Rho-omega Mixing Research Articles

Charge-symmetry breaking forces and isospin mixing in8Be

We report Green's function Monte Carlo calculations of isospin-mixing (IM) matrix elements for the 2+, 1+, and 3+ T=0,1 pairs of states at 16--19 MeV excitation in 8Be. The realistic Argonne v18 (AV18) two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions from the full electromagnetic interaction and strong class III charge-symmetry-breaking (CSB) components of the AV18 potential are evaluated. We also examine two theoretically more complete CSB potentials based on rho-omega mixing, tuned to give the same neutron-neutron scattering length as AV18. The contribution of these different CSB potentials to the 3H-3He, 7Li-7Be, and 8Li-8B isovector energy differences is evaluated and reasonable agreement with experiment is obtained. Finally, for the 8Be IM calculation we add the small class IV CSB terms coming from one-photon, one-pion, and one-rho exchange, as well as rho-omega mixing. The expectation values of the three CSB models vary by up to 20% in the isovector energy differences, but only by 10% or less in the IM matrix element. The total matrix element gives 85--90% of the experimental IM value of -145 keV for the 2+ doublet, with about two thirds coming from the Coulomb interaction. We also report the IM matrix element to the first 2+ state at 3 MeV excitation, which is the final state for various tests of the Standard Model for beta-decay.

Erratum: Rho-omega mixing and the pion form factor in the timelike region [Phys. Rev. D57, 2716 (1998)

We determine the magnitude, phase, and $s$-dependence of $\rho$-$\omega$ ``mixing'' in the pion form factor in the time-like region through fits to $e^+e^- \ra \pi^+ \pi^-$ data. The associated systematic errors in these quantities, arising from the functional form used to fit the $\rho$ resonance, are small. The systematic errors in the $\rho$ mass and width, however, are larger than previously estimated.

Rho-omega mixing and the pion form factor in the timelike region

We determine the magnitude, phase, and $s$ dependence of $\ensuremath{\rho}$-$\ensuremath{\omega}$ ``mixing'' in the pion form factor in the timelike region through fits to ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ data. The associated systematic errors in these quantities, arising from the functional form used to fit the $\ensuremath{\rho}$ resonance, are small. The systematic errors in the $\ensuremath{\rho}$ mass and width, however, are larger than previously estimated.

Vector meson mixing and charge symmetry violation

We discuss the consistency of the traditional vector meson dominance (VMD) model for photons coupling to matter, with the vanishing of vector meson-meson and meson-photon mixing self-energies at q 2 = 0. This vanishing of vector mixing has been demonstrated in the context of rho-omega mixing for a large class of effective theories. As a further constraint on such models, we here apply them to a study of photon-meson mixing and VMD. As an example we compare the predicted momentum dependence of one such model with a momentum-dependent version of VMD discussed by Sakurai in the 1960's. We find that it produces a result which is consistent with the traditional VMD phenomenology. We conclude that comparison with VMD phenomenology can provide a useful constraint on such models.

Rho-omega mixing and the Nolen-Schiffer anomaly in relativistic nuclear models

We calculate within the framework of relativistic nuclear models the contribution of the ϱ 0 - ω mixing interaction to the binding energy differences of the mirror nuclei in the neighborhood of A = 16 and A = 40. We use two relativistic models for the nuclear structure, one with scalar and vector Woods-Saxon potentials, and the Walecka model. The ϱ 0 - ω interaction is treated in first order perturbation theory. When using the Walecka model the ϱ- and ω-nucleon coupling constants are the same for calculating bound state wave functions and the perturbation due to the mixing. We find that the relativistic results on the average are of the same order as the ones obtained with nonrelativistic calculations.

Rho-omega mixing and the pion electromagnetic form-factor

The suggestion of momentum dependence in the amplitude for rho-omega mixing has generated concern over related implications for vector meson dominance and the photon-rho coupling. We discuss two established and formally equivalent representations of vector meson dominance and show that in one of these such a coupling is an automatic consequence of the model. We then apply it to a calculation of the pion electromagnetic form-factor. Our analysis leads to a revised value for the on-shell rho-omega mixing amplitude of −3800 ± 370 MeV 2.

