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 Schrödinger 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 3 P0,2 states as well as the 1 S0. The two-gamma quarkonium decays that we investigate are for the η c , η ′ c , χ c0 , χ c2 , π 0 , π2, a2,and f ′ 2 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.

Potential models and lattice gauge current-current correlators

“…It will also be of interest to study the relativistic effects by examining relativistic two-body potential models along the lines of Dirac's constraint dynamics as in Ref. [4,5], which will allow us to study the stability of light-quark systems within the potential model.…”

Quarkonia and quark drip lines in a quark-gluon plasma

“…As in the case of T = 0, where light quarks with a constituent-quark mass of about 350 MeV mimic the effects of chiral symmetry breaking and non-relativistic constituent quark models have been successfully used for light hadron spectroscopy [62,63], so the large value of the estimated quasiparticle mass (from 0.3 to 0.4 GeV) may allow the use of a non-relativistic potential model as an effective tool to estimate the stability of light quarkonia at T c < T < 2T c . It will be of interest to investigate the relativistic effects [48,49] in the future.…”

Effective Lagrangian for two-photon and two-gluon decays ofP-wave heavy quarkoniumχc0,2andχLansberg1, Pham2 2009Phys. Rev. D331220View full textAdd to dashboardCite

“…In the traditional non-relativisitic bound state calculation, the two-photon widths for the P -wave quarkonium state depend on the derivative at the origin of the spatial wave function which has to be extracted from potential models [5]. Though the physics of quarkonium decay seems to be better understood within the conventional framework of QCD [6], unlike the two-photon width of S-wave η c and η b quarkonia which can be predicted from the corresponding J/ψ and Υ leptonic widths using HQSS, there is no similar prediction for the Pwave χ c and χ b states and all the existing theoretical values for the decay rates are based on potential model calculations [5,7,8,9,10,11,12,13,14,15,16,17]. To have a prediction for the two-photon width of P -wave quarkonia, one need to express the decay amplitude in terms of the matrix element of a heavy quark field local operator extracted from some known physical processes or computed in an essentially model-independent manner, such as QCD sum rules technique [18,19] or lattice simulations [20].…”