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 $\psi (nS)\to {\chi }_{cJ}\gamma$ and ${\rm Y}(nS)\to {\chi }_{bJ}\gamma$, 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.

30 pages, 2 figures, uses Feynmf. Submitted to Nucl. Phys. