\,\rm GeV$ ($\Xi_{cc}^{(\ast)}$) under the heavy quark limit, $3.53\sim3.56\,\rm GeV$ for $\Xi_{cc}$ and $3.61\sim3.63\,\rm GeV$ for $\Xi_{cc}^\ast$ without taking the heavy quark limit. The masses of $\Xi_{bc}^\prime$, $\Xi_{bc}^{(\ast)}$, $\Xi_{bb}^{(\ast)}$, $\Omega_{cc}^{(\ast)}$, $\Omega_{bc}^\prime$, $\Omega_{bc}^{(\ast)}$ and $\Omega_{bb}^{(\ast)}$ are also predicted in the same way. We find that the corrections to the results in the heavy quark limit are about $-0.02\,\rm GeV\sim-0.11\,\rm GeV$ for the masses of the doubly heavy baryons

Strong decay mode J/ψpJ/\psi p of hidden charm pentaquark states Pc+(4380)P_c^+(4380) and Pc+(4450)P_c^+(4450) in ΣcDˉ∗\Sigma_c \bar{D}^* molecular scenario

We study the strong decay channels $P_c^+(4380) \to J/\psi p$ and $P_c^+(4450) \to J/\psi p$ under $\Sigma_c \bar{D}^*$ molecular state ansatz. With various spin-parity assignments, the partial decay widths of $J/\psi p$ final state are calculated. Our results show that all the $P$ wave $\Sigma_c {\bar D}^*$ assignments are excluded, while $S$ wave $\Sigma_c {\bar D}^*$ pictures for $P_c(4380)$ and $P_c(4450)$ are both allowed by present experimental data. The $J^P=3/2^-$ $\Sigma_c^* \bar{D}$ and $\Sigma_c^* \bar{D}^*$ molecules are also discussed in the heavy quark limit, and find that the $\Sigma_c^* \bar{D}$ system for $P_c(4380)$ is possible. More experimental information on spin-parities and partial decay widths and theoretical investigations on other decay modes are needed to clarify the nature of the two $P_c$ states.Comment: 7 pages, 6 figures, 2 tables. More discussions are added. Version accepted by Phys. Rev.

The Instantaneous Approximation to the Transition Matrix Elements between Two Bound States

Under the framework of the Bethe-Salpeter (B.S.) wave functions and the Mandelstam formalism as well, to make ``instantaneous approximation'' to a transition matrix element (a current operator sandwiched between two bound-states of double heavy quarks) is described. By taking the typical concerned decays as examples, such as $B_c$ meson decaying to $J/\psi + (\bar l \nu)$, the advantages of the approach and its limitations are illustrated. Finally, potential applications to various processes for possible double heavy flavoured systems, such as those of $(Q' \bar Q)$ and $(Q' Q)$ ($m_Q, m_{Q'}\gg \Lambda_{QCD}$), are discussed.Comment: 27 pages, 3 figures ( not included ), AS-ITP-93-8