Relativistic Generalization of the Post-Prior Equivalence for Reaction of Composite Particles

In the non-relativistic description of the reaction of composite particles, the reaction matrix is independent of the choice of post or prior forms for the interaction. We generalize this post-prior equivalence to the relativistic reaction of composite particles by using Dirac's constraint dynamics to describe the bound states and the reaction process.Comment: 3 pages in LaTex. Invited talk presented at the Third Joint Meeting of Chinese Physicists Worldwide in Hong Kong, 2000, to be published in the proceeding

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

Meson-Meson Scattering in Relativistic Constraint Dynamics

Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. We use this formalism to describe a microscopic theory of meson-meson scattering as a relativistic generalization of the nonrelativistic quark-interchange model developed by Barnes and Swanson.Comment: 5 pages, 1 figure in LaTex, talk present at the First Meeting of the APS Topical Group on Hadronic Physics (Fermilab, October 24-26, 2004

Applications of Two Body Dirac Equations to Hadron and Positronium Spectroscopy

We review recent applications of the Two Body Dirac equations of constraint dynamics to meson spectroscopy and describe new extensions to three-body problems in their use in the study of baryon spectroscopy. We outline unique aspects of these equations for QED bound states that distinguish them among the various other approaches to the relativistic two body problem. Finally we discuss recent theorectial solutions of new peculiar bound states for positronium arising from the Two Body Dirac equations of constraint dynamics, assuming point particles for the electron and the positron.Comment: Invited talk: CST-MISC joint international symposium on particle physics - From spacetime dynamics to phenomenology - Tokyo, March 15-16, 201

Angular distributions in the radiative decays of the 3D3^3D_3 state of charmonium originating from polarized pˉp\bar{p}p collisions

Using the helicity formalism, we calculate the combined angular distribution function of the two gamma photons ($\gamma_1$ and $\gamma_2$) and the electron ($e^-$) in the triple cascade process $\bar{p}p\rightarrow{}^3D_3\rightarrow{}^3P_2+\gamma_1\rightarrow(\psi+\gamma_2) +\gamma_1 \rightarrow (e^- + e^+) +\gamma_2 +\gamma_1$, when $\bar{p}$ and $p$ are arbitrarily polarized. We also derive six different partially integrated angular distribution functions which give the angular distributions of one or two particles in the final state. Our results show that by measuring the two-particle angular distribution of $\gamma_1$ and $\gamma_2$ and that of $\gamma_2$ and $e^-$, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two charmonium radiative transitions ${}^3D_3\rightarrow{}^3P_2+\gamma_1$ and $^3P_2\rightarrow \psi+\gamma_2$.Comment: arXiv admin note: substantial text overlap with arXiv:1311.464

Angular distributions of the polarized photons and electron in the decays of the 3D3^3D_3 state of charmonium

We calculate the combined angular distribution functions of the polarized photons ($\gamma_1$ and $\gamma_2$) and electron ($e^-$) produced in the cascade process $\bar{p}p\rightarrow$ $^3D_3\rightarrow$ $^3P_2+\gamma_1\rightarrow$ $(\psi+\gamma_2)+\gamma_1\rightarrow(e^++e^-)+\gamma_1+\gamma_2$, when the colliding $\bar{p}$ and $p$ are unpolarized. Our results are independent of any dynamical models and are expressed in terms of the spherical harmonics whose coefficients are functions of the angular-momentum helicity amplitudes of the individual processes. Once the joint angular distribution of ($\gamma_1$, $\gamma_2$) and that of ($\gamma_2$, $e^-$) with the polarization of either one of the two particles are measured, our results will enable one to determine the relative magnitudes as well as the relative phases of all the angular-momentum helicity amplitudes in the radiative decay processes $^3D_3\rightarrow$ $^3P_2+\gamma_1$ and $^3P_2\rightarrow\psi+\gamma_2$

Singularity-Free Breit Equation from Constraint Two-Body Dirac Equations

We examine the relation between two approaches to the quantum relativistic two-body problem: (1) the Breit equation, and (2) the two-body Dirac equations derived from constraint dynamics. The Breit equation is known to be pathological when singularities appear at finite separations $r$ in the reduced set of coupled equations for attractive potentials even when the potentials themselves are not singular there. They then give rise to unphysical bound states and resonances. In contrast, the two-body Dirac equations of constraint dynamics do not have these pathologies in many nonperturbative treatments. To understand these marked differences, we first express these contraint equations in a hyperbolic form. These coupled equations are then re-cast into two equivalent equations: (1) a covariant Breit-like equation with potentials that are exponential functions of certain ``generator'' functions, and (2) a covariant orthogonality constraint on the relative momentum. This reduction enables us to show in a transparent way that finite-$r$ singularities do not appear as long as the the exponential structure is not tampered with and the exponential generators of the interaction are themselves nonsingular for finite $r$. These Dirac or Breit equations, free of the structural singularities which plague the usual Breit equation, can then be used safely under all circumstances, encompassing numerous applications in the fields of particle, nuclear, and atomic physics which involve highly relativistic and strong binding configurations.Comment: 38 pages (REVTeX), (in press in International Journal of Modern Physics