Exchange Current Operators and Electromagnetic Dipole Transitions in Heavy Quarkonia

Abstract

The electromagnetic E1 and M1 transitions in heavy quarkonia ($c\bar c$, $b\bar b$, $c\bar b$) and the magnetic moment of the $B_c^\pm$ are calculated within the framework of the covariant Blankenbecler-Sugar (BSLT) equation. The aim of this paper is to study the effects of two-quark exchange current operators which involve the $Q\bar Q$ interaction, that arise in the BSLT (or Schrödinger) reduction of the Bethe-Salpeter equation. These are found to be small for E1 dominated decays such as $ψ(nS)\to χ_{cJ} γ$ and $Υ(nS)\to χ_{bJ} γ$, but significant for the M1 dominated transitions. It is shown that a satisfactory description of the empirical data on E1 and M1 transitions in charmonium and bottomonium requires unapproximated treatment of the Dirac currents of the quarks. Finally, it is demonstrated that many of the transitions are sensitive to the form of the $Q\bar Q$ wavefunctions, and thus require a realistic treatment of the large hyperfine splittings in the heavy quarkonium systems.