Vector Dominance Model Research Articles

Analysis of Vector-Meson-Photoproduction Experiments in theρ−ωInterference Region

Vector-meson photoproduction on nuclei in the ${\ensuremath{\rho}}^{0}\ensuremath{-}\ensuremath{\omega}$ interference region has been observed both by means of experiments detecting photoproduction of ${e}^{+}{e}^{\ensuremath{-}}$ pairs and by means of experiments detecting photoproduction of ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ pairs. These two phenomena are closely related to each other and to the corresponding interference phenomenon in ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$. It is shown how the data on all such phenomena can be expressed in terms of three model-independen complex parameters: $\ensuremath{\epsilon}$, the intrinsic $\ensuremath{\rho}\ensuremath{-}\ensuremath{\omega}$ mixing parameter, ${r}_{\ensuremath{\omega}}$, the ratio of $\ensuremath{\omega}$-photon to $\ensuremath{\rho}$-photon coupling at an energy corresponding to the mass of the $\ensuremath{\omega}$, and $\frac{{P}_{\ensuremath{\omega}}}{{P}_{\ensuremath{\rho}}}$, the ratio of nuclear photoproduction amplitudes for $\ensuremath{\omega}$ and $\ensuremath{\rho}$. Existing data on the interference phenomena are combined with data on the ratios of $\ensuremath{\rho}$ and $\ensuremath{\omega}$ production cross sections to determine these parameters. It is found that $|\ensuremath{\epsilon}|=0.034\ifmmode\pm\else\textpm\fi{}0.004$, $|{r}_{\ensuremath{\omega}}|\ensuremath{\equiv}\frac{{\ensuremath{\gamma}}_{\ensuremath{\rho}}}{{\ensuremath{\gamma}}_{\ensuremath{\omega}}}=0.34\ifmmode\pm\else\textpm\fi{}0.07$, and $|\frac{{P}_{\ensuremath{\rho}}}{{P}_{\ensuremath{\omega}}|}=3.44\ifmmode\pm\else\textpm\fi{}0.19$ is the most consistent representation of the data. Because present experiments have uncertainties at the 10% level, it turns out that only relative phases can be determined. If ${r}_{\ensuremath{\omega}}$ is assumed to be real, the most consistent representation yields $\mathrm{arg}\ensuremath{\epsilon}={95}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{15}^{\ensuremath{\circ}}$ and $\mathrm{arg}(\frac{{P}_{\ensuremath{\omega}}}{{P}_{\ensuremath{\rho}}})={0}^{\ensuremath{\circ}}\ifmmode\pm\else\textpm\fi{}{21}^{\ensuremath{\circ}}$. The former result is in agreement with the expectations from mixing theory. The latter is interpreted in terms of a simple vector-dominance model and is shown to agree with simple peripheralism, that is, equality of the $\ensuremath{\rho}$ and $\ensuremath{\omega}$ forward scattering amplitudes. Because of disagreements in the data from different laboratories, there may be some doubt about the reality of ${r}_{\ensuremath{\omega}}$. It appears that the phase of ${r}_{\ensuremath{\omega}}$ could be determined in a model-independent way by an electron-positron colliding-beam experiment on interference in ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ production at the 1% level.

An experimental method for studying pion-vector-meson elastic-scattering amplitudes

Within the framework of the vector-dominance model, a method for an experimental study of the energy dependence of the pion-vector-meson scattering amplitudes is proposed for the reaction γN → ΔV0π. The method is based on an analysis of the moments of the spherical harmonics of the γπ → V0π process. This analysis is attractive, in particular, in the case thats-channel helicity conservation can be assumed for the V0π scattering process where then all the moments 〈Y i m 〉 withm ≠ 0 vanish.

Vector-Dominance Model, Partial Conservation of the Axial-Vector Current, and the Decoupling ofπρω

We show that partial conservation of the axial-vector current and vector dominance together imply that ${g}_{\ensuremath{\pi}\ensuremath{\rho}\ensuremath{\omega}}=0$. We discuss the relevance of this result to the failure of vector dominance in polarized photoproduction of pions. We also provide a simple interpretation of the $\ensuremath{\rho}$-meson mass shift in photoproduction experiments based on unitarity.

