arXiv subjects

A. G. Williams

Publications and source records attributed to A. G. Williams.

144 records · Page 8Linked to original sources

arXiv1997

Near-threshold Isospin Violation in the Pion Form Factor from Chiral Perturbation Theory

We examine the isospin violation in the timelike pion form factor near threshold at next-to-leading order in the chiral expansion using the techniques of Chiral Perturbation Theory. This next-to-leading order contribution contains the first nonvanishing isospin violation. This isospin violation is found to be very small near threshold. In particular, the isospin violation at threshold is found to be of order 10^-4, which should be compared with the few percent level seen in the vector meson resonance region.

hep-ph↗

arXiv1997

On extracting the rho-omega mixing amplitude from the pion form-factor

In this paper we improve and extend a recent analysis which showed that the rho-omega mixing amplitude cannot be unambiguously extracted from the pion electromagnetic form-factor in a model independent way. In particular, we focus on the argument that the extraction is sensitive to the presence of any intrinsic omega_I -> pi pi coupling. Our extended analysis confirms the original conclusion, with only minor, quantitative differences. The extracted mixing amplitude is shown to be sensitive to both the intrinsic coupling omega_I -> pi pi and to the value assumed for the mass of the rho^0-meson.

hep-ph↗

arXiv1997

In-medium electron-nucleon scattering

In-medium nucleon electromagnetic form factors are calculated in the quark meson coupling model. The form factors are typically found to be suppressed as the density increases. For example, at normal nuclear density and $Q^2 \sim 0.3 { GeV}^2$, the nucleon electric form factors are reduced by approximately 8% while the magnetic form factors are reduced by only 1 - 2%. These variations are consistent with current experimental limits but should be tested by more precise experiments in the near future.

nucl-th↗

arXiv1997

Optimization of Monte-Carlo calculations of the effective potential

We study Monte Carlo calculations of the effective potential for a scalar field theory using three techniques. One of these is a new method proposed and tested for the first time. In each case we extract the renormalised quantities of the theory. The system studied in our calculations is a one component $ϕ^4$ model in two dimensions. We apply these methods to both the weak and strong coupling regime. In the weak coupling regime we compare our results for the renormalised quantities with those obtained from two-loop lattice perturbation theory. Our results are verified in the strong coupling regime through comparison with the strong coupling expansion. We conclude that effective potential methods, when suitably chosen, can be accurate tools in calculations of the renormalised parameters of scalar field theories.

hep-lat↗

arXiv1996

Delta electroproduction in a chiral bag model approach

We study the γ^* N -> Δtransition amplitudes in a recoil corrected cloudy bag model approach. A modified Peierls-Thouless projection method is used to construct the Galilean invariant baryon states. The pionic contribution is found to be significant. The effect of the recoil correction is to reduce the magnitude of the transition amplitudes at small momentum transfer and to enhance them at modest momentum transfers.

nucl-th↗

arXiv1996

A chiral bag model approach to delta electroproduction

Helicity amplitudes for the $γ^* N \to Δ$ transition are calculated using the cloudy bag model. A correction for center-of-mass motion is carried out using a modified Peierls-Thouless projection method. This reduces the magnitude of the transition amplitudes at small momentum transfer and enhances them at modest momentum transfers. Our calculation shows that the pion cloud contributes substantially to the transition helicity amplitudes, with the final result giving reasonable agreement with the corresponding experimental values.

nucl-th↗

arXiv1996

Deep Inelastic Structure Functions in a Covariant Spectator Model

Deep-inelastic structure functions are studied within a covariant scalar diquark spectator model of the nucleon. Treating the target as a two-body bound state of a quark and a scalar diquark, the Bethe-Salpeter equation (BSE) for the bound state vertex function is solved in the ladder approximation. The valence quark distribution is discussed in terms of the solutions of the BSE.

hep-ph↗

arXiv1996

Analysis of rho-omega interference in the pion form-factor

The formalism underlying the analysis of e+e- -> pi+pi- in the rho-omega interference region is carefully revisited. We show that the standard neglect of the pure I=0 omega, omega_I, `direct'' coupling to pi-pi is not valid, and extract those combinations of the direct coupling and ρ-omega mixing allowed by experiment. The latter is shown to be only very weakly constrained by experiment, and we conclude that data from the e+e- -> pi+pi- interference region cannot be used to fix the value of rho-omega mixing in a model-independent way unless the errors on the experimental phase can be significantly reduced. Certain other modifications of the usual formalism necessitated by the unavoidable momentum-dependence of rho-omega mixing are also discussed.

hep-ph↗

arXiv1996

Covariant Solutions of the Bethe-Salpeter Equation

There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes, which makes a direct solution in Minkowski space (without any 3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved for arbitrary scattering kernels in terms of a generalized spectral representation directly in Minkowski space (K. Kusaka et al., PRD 51, 7026 '95). This differs from the conventional Euclidean approach, where the BSE can only be solved in ladder approximation after a Wick rotation.

hep-ph↗

arXiv1996

Structure Functions of the Nucleon in a Covariant Scalar Spectator Model

Nucleon structure functions, as measured in deep-inelastic lepton scattering, are studied within a covariant scalar diquark spectator model. Regarding the nucleon as an approximate two-body bound state of a quark and diquark, the Bethe-Salpeter equation (BSE) for the bound state vertex function is solved in the ladder approximation. The valence quark distribution is discussed in terms of the solutions of the BSE.

hep-ph↗

arXiv1996

Solving the Bethe-Salpeter Equation in Minkowski Space: Scalar Theories and Beyond