Constraints on the momentum dependence of rho-omega mixing

Within a broad class of models we show that the amplitude for ϱ 0-ω mixing must vanish at the transition from time-like to space-like four momentum. Hence in such models the mixing is either zero everywhere or is necessarily momentum-dependent. This lends support to the conclusions of other studies of rho-omega mixing and calls into question standard assumptions about the role of rho-omega mixing in the theoretical understanding of charge-symmetry breaking in nuclear systems.

Charge-symmetry breaking, rho-omega mixing, and the quark propagator

The momentum dependence of the ϱ0-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 ϱ0-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.

Rho-omega mixing and neutron-proton self-energies in the Walecka model

We use the Walecka model to investigate the influence of the charge symmetry breaking ϱ 0−ω mixing interaction on the neutron-proton self-energy difference in nuclear matter. Using 2 m ϱ 〈 ϱ 0| H| ω〉 = −4500 Mev 2, and employingthe Dirac-Hartree-Fock approximation, we find that the neutron-proton self-energy difference is a decreasing function of the nuclear matter density, and that it has a value of the order of 700 keV at the normal density. The results indicate that the Nolen-Schiffer anomaly might be explained by means of relativistic nuclear models in a similar way as it is explained by means of non-relativistic models.

Erratum: Charge-symmetry breaking in neutron-proton scattering: Isospin-mixing parameter

An isospin-mixing parameter due to charge-symmetry breaking in the neutron-proton system is calculated in a new way, using the distorted-wave Born approximation. Three mechanisms of charge-symmetry breaking are investigated: one-photon exchange, rho-omega mixing, and the nucleon mass-difference effect in one-pion exchange. Numerical calculation of this parameter for a number of energies and angular momenta yields some interesting systematic behavior. In particular, for center-of-mass energies 100 MeV and greater, the largest values are obtained for total angular momentum J = 2 (or 4). The mass-difference effect is the most dominant one for all energies greater than 100 MeV. The analyzing-power difference, which is measurable experimentally, is also calculated.

Charge-symmetry breaking in neutron-proton scattering: Isospin-mixing parameter.

An isospin-mixing parameter due to charge-symmetry breaking in the neutron-proton system is calculated in a new way, using the distorted-wave Born approximation. Three mechanisms of charge-symmetry breaking are investigated: one-photon exchange, rho-omega mixing, and the nucleon mass-difference effect in one-pion exchange. Numerical calculation of this parameter for a number of energies and angular momenta yields some interesting systematic behavior. In particular, for center-of-mass energies 100 MeV and greater, the largest values are obtained for total angular momentum J = 2 (or 4). The mass-difference effect is the most dominant one for all energies greater than 100 MeV. The analyzing-power difference, which is measurable experimentally, is also calculated.

An S matrix description of state mixing: Part I: General formalism, with Rho-Omega mixing as an Illustration

The notion of state mixing is formulated in terms of S matrix language alone. The object is to work with quantities which are closely related to experiment, while avoiding the particularities of Hamiltonian theory or field theory. The scheme applies to particles of any spin, it is explicitly unitary, and useful in phenomenology as well as in dynamical S matrix models. Unlike the mass matrix method, it avoids the assumption that the states to be mixed evolve from discrete eigenstates of an unperturbed Hamiltonian. The main ingredient is a perturbation method by which the inverse of the K matrix is related to a corresponding unperturbed matrix. In some cases the latter can be defined directly from physical scattering matrices, without the device of turning off interactions. In this and following papers the method is applied to ϱ - ω, ϕ - ω, and K 0 - K 0 mixing. The results amount to more than a simple rephrasing of earlier treatments. As the discussion of ϱ - ω mixing in this paper illustrates, the physical arguments take quite a different form, and some new aspects of mixing questions are brought out.