146 research outputs found
Two gamma quarkonium and positronium decays with Two-Body Dirac equations of constraint dynamics
Two-Body Dirac equations of constraint dynamics provide a covariant framework
to investigate the problem of highly relativistic quarks in meson bound states.
This formalism eliminates automatically the problems of relative time and
energy, leading to a covariant three dimensional formalism with the same number
of degrees of freedom as appears in the corresponding nonrelativistic problem.
It provides bound state wave equations with the simplicity of the
nonrelativistic Schroedinger equation. Unlike other three-dimensional
truncations of the Bethe-Salpeter equation, this covariant formalism has been
thoroughly tested in nonperturbatives contexts in QED, QCD, and nucleon-nucleon
scattering. Here we continue the important studies of this formalism by
extending a method developed earlier for positronium decay into two photons to
tests on the sixteen component quarkonium wave function solutions obtained in
meson spectroscopy. We examine positronium decay and then the two-gamma
quarkonium decays of eta_c, eta'_c, chi_0c, chi_2c, and pi-zero The results for
the pi-zero, although off the experimental rate by 13%, is much closer than the
usual expectations from a potential model.Comment: 4 pages. Presented at Second Meeting of APS Topical Group on Hadron
Physics, Nashville, TN, Oct 22-24. Proceedings to be published by Journal of
Physics (UK), Conference Serie
The Relativistic N-body Problem in a Separable Two-Body Basis
We use Dirac's constraint dynamics to obtain a Hamiltonian formulation of the
relativistic N-body problem in a separable two-body basis in which the
particles interact pair-wise through scalar and vector interactions. The
resultant N-body Hamiltonian is relativistically covariant. It can be easily
separated in terms of the center-of-mass and the relative motion of any
two-body subsystem. It can also be separated into an unperturbed Hamiltonian
with a residual interaction. In a system of two-body composite particles, the
solutions of the unperturbed Hamiltonian are relativistic two-body internal
states, each of which can be obtained by solving a relativistic
Schr\"odinger-like equation. The resultant two-body wave functions can be used
as basis states to evaluate reaction matrix elements in the general N-body
problem. We prove a relativistic version of the post-prior equivalence which
guarantees a unique evaluation of the reaction matrix element, independent of
the ways of separating the Hamiltonian into unperturbed and residual
interactions. Since an arbitrary reaction matrix element involves composite
particles in motion, we show explicitly how such matrix elements can be
evaluated in terms of the wave functions of the composite particles and the
relevant Lorentz transformations.Comment: 42 pages, 2 figures, in LaTe
Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
A large number of treatments of the meson spectrum have been tried that
consider mesons as quark - anti quark bound states. Recently, we used
relativistic quantum "constraint" mechanics to introduce a fully covariant
treatment defined by two coupled Dirac equations. For field-theoretic
interactions, this procedure functions as a "quantum mechanical transform of
Bethe-Salpeter equation". Here, we test its spectral fits against those
provided by an assortment of models: Wisconsin model, Iowa State model,
Brayshaw model, and the popular semi-relativistic treatment of Godfrey and
Isgur. We find that the fit provided by the two-body Dirac model for the entire
meson spectrum competes with the best fits to partial spectra provided by the
others and does so with the smallest number of interaction functions without
additional cutoff parameters necessary to make other approaches numerically
tractable. We discuss the distinguishing features of our model that may account
for the relative overall success of its fits. Note especially that in our
approach for QCD, the resulting pion mass and associated Goldstone behavior
depend sensitively on the preservation of relativistic couplings that are
crucial for its success when solved nonperturbatively for the analogous
two-body bound-states of QED.Comment: 75 pages, 6 figures, revised content
A Tale of Three Equations: Breit, Eddington-Guant, and Two-Body Dirac
G.Breit's original paper of 1929 postulates the Breit equation as a
correction to an earlier defective equation due to Eddington and Gaunt,
containing a form of interaction suggested by Heisenberg and Pauli. We observe
that manifestly covariant electromagnetic Two-Body Dirac equations previously
obtained by us in the framework of Relativistic Constraint Mechanics reproduce
the spectral results of the Breit equation but through an interaction structure
that contains that of Eddington and Gaunt. By repeating for our equation the
analysis that Breit used to demonstrate the superiority of his equation to that
of Eddington and Gaunt, we show that the historically unfamiliar interaction
structures of Two-Body Dirac equations (in Breit-like form) are just what is
needed to correct the covariant Eddington Gaunt equation without resorting to
Breit's version of retardation.Comment: 15 pages latex, published in Foundations of Physics, Vol 27, 67
(1997
Relativistic Modification of the Gamow Factor
In processes involving Coulomb-type initial- and final-state interactions,
the Gamow factor has been traditionally used to take into account these
additional interactions. The Gamow factor needs to be modified when the
magnitude of the effective coupling constant increases or when the velocity
increases. For the production of a pair of particles under their mutual
Coulomb-type interaction, we obtain the modification of the Gamow factor in
terms of the overlap of the Feynman amplitude with the relativistic wave
function of the two particles. As a first example, we study the modification of
the Gamow factor for the production of two bosons. The modification is
substantial when the coupling constant is large.Comment: 13 pages, in LaTe
Relativistic Corrections in a Three-Boson System of Equal Masses
Three-body systems of scalar bosons are described in the framework of
relativistic constraint dynamics. With help of a change of variables followed
by a change of wave function, two redundant degrees of freedom get eliminated
and the mass-shell constraints can be reduced to a three-dimensional eigenvalue
problem.
In general, this problem is complicated, but for three equal masses a drastic
simplification arises at the first post-Galilean order: the reduced wave
equation becomes tractable, and we can compute a first-order correction beyond
the nonrelativistic limit. The harmonic interaction is displayed as a toy
model.Comment: 16 pages, no figure. Several points clarified, one typo corrected.
References added. To appear in Physical Review
Relativistic Generalization of the Gamow Factor for Fermion Pair Production or Annihilation
In the production or annihilation of a pair of fermions, the initial-state or
final-state interactions often lead to significant effects on the reaction
cross sections. For Coulomb-type interactions, the Gamow factor has been
traditionally used to take into account these effects. However the Gamow factor
needs to be modified when the magnitude of the coupling constant or the
relative velocity of two particles increases. We obtain the relativistic
generalization of the Gamow factor in terms of the overlap of the Feynman
amplitude with the relativistic wave function of two fermions with an
attractive Coulomb-type interaction. An explicit form of the corrective factor
is presented for the spin-singlet S-wave state. While the corrective factor
approaches the Gamow factor in the non-relativistic limit, we found that the
Gamow factor significantly over-estimates the effects when the coupling
constant or the velocity is large.Comment: 16 pages, 4 figures in LaTe
Correction Factors for Reactions involving Quark-Antiquark Annihilation or Production
In reactions with production or annihilation, initial-
and final-state interactions give rise to large corrections to the lowest-order
cross sections. We evaluate the correction factor first for low relative
kinetic energies by studying the distortion of the relative wave function. We
then follow the procedure of Schwinger to interpolate this result with the
well-known perturbative QCD vertex correction factors at high energies, to
obtain an explicit semi-empirical correction factor applicable to the whole
range of energies. The correction factor predicts an enhancement for
in color-singlet states and a suppression for color-octet states, the effect
increasing as the relative velocity decreases. Consequences on dilepton
production in the quark-gluon plasma, the Drell-Yan process, and heavy quark
production processes are discussed.Comment: 25 pages (REVTeX), includes 2 uuencoded compressed postscript figure
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