The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is solved in Euclidean space after a Wick rotation. For all but the lowest-order (i.e., ladder) approximation to the scattering kernel, the {\it naive} Wick rotation is invalid. Our approach generates the vertex function and Bethe-Salpeter amplitude for the entire allowed range of momenta, whereas these cannot be directly obtained from the Euclidean space solution. Our method is quite general and can be applied even in cases where the Wick rotation is not possible.

hep-ph↗

arXiv1995

Chiral Symmetry Breaking in Strongly Coupled Quenched QED$_4$ Using the Dyson-Schwinger Equation Formalism

We study chiral symmetry breaking in quenched strong-coupling QED$_4$ in arbitrary covariant gauge within the Dyson-Schwinger equation formalism. A recently developed numerical renormalization program is fully implemented. Results are compared for three different fermion-photon proper vertex {\it Ansätze\/}: bare $γ^μ$, minimal Ball-Chiu, and Curtis-Pennington. The procedure is straightforward to implement and numerically stable. We discuss the chiral limit and observe that in this limit the renormalized axial current is conserved. A detailed study of residual gauge dependence due to the vertex choice is in progress. The relevance for lattice studies is discussed.

hep-lat↗

arXiv1994

Dyson-Schwinger equations and their application to nonperturbative field theory

Two examples of recent progress in applications of the Dyson-Schwinger equation (DSE) formalism are presented: (1) Strong coupling quantum electrodynamics in 4 dimensions (QED$_4$) is an often studied model, which is of interest both in its own right and as an abelian model of quantum chromodynamics (QCD). We present results from a study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in massive strong-coupling quenched QED$_4$. The procedure is straightforward to implement and numerically stable. (2) The Bethe-Salpeter equation (BSE) with a class of non-ladder scattering kernels is solved in {\it Minkowski space} in terms of the perturbation theory integral representation (PTIR). We consider a bound state of two spinless particles with the formal expression of the full scattering kernel in a $ϕ^2σ$ scalar model. We derive an integral equation for the weight function with a real kernel. We recover as a check results for the massive scalar ladder approximation.

hep-ph↗

arXiv1994

Relativistic Quark-Antiquark Bound State Problem with Spin-dependent Interactions in Momentum Space

The work described in this paper is the first step toward a relativistic three-quark bound-state calculation using a Hamiltonian consistent with the Wigner-Bargmann theorem and macroscopic locality. We give an explicit demonstration that we can solve the two-body problem in momentum space with spin-dependent interactions. The form of the potential is a combination of linear+Coulomb+spin-spin+% spin-orbit+tensor, which includes confinement and is of the general form consistent with rotation, space-reflection and time-reversal invariance. Comparison is made with previous calculations using an alternate technique and with the experimental meson mass spectrum. The results obtained suggest that the model is realistic enough to provide a two-body basis for the three quark baryon problem in which the Poincaré group representation is unitary and cluster separability is respected.

hep-ph↗

arXiv1993

Medium Modification to the $Ω$-Meson Mass in the Walecka Model

We calculate the effective mass of the $ω$ meson in nuclear matter in a relativistic random-phase approximation to the Walecka model. The dressing of the meson propagator is driven by its coupling to particle-hole pairs and nucleon-antinucleon ($N\bar{N}$) excitations. We report a reduction in the $ω$-meson mass of about 170~MeV at nuclear-matter saturation density. This reduction arises from a competition between the density-dependent (particle-hole) dressing of the propagator and vacuum polarization ($N\bar{N}$ pairs). While density-dependent effects lead to an increase in the mass proportional to the classical plasma frequency, vacuum polarization leads to an even larger reduction caused by the reduced effective nucleon mass in the medium.

nucl-th↗

arXiv1993

Pion Form Factors at Intermediate Momentum Transfer in a Covariant Approach

We study the pion electromagnetic and $γ^* + π^0 \to γ$ transition form factors at intermediate momentum transfer. We calculate soft, nonperturbative corrections to the leading perturbative amplitudes which arise from the $q\bar q$-component of the pion wave function. We work in Minkowski space and use a Lorentz covariant, gauge-invariant generalized perturbative integral representation for the $q\bar q$ amplitudes. For the transition form factor we find relative insensitivity to the detailed nonperturbative structure of the wavefunction for $|q^2|\gsim 10$~GeV$^2$, whereas considerable sensitivity is found for the electromagnetic form factor.

hep-ph↗

arXiv1993

Charge-Symmetry Breaking, Rho-Omega Mixing and the Quark Propagator

The momentum-dependence of the $ρ^0$-$ω$ mixing contribution to charge-symmetry breaking (CSB) in the nucleon-nucleon interaction is compared in a variety of models. We focus in particular on the role that the structure of the quark propagator plays in the predicted behaviour of the $ρ^0$-$ω$ mixing amplitude. We present new results for a confining (entire) quark propagator and for typical propagators arising from explicit numerical solutions of quark Dyson-Schwinger equations. We compare these to hadronic and free quark calculations. The implications for our current understanding of CSB experiments is discussed.

nucl-th↗

arXiv1993

The Momentum Dependence of the $ρ-ω$ Mixing Amplitude in a Hadronic Model

We calculate the momentum dependence of the $ρ-ω$ mixing amplitude in a purely hadronic model. The basic assumption of the model is that the mixing amplitude is generated by $N{\bar{N}}$ loops and thus driven entirely by the neutron-proton mass difference. The value of the amplitude at the $ω$-meson point is expressed in terms of only the $NNω$ and the $NNρ$ coupling constants. Using values for these couplings constrained by empirical two-nucleon data we obtain a value for the mixing amplitude in agreement with experiment. Extending these results to the spacelike region, we find a $ρ-ω$ contribution to the NN interaction that is strongly suppressed and opposite in sign relative to the conventional contribution obtained from using the constant on-shell value for the mixing amplitude.

nucl-th↗