Vector Susceptibility of QCD Vacuum from an Effective Quark-Quark Interaction

A new approach for calculating vacuum susceptibilities from an effective quark-quark interaction model is derived. As a special case, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is given.     

Vector Susceptibility of QCD Vacuum from an Effective Quark-Quark Interaction

.A new approach for calculating vacuum susceptibilities from an effective quark-quark interaction model is derived. As a special case, the vector vacuum susceptibility is calculated. A comparison with the results of the previous approaches is given.     

Effective Hamiltonains and degenerate perturbation theory calculations of the mass spectrum in lattice QCD

Hamiltonian quantum chromodynamics has been formulated on a discrete lattice, in an attempt to calculate the hadronspectrum using strong coupling expansions. Previous attempts have involved including an irrelevant four-fermion interaction term in the Hamiltonian. As well as making the quark content of the zeroth order states the same as that of the simple additive quark model, this term splits the infinite zeroth order degeneracies of the original Hamiltonian. In this paper we calculate the masses of low lying states in the absence of such a term, using an effective Hamiltonian method to solve the degeneracy problem. We discuss the problems of continuing our series to the continuum limit in the presence of level repulsion.     

QCD axion from a higher dimensional gauge field theory

We point out that a QCD axion solving the strong CP problem can arise naturally from a parity-odd gauge field in five-dimensional (5D) orbifold field theory. The required axion coupling to the QCD anomaly comes from the 5D Chern-Simons coupling, and all other unwanted U(1)PQ breaking axion couplings can be avoided naturally by the 5D gauge symmetry and locality. If the fifth dimension is warped, the resulting axion scale is suppressed by a small warp factor compared to the Planck scale, thereby the model can generate naturally an intermediate axion scale fa = 10(10)-10(12) GeV.     

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.     

Derivation of Effective Chiral Lagrangian Involving PSGB and Vector Bosons from QCD

The effective chiral Lagrangian for a matter field content consisting of pseudo-scalar Goldstone bosons and vector bosons (with hidden symmetry) is derived from the underlying QCD theory. No approximations are made. All the free parameters of the effective chiral Lagrangian are expressed in terms of QCD-based Green's functions. These may be regarded as the QCD definitions of these Lagrangian coefficients.     

Multicolor QCD as a dual-resonance theory

The quantum chromodynamics with massless quarks and an infinite number of colors is represented as a theory of the noninteracting mesons which lie on rising Regge trajectories. The perturbation theory for these trajectories is developed. The expansion parameter (effective coupling) is calculated and appears to be about $\text{1}\text{2}$. The expansion coefficients can also be calculated analytically as functions of spin and other quantum numbers. The calculations are carried through to the end in the zeroth and first order. The resulting trajectories look reasonable and are in qualitative agreement with experiment. The corrections from finite numbers of colors and from quark masses can also be found, but are not considered here.     

Effective operators with potentials from meson theory

We have studied the effective charge and interaction in the (sd) shell with the Bonn-Jülich and Paris potentials. Incorporating essentially all the low-energy correlations of known importance, we find that the former potential gives quite a good account of the data when allowance is made for the effect of low-lying particle-hole states. The Paris potential gives somewhat less core polarization and a less attractive bare T=0 spectrum due to weaker T=0 matrix elements.     

Effective Hamiltonian for QCD evolution at high energy

We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which involves two types of Wilson lines: longitudinal Wilson lines which describe gluon recombination (or merging) and temporal Wilson lines which account for gluon bremsstrahlung (or splitting). The Hamiltonian is self-dual, i.e., it is invariant under the exchange of the two types of Wilson lines. In the high density regime where one can neglect gluon number fluctuations, the general Hamiltonian reduces to that for the JIMWLK evolution. In the dilute regime where gluon recombination becomes unimportant, it reduces to the dual partner of the JIMWLK Hamiltonian, which describes bremsstrahlung.     

Effective potentials in QCD and chiral symmetry breaking

We consider chiral symmetry breaking through nontrivial vacuum structure with an explicit construct for the vacuum with quark antiquark condensates in QCD with Coulomb gauge for different phenomenological potentials. The dimensional parameter for the condensate function gets related to \(\left\langle {\bar \psi \psi } \right\rangle \) of Shifman, Vainshtein and Zakharov. We then relate the condensate function to the wave function of pion as a Goldstone mode. This simultaneously yields the pion also as a quark antiquark bound state as a localised zero mode of vacuum. We then calculate different pionic properties using the wave function as obtained from the vacuum structure.     

How to extract QCD baryons from a lattice theory with staggered fermions

The explicit form of the correlation function for the most general local baryon operators is obtained for staggered fermions, in the center of mass. From the discrete symmetries of the action, it is shown that all operators couple to spin-$\text{1}\text{2}$ states only. The whole physical information coming from any numerical simulation, including parity assignments, can be extracted from only one real function of the lattice time. All other correlation functions which can be measured vanish in the limit of large samples of gauge configurations, which may be used as a measure of the statistical significance of data.     

QCD perturbation theory in the temporal gauge

In this paper we present a non-trivial check of the consistency of the quantization of a gauge theory with fermions (QCD) in the temporal gauge. We use the approach based on the finite time Feynman propagation kernel, in which the Gauss law is imposed as a constraint on the states by means of a functional integration over all the time independent gauge transformations acting on the boundary values of the fields. We spell out in detail the “Feynman rules” when fermions are present and we compute, as an example, the gauge invariant correlation function $$\begin{gathered} G(t) = \left\langle {\bar \psi (0,t)(\gamma _5 \gamma _0 )\frac{{1 - \gamma _0 }}{2}P} \right. \hfill \\ \left. { \cdot \exp \left( {ig\int\limits_0^t {A_0 (0,t')dt'} } \right)(\gamma _5 \gamma _0 )^ + (0,0)} \right\rangle \hfill \\ \end{gathered} $$ up to orderg ², obtaining the expected result.