arXiv subjects

J. W. Van Orden

Publications and source records attributed to J. W. Van Orden.

32 records · Page 2Linked to original sources

arXiv2005

Scaling of Dirac Fermions and the WKB approximation

We discuss a new method for obtaining the WKB approximation to the Dirac equation with a scalar potential and a time-like vector potential. We use the WKB solutions to investigate the scaling behavior of a confining model for quark-hadron duality. In this model, a light quark is bound to a heavy di-quark by a linear scalar potential. Absorption of virtual photons promotes the quark to bound states. The analog of the parton model for this case is for a virtual photon to eject the bound, ground-state quark directly into free continuum states. We compare the scaling limits of the response functions for these two transitions.

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arXiv2005

Modeling quark-hadron duality in polarization observables

We apply a model for the study of quark-hadron duality in inclusive electron scattering to the calculation of spin observables. The model is based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss the onset of scaling and duality for the responses, spin structure functions, and polarization asymmetries. Duality may be applied to gain access to kinematic regions which are hard to access in deep inelastic scattering, namely for $x_{Bj} \to 1$, and we discuss which observables are most suitable for this application of duality.

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arXiv2004

A comprehensive treatment of electromagnetic interactions and the three-body spectator equations

We present a general derivation the three-body spectator (Gross) equations and the corresponding electromagnetic currents. As in previous paper on two-body systems, the wave equations and currents are derived from those for Bethe-Salpeter equation with the help of algebraic method using a concise matrix notation. The three-body interactions and currents introduced by the transition to the spectator approach are isolated and the matrix elements of the e.m. current are presented in detail for system of three indistinguishable particles, namely for elastic scattering and for two and three body break-up. The general expressions are reduced to the one-boson-exchange approximation to make contact with previous work. The method is general in that it does not rely on introduction of the electromagnetic interaction with the help of the minimal replacement. It would therefore work also for other external fields.

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arXiv2003

Modeling quark-hadron duality for relativistic, confined fermions

We discuss a model for the study of quark-hadron duality in inclusive electron scattering based on solving the Dirac equation numerically for a scalar confining linear potential and a vector color Coulomb potential. We qualitatively reproduce the features of quark-hadron duality for all potentials considered, and discuss similarities and differences to previous models that simplified the situation by treating either the quarks or all particles as scalars. We discuss the scaling results for PWIA and FSI, and the approach to scaling using the analog of the Callan-Gross relation for y-scaling.

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arXiv2002

Quark-Hadron Duality

Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.

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arXiv2002

Covariant description of inelastic electron--deuteron scattering:predictions of the relativistic impulse approximation

Using the covariant spectator theory and the transversity formalism, the unpolarized, coincidence cross section for deuteron electrodisintegration, $d(e,e'p)n$, is studied. The relativistic kinematics are reviewed, and simple theoretical formulae for the relativistic impulse approximation (RIA) are derived and discussed. Numerical predictions for the scattering in the high $Q^2$ region obtained from the RIA and five other approximations are presented and compared. We conclude that measurements of the unpolarized coincidence cross section and the asymmetry $A_ϕ$, to an accuracy that will distinguish between different theoretical models, is feasible over most of the wide kinematic range accessible at Jefferson Lab.

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arXiv2002

Quark-hadron duality in a relativistic, confining model

Quark-hadron duality is an interesting and potentially very useful phenomenon, as it relates the properly averaged hadronic data to a perturbative QCD result in some kinematic regions. While duality is well established experimentally, our current theoretical understanding is still incomplete. We employ a simple model to qualitatively reproduce all the features of Bloom-Gilman duality as seen in electron scattering. In particular, we address the role of relativity, give an explicit analytic proof of the equality of the hadronic and partonic scaling curves, and show how the transition from coherent to incoherent scattering takes place.

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arXiv2001

Quark-Hadron Duality in Structure Functions

While quark-hadron duality is well-established experimentally, the current theoretical understanding of this important phenomenon is quite limited. To expose the essential features of the dynamics behind duality, we use a simple model in which the hadronic spectrum is dominated by narrow resonances made of valence quarks. We qualitatively reproduce the features of duality as seen in electron scattering data within our model. We show that in order to observe duality, it is essential to use the appropriate scaling variable and scaling function. In addition to its great intrinsic interest in connecting the quark-gluon and hadronic pictures, an understanding of quark-hadron duality could lead to important benefits in extending the applicability of scaling into previously inaccessible regions.

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arXiv2001

The deuteron: structure and form factors

A brief review of the history of the discovery of the deuteron in provided. The current status of both experiment and theory for the elastic electron scattering is then presented.

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arXiv1999

Origin of Relativistic Effects in the Reaction D(e,e'p)n at GeV Energies

In a series of recent publications, a new approach to the non-relativistic reduction of the electromagnetic current operator in calculations of electro-nuclear reactions has been introduced. In one of these papers, the conjecture that at energies of a few GeV, the bulk of the relativistic effects comes from the current and not from the nuclear dynamics was made, based on the large relativistic effects in the transverse-longitudinal response. Here, we explicitly compare a fully relativistic, manifestly covariant calculation performed with the Gross equation, with a calculation that uses a non-relativistic wave function and a fully relativistic current operator. We find very good agreement up to missing momenta of 400 MeV/c, thus confirming the previous conjecture. We discuss slight deviations in cross sections for higher missing momenta and their possible origin, namely p-wave contributions and off-shell effects.

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arXiv1998

Normalization of the covariant three-body bound state vertex function

The normalization condition for the relativistic three nucleon Bethe-Salpeter and Gross bound state vertex functions is derived, for the first time, directly from the three body wave equations. It is also shown that the relativistic normalization condition for the two body Gross bound state vertex function is identical to the requirement that the bound state charge be conserved, proving that charge is automatically conserved by this equation.

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arXiv1997

Electromagnetic interactions for the two-body spectator equations

This paper presents a new non-associative algebra which is used to (i) show how the spectator (or Gross) two-body equations and electromagnetic currents can be formally derived from the Bethe-Salpeter equation and currents if both are treated to all orders, (ii) obtain explicit expressions for the Gross two-body electromagnetic currents valid to any order, and (iii) prove that the currents so derived are exactly gauge invariant when truncated consistently to any finite order. In addition to presenting these new results, this work complements and extends previous treatments based largely on the analysis of sums of Feynman diagrams.

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arXiv1997

Lagrangian with off-shell vertices and field redefinitions

Meson exchange diagrams following from a lagrangian with off-shell meson-nucleon couplings are compared with those generated from conventional dynamics. The off-shell interactions can be transformed away with the help of a nucleon field redefinition. Contributions to to the $NN$- and $3N$-potentials and nonminimal contact e.m. meson-exchange currents are discussed, mostly for an important case of scalar meson exchange. (pacs 11.10.Lm, 13.75.Cs, 21.30.-x, 24.10.Jv)

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arXiv1994

Heavy Mesons In A Relativistic Model

Motivated by the present interest in the heavy quark effective theory, we use the spectator equation to treat the mesonic bound states of heavy quarks. The kernel we use is based on scalar confining and vector Coulomb potentials. Wave functions are treated to leading order and energies to order $1/m_Q$ in the heavy-light systems, and order $1/m_Q^2$ in heavy-heavy systems. Our results are in reasonable agreement with experimental measurements. We estimate two of the parameters of the heavy quark effective theory, and propose further calculations that may be undertaken in the future.

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