Meson Operators Research Articles

QCD sum rules, the spontaneous breakdown of chiral symmetry and short-distance behaviour in lattice gauge theories

We analyze the behaviour that correlation functions ought to have on the lattice in order to reproduce QCD sum rules in the continuum limit. We formulate a set of relations between lattice correlation functions of meson operators at small time separation and the quark condensates responsible for spontaneous breakdown of chiral symmetery. We suggest that the degree to which such relations are satisfied will provide a set of consistency checks on the ability of lattice Monte Carlo simulations to reproduce the correct spontaneous chiral symmetry breaking of the continuum theory.

Field-operator decomposition in the Lee model

The decomposition of the meson field operator into internal and external parts is shown to provide a new, relatively simple approximation scheme that gives approximate eigenvalues, eigenvectors, and scattering phase shifts in all sectors of the Lee model. The form of the internal meson mode functions involves an energy parameter $\ensuremath{\epsilon}$ that is determined in a physical way that is peculiar to systems in which the ground-state expectation value of the meson source current operator is required by the internal symmetry of the system to be zero.

Unified theory of meson and nucleon scattering by nuclei

In the meson-nucleon model of nuclei, the decomposition of the meson and nucleon field operators into internal and external parts provides a way of treating orthogonality effects in the scattering of hadrons by a nucleus. Under this decomposition, the Hamiltonian of the system splits into an internal part and terms that couple external modes. The internal part of the Hamiltonian is the Hamiltonian of the meson-nucleon shell model, and its eigenstates are approximations to the bound nuclear states. The rest of the Hamiltonian describes the external quanta of the fields and their interactions with the internal states. The internal mode functions are chosen so as to minimize the coupling of the external modes to the low-lying internal states. The Green's functions for the external fields and the diagrammatic representation of the perturbation series are presented and used to describe the treatment of hadron scattering in the one-external-hadron sector.NUCLEAR STRUCTURE $\ensuremath{\pi}$-nucleus and nucleon-nucleus scattering theory.

Renormalization and Short Distance Properties of Gauge Invariant Gluonium and Hadron Operators

AbstractVarious expressions for nonlocal gauge invariant meson, baryon and gluonium operators are considered which differ from one another not only by the colour representations of the phase factors used but also with respect to the underlying contours. Renormalization and short distance properties of these operators turn out to be unique as long as the contours chosen are smooth ones. Anomalous dimensions of mesons and baryons can be expressed in terms of a gauge independent anomalous dimension of the quark field. Furthermore, composite operators distinguished by the absence of renormalization are discussed.

One-meson sector in static models

The explicit T matrix is given for a general static model in the one-meson subspace of the Tomonaga resolution of the meson field operator. A particular choice of the meson internal-mode function is made. The effective raising of the phase-shift threshold in the ground channel that is observed in pion-nucleon scattering is shown to occur in a natural way in the static model.

Construction of local meson operator from the path-ordered operator in QCD 2

A local meson operator is constructed from the path-ordered operator on QCD 2. The meson operator satisfies the Klein-Gordon equation with the mass identical to the eigenvalue of the 't Hooft equation. The interaction of the meson is shown to be nonlocal and to have a coupling proportional to 1/ N c.

High-energy behavior, duality, and theSU(6)Wstructure of the electromagnetic and mesonic transition operators

Using duality and the high-energy behavior of the pseudoscalar-meson photoproduction helicity amplitudes, we perform an analysis of the $\mathrm{SU}{(6)}_{W}$ structure of the electromagnetic and mesonic transition operators. It is found that spin-orbit terms might be present if the magnetic term is present. If this is not the case, one finds some strong restrictions on hadron couplings.

Schwinger terms and pseudoscalar mesons

Effective meson operators are exhibited for a class of chiral SU(2) current models, and the general ( 1 2 N, 1 2 N) symmetry breaking Hamiltonian is constructed from Schwinger terms. A closed form is thus found for the corresponding non-linear pion Lagrangian in general coordinates.

Chew-Low formalism for two nucleon-meson systems

The system of two nonrelativistic nucleons interacting with symmetric pseudoscalar mesons is considered via an expansion in terms of the meson cloud of fixed nucleons. A Chew-Low formalism is constructed for the fixed two-nucleon system. Matrix elements of meson field operators between physical states can be expressed in terms of matrix elements of spin-isospin operators and propagators. It is demonstrated that for a class of nonsingular propagators the latter as a function of separation of the fixed nucleons can be expanded in a convergent expansion about infinite separation. The energies of the bound meson states are just the static nuclear potentials, and an integral equation for them is derived.

The physical nucleon in static source meson theory

A wave function for the physical nucleon in static source meson theory has been constructed by the method of moments. The wave function includes contributions from states containing as many as five mesons, and is shown to be a good approximation to the ground state of the Hamiltonian. Because of the restrictive nature of the static model, the probability that the meson cloud have a particular angular momentum or isotopic spin turns out to be almost independent of the dynamics of the system. Since the matrix elements of the nucleon spin and isotopic spin operators can be expressed in terms of these probabilities, such matrix elements are determined essentially by the kinematics of the meson cloud. This fact renders unreliable any predictions of the static model which depend on matrix elements of the nucleon operators. The consistent failure of the static model to explain satisfactorily the scalar part of the magnetic moment may be ascribed to this cause. The quantities which depend on meson operators are more closely related to the dynamics of the system. The vector part of the magnetic moment is in agreement with experiment, and the electron-neutron interaction turns out much too large; these results differ little from those obtained by the Chew—Low one-meson approximation. However, the contributions of the many meson states are not negligible, and the mean number of mesons is found to be closer to two than to one. Evaluation of the charge renormalization enables us to test the scattering amplitudes predicted by the static model against the sum rules of Cini and Fubini. It is found that, for the conventional value of renormalized coupling constant, the sum rules are strongly violated. This result, together with the substantial many meson component of the wave function, casts doubt on the validity of the one-meson approximation in the static model.

Contribution of Recoil to Charge Distribution of Nucleons

Mean-square radii of the charge distribution of nucleons are obtained in closed form in terms of meson field operators, by applying a certain transformation to a relativistic one-nucleon theory. They are evaluated by using the pion distribution as given by a modified extended-source theory which takes into account part of the recoil energy of the nucleon. Such a theory derives from the original one-nucleon theory as a result of an expansion in inverse powers of the nucleon mass. The result shows that the radius of the nucleon core, which arises solely from recoil, is much smaller than the one inferred from electron-proton scattering experiments. On the other hand, the recoil correction to the static charge distribution of the pion cloud is negative and so large as almost to cancel the latter.

A soluble model of meson-nucleonS-state scattering

We consider the interaction Hamiltonian\((1) (*) H_1 = g\int {d_3 x\bar \psi (x)} \varphi (x) \cdot \varphi (x)\psi (x) + \lambda \int {d_3 x\bar \psi (x)} (\pi (x) \times \varphi (x))\tau \psi (x)\) There is evidence (1,2) that for meson-nucleon scattering (1) represents a large part of theps(ps)s-state interaction for intermediate as well as as weak coupling, providing that λ/g is suitably altered. The first term of (1) has long been known to be diagonalizable in the static nucleon limit (3). The isotopic spin coupling of the second term requires that the isotopic spin variable of the nucleon be left free (non-static) thus complicating the diagonalization. By combining the nucleon spin operator with the meson field operators we have succeeded in diagonalizing (1). The parameters determined by experiment are reasonable. One can examine many formal aspects. The point source limit exists.