Effective low energy Lagrangian for QCD

The peculiar collective excitations of gluons, related to the Lorentz transformations of the conjugate field tensor, were proposed in a previous paper. The pseudoscalar mesons are related in the same way to the chiral transformations of quarks. We discuss these relations, including the U (1) problem, and derive the low energy effective Lagrangian for all these collective excitations. This Lagrangian contains the potential for the U (1) field due to axial anomalies.     

A Light-Cone QCD Inspired Effective Hamiltonian Model for Pseudoscalar and Scalar Mesons

Considering the one-gluon exchange interaction and phenomenological quark confinement potential, an improved light-cone effective Hamiltonian for mesons and the corresponding radial mass eigen equations in angular momentum representation is obtained. Solving the J = 0 eigen equations numerically and using a set of adjustable parameters, the obtained solutions for ground states and radial excited states can simultaneously describe both pseudoscalar and scalar flavour-off-diagonal mesons. Some radial excited states are also predicted and wait for experimental test. More results for the vector and axial vector mesons are expected.     

Perturbative versus lattice QCD energy density correlators at high temperatures

Correlators of magnetic and electric field energy density are investigated for SU(N_c) gauge theory at high temperatures T. A separations z ⩽ 2/T the correlators are shown to be dominated by a power-law behavior even for finite gluon screening masses. This continuum behavior is well approximated on current 4 × 16³-lattices in the perturbative limit and leads to a considerable overestimate of screening masses deduced from fitting the lattice correlators with conventional exponential forms. The use of extended sources and sinks to enhance the signal improves the situation for screening masses m ⪢ T but leads to a largely uncontrolled error for masses less than T. In fact, we show that recent lattice QCD data of Grossmann et al., from which a magnetic screening mass m_M ∼ 2.9T was deduced, may even be consistent with a vanishing actual magnetic screening mass.     

Hamiltonian for Reggeon interactions in QCD

It is shown, that the interaction of the reggeized gluons in the leading logarithmic approximation of the multicolour QCD has a number of remarkable properties including the duality symmetry. The duality relation for the Odderon wave function takes a form of the one-dimensional Schrödinger equation. It gives a possibility to express the Odderon Hamiltonian as a function of its integrals of motion.     

Renormalization of Hamiltonian QCD

We study to one-loop order the renormalization of QCD in the Coulomb gauge using the Hamiltonian formalism. Divergences occur which might require counter-terms outside the Hamiltonian formalism, but they can be cancelled by a redefinition of the Yang–Mills electric field.     

Perturbative QCD at high energies

A partial review of QCD at high energies is given. Factorization and the use of the renormalization group equation are emphasized. Topics discussed are the parton model, cut vertices in covariant and axial gauges, μ-pair production, jets, form factors, x → 1 limit of structure fu nctions, wide angle elastic scattering and heavy quarkonium exclusive decays. A discussion of mass and infrared singularities and a discussion of Sudakov effects are also included.     

Statistical physics in QCD evolution towards high energies

The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies and at a fixed impact parameter is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects(such as gluon recombination) is a reaction-diffusion process. In this review article, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.     

A Light-Cone QCD Inspired Effective Hamiltonian Model with SU（3） Flavor Mixing

The effective light-cone Harniltonian is extended to include the SU（3） flavor mixing interaction besides the confining potential. Solving the coupled J = 0 mass eigen equations for the up, down, and strange quark components numerically, the masses of π^0 and η, their radial wave functions, and rms radii are obtained in agreement with the experimental data.     

On confinement in a light-cone Hamiltonian for QCD

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions and in the light-cone gauge is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fock-space amplitudes can be retrieved self-consistently from solutions in the -space. The approach is based on the novel method of iterated resolvents and on discretized light-cone quantization driven to the continuum limit. It is free of the usual perturbative Tamm-Dancoff truncations in particle number and coupling constant and respects all symmetries of the Lagrangian including covariance and gauge invariance. Approximations are done to the non-truncated formalism. Together with vertex as opposed to Fock-space regularization, the method allows to apply the renormalization programme non-perturbatively to a Hamiltonian. The conventional QCD scale is found arising from regulating the transversal momenta. It conspires with additional mass scales to produce possibly confinement. Received: 27 March 1998 / Revised version: 3 June 1998 / Published online: 16 September 1998     

QCD factorization for forward hadron scattering at high energies

We calculate the branching ratios and CP asymmetries of the B???Ц?, ?Ц? decays in the perturbative QCD factorization approach up to the next-to-leading-order contributions. We find that the next-to-leading-order contributions can interfere with the leading-order part constructively or destructively for different decay modes. Our numerical results have a much better agreement with current available data than previous leading-order calculations, e.g., the next-to-leading-order corrections enhance the B ⁰???? ⁰ ?? ⁰ branching ratios by a factor 2.5, which is helpful to narrow the gaps between theoretic predictions and experimental data. We also update the direct CP-violation parameters, the mixing-induced CP-violation parameters of these modes, which show a better agreement with experimental data than many of the other approaches.     

Effective Hamiltonian for fluid interfaces

Based on a microscopic theory of inhomogeneous fluids we derive a non-Gaussian and nonlocal effetive Hamiltonian of a liquid-vapor interface. A partial resummation of a gradient expansion yields terms proportional to the area as well as to the Gaussian and the square of the mean curvature of the interface. For van der Waals fluids the gradient expansion breaks down and leads to a singularity in the momentum dependent surface tension. The nonlocal Hamiltonian and various approximations thereof are compared quantitatively.