Does Duality Hold in Current Interactions?

Deep-inelastic electron-proton scattering is shown to be naturally interpreted in a field theory where the current is given by a bilinear form in some fields. It is proved that in such a theory the Compton-scattering amplitude is not saturated with the vector-dominance model and that the term which scales in the Bjorken limit does not obey Freund-Harari duality.

Forward Compton Scattering from Hydrogen and Deuterium at 8 and 16 GeV

Compton-scattering cross sections from hydrogen ($\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\gamma}p$) and from deuterium have been measured at four-momentum transfer $t$ in the range $0.014<~\ensuremath{-}t<~0.17$ Ge${\mathrm{V}}^{2}$ and photon energies of 8 and 16 GeV. Fits to our proton data of the form $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}={\mathrm{Ae}}^{\mathrm{Bt}}$ give $B\ensuremath{\approx}7.8$ Ge${\mathrm{V}}^{\ensuremath{-}2}$ and an intercept $A$ which is in agreement with the optical point. Both coherent scattering from deuterons and incoherent scattering from neutrons and protons are seen from deuterium. A small difference between the neutron and proton cross sections is seen, indicating the presence of about a 3% isovector $t$-channel exchange amplitude in addition to the predominant isoscalar amplitude. The vector-dominance model predicts lower cross sections (by at least 20%) for both the hydrogen and deuterium cases.

Comparison ofπ−p→ρ0nwith Single-Pion Photoproduction at 15GeVc

We present a comparison of new data on ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}n$ at 15 $\frac{\mathrm{GeV}}{c}$ with polarized and unpolarized single-pion photoproduction data. Particular emphasis is placed upon the behavior of the differential cross sections and asymmetries in the forward direction ($\ensuremath{-}t<{{m}_{\ensuremath{\pi}}}^{2}$). Qualitative agreement with the vector-dominance model is found. Quantitative agreement is found for the unnatural-parity---exchange cross section and for the asymmetry at low momentum transfer. Elsewhere there are disagreements in detail which may not be explained by changes of normalization.

Is There a Vector-Dominance Frame Problem?

We argue that it is not meaningful to discuss the vector-dominance model using the language of longitudinal projections. We find that a more suitable language for vector dominance is in terms of electric and magnetic couplings rather than in terms of longitudinal and transverse ones. We advocate the use only of the off-shell invariant amplitudes ("Ball amplitudes"). The experimental failure of the model for polarized photoproduction of pions then implies either that some of the Ball amplitudes require subtractions in ${k}^{2}$, the mass of the current, or that states other than $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\phi}$ also couple to the electromagnetic current.

Phenomenological investigation of inelastic electron-proton scattering

Contour lines for the structure function νW 2 are drawn. Scaling behaviour is clearly exhibited for ω⪅8. For larger ω a diffractive mechanism seems to dominate. Combining data from inelastic ep scattering with those from photoproduction and complex nuclei we study the region of validity of the vector-dominance model. A qualitative change seems to take place at Q 2≈0.

Total photoproduction cross section of hadrons on nuclei

The total cross section for photoproduction of hadrons σ( γA) was measured on 7 nuclei (Be, C, Al, Ti, Cu, Ag and Au) at 5.4 GeV photon energy. In addition the energy dependence of σ( γA) was measured for Be, C and Ti between 1.5 and 5.7 GeV. A small shadow effect is observed which is in reasonable agreement with the prediction of the vector dominance model.

Photoproduction ofN * (1236) resonance and the vector dominance model* (1236) resonance and the vector dominance model

Photoproduction ofN * (1236) resonance and the vector dominance model* (1236) resonance and the vector dominance model

Vector dominance model and the P, P' and a regge-pole trajectory effects in high energy compton scattering

The forward Compton scattering is investigated assuming that the high energy scattering of the ϱ°, ω and Φ mesons is dominated by the exchanges of the P, P′ and A trajectories. Reasonable agreement with experiment has been obtained.

