Tests of two-body Dirac equation wave functions in the decays of quarkonium and positronium into two photons

Journal Article · Fri Sep 01 00:00:00 EDT 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.74.054028· OSTI ID:20871116

Crater, Horace W; Wong, C -Y; Van Alstine, Peter ^[1]

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1. University of Tennessee Space Institute, Tullahoma, Tennessee 37388 (United States)

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 16 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 {sup 3}P{sub 0,2} states as well as the {sup 1}S{sub 0}. The two-gamma quarkonium decays that we investigate are for the {eta}{sub c}, {eta}{sub c}{sup '}, {chi}{sub c0}, {chi}{sub c2}, {pi}{sup 0}, {pi}{sub 2}, a{sub 2}, and f{sub 2}{sup '} 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 c.m. energy dependent potential effects on the norm and amplitude. The results for the {pi}{sup 0}, although off the experimental rate by 13%, are 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.

• OSTI ID: 20871116
• Journal Information: Physical Review. D, Particles Fields, Vol. 74, Issue 5; Other Information: DOI: 10.1103/PhysRevD.74.054028; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
A2-1320 MESONS
AMPLITUDES
CHI0-3415 MESONS
CHI2-3555 MESONS
COMPARATIVE EVALUATIONS
DEGREES OF FREEDOM
DIRAC EQUATION
ENERGY DEPENDENCE
ETA C-2980 MESONS
ETA C-3590 MESONS
F2 PRIME-1525 MESONS
MATHEMATICAL SOLUTIONS
MESON SPECTROSCOPY
PHOTONS
PI2-1670 MESONS
PI2-2100 MESONS
PIONS NEUTRAL
POSITRONIUM
POTENTIALS
QUARK MODEL
QUARKS
RADIATIVE DECAY
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
TWO-BODY PROBLEM
WAVE FUNCTIONS