Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons

Abstract

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. Here we begin important tests of the relativistic sixteen component wave function solutions obtained in a recent work on meson spectroscopy, extending a method developed previously for positronium decay into two photons. Preliminary to this we examine the positronium decay in the 3P_{0,2} states as well as the 1S_0. The two-gamma quarkonium decays that we investigate are for the η_{c}, η_{c}^{\prime}, χ_{c0}, χ_{c2}, π^{0}, π_{2}, a_{2}, and f_{2}^{\prime} mesons. Our results for the four charmonium states compare well with those from other quark models and show the particular importance of including all components of the wave function as well as strong and CM energy dependent potential effects on the norm and amplitude. The results for the π^{0}, although off the experimental rate by 15%, is much closer than the usual expectations from a potential model. We conclude that the Two-Body Dirac equations lead to wave functions which provide good descriptions of the two-gamma decay amplitude and can be used with some confidence for other purposes.

79 pages, included new sections on covariant scalar product and added pages on positronium decay for 3P0 and 3P_2 states

Cited by in corpus (25)

• Lattice QCD and QCD Sum Rule determination of the decay constants of eta_c, J/psi and hc states
• Annihilation Rate of $2^{++}$ Charmonium and Bottomonium
• Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• Scalar Quarkonia at Finite Temperature
• Leptonic and Digamma decay Properties of S-wave quarkonia states
• Two-photon and two-gluon decays of p-wave heavy quarkonium using a covariant light-front approach
• Effective Lagrangian for Two-photon and Two-gluon Decays of $P$-wave Heavy Quarkonium ${\chi }_{c0,2}$ and ${\chi }_{b0,2}$ states
• Decay rates of charmonia within a quark-antiquark confining potentials
• Potential Models and Lattice Gauge Current-Current Correlators
• Annihilation Rate of Heavy 0^{++} P-wave Quarkonium in Relativistic Salpeter Method
• Two-Photon, Two-gluon and Radiative Decays of Heavy Flavoured Mesons
• Quarkonia and Quark Drip Lines in Quark-Gluon Plasma
• Relativistic two-body equation based on the extension of the SL(2,C) group
• η_b and η_c radiative decays in the Salpeter model with the AdS/QCD inspired potential
• Magnetic States at Short Distances
• Perturbation Theory for Metastable States of the Dirac Equation with Quadratic Vector Interaction
• On the stability of the open-string QED neutron and dark matter
• Two-photon decay of P-wave positronium: a tutorial
• On the question of current conservation for the Two-Body Dirac equations of constraint theory
• Klein-Gordon Equation in Hydrodynamical Form
• Two gamma quarkonium and positronium decays with Two-Body Dirac equations of constraint dynamics
• Semileptonic transition of P wave bottomonium ${\chi }_{b0}(1P)$ to $B_c$ meson
• Lattice calculation of ${\chi }_{c0}\to 2\gamma$ decay width
• Study of meson properties in quark models (Ph.D. Thesis, University of Pittsburgh, October 2006)