Meson exchange currents in nuclear weak and electromagnetic interactions

Meson theory is applied to the study of the exchange magnetic moment and Gamow-Teller operators. We consider contributions due to the exchange of one pion and of vector mesons and give their detailed expressions in terms of a general classification of the operators. The one-pion-exchange process is separated into Born and non-Born parts corresponding respectively to the Born and non-Born parts in the process of weak or photoproduction of a pion by the nucleon. The results of low-energy theorems for this process enable us to reach a model-independent description of the non-Born parts. Corrections to the soft-pion limit are studied by means of simple dynamical models: a phenomenological Lagrangian for the weak current and the Chew-Low model for the e.m. current. The exchange operators due to the exchange of ρ− and ω-mesons are evaluated in the vector dominance model. The applications are concerned with the exchange effect in the isovector and isoscalar magnetic moments of 3He and3H and in the Gamow-Teller matrix element for3H β-decay. The results are obtained with the dominant S-state with a Gaussian radial function. We also discuss their dependence on short-range correlations described in terms of Jastrow factors. The exchange corrections are found to be too small for the current wave functions of the trinucleons. We discuss briefly other agencies that may account for the remaining discrepancies.

On incoherent pion photoproduction from complex nuclei

A violation of the vector-dominance model suggested by experimental data on photoproduction of pions with polarized photons on protons has been included in the Gottfried-Yennie formulation of the theory of incoherent pion photoproduction in complex nuclei. An approximate calculation can explain the lack of energy dependence of the effective proton numberZeff experimentally found between 8 and 16 GeV, and a variation with nuclear size of the asymmetry of production of pions with linearly polarized photons in complex nuclei is predicted.

Experimental tests of the vector dominance model in pseudoscalar meson photoproduction

Experimental tests of the VMD model in pseudoscalar meson photoproduction are reviewed. The difficulties associated with the model are discussed. The so-called “failures” of the model are analyzed and their possible origins are pointed out. Impressive evidence supporting the model is emerging. New possible tests of the model are proposed.

Non evasive contributions to forward rho-production and vector dominance

Abstract It is shown that the small t background to rho production as determined from fits to experiment agrees rather well with the predictions from simple theoretical models, leading to a quantitative agreement with the vector dominance model and an overall picture of the background to OPE for use in ππ phenomenology.

Kaon and nucleon form factors using vector dominance

The nucleon form factorsG E (t) andG M (t) are related to the K-meson isoscalar and isovector electromagnetic form factors in the vector-dominance model assuming the existence of universality among form factors. The mean charge radius of the nucleon is calculated along with that of the K-meson. Relationships among the total cross-sections for the processes e+e−→KK, ππ are stated.

Vector-dominance model and the background photoproduction of pions

Vector-dominance model and the background photoproduction of pions

Fixed Poles in High-Energy Compton Scattering, Electroproduction, and the Vector-Dominance Models

It is shown that the vector dominance of $s$-channel helicity amplitudes requires the existence of a nonsense wrong-signature fixed pole at $J=1$ in virtual photon-hadron scattering. Furthermore, in the amplitudes for electroproduction, where the virtual photon masses are spacelike, it is argued that such fixed poles must exist simply from such general requirements as analyticity, gauge invariance, and positivity of cross sections. This fixed pole occurs multiplicatively with the Pomeranchuk pole if the photon-hadron cross sections ${\ensuremath{\sigma}}_{L}$ or ${\ensuremath{\sigma}}_{S}$ are constant asymptotically with energy. A minimal amount of analyticity then allows one to extend this result to general values of the virtual photon masses. If the asymptotic cross section for photoproduction of $\ensuremath{\rho}$ mesons is dominated by Pomeranchuk exchange and if it conserves helicity, then the multiplicative fixed pole is present there, too. Further, the presence of this fixed pole tests for the compositeness of the $\ensuremath{\rho}$ meson or third-double-spectral-function effects.

On the importance of pion electroproduction at high energy

High energy pion electroproduction is analyzed and shown to be very useful as a source of the pion electromagnetic form factor and as a means of testing the vector dominance model and finite energy sum rule predictions for electromagnetic processes.

The vector-meson dominance model and inelastic electron-proton scattering

We discuss the ambiguities of the vector-dominance model as applied to inelastic electron-proton scattering. The region s ⪢ | q 2| seems to be the only region in which the model could, even in principle, be meaningful. The region closest to the pole, namely q 2 ≈ 0, is of primary significance for testing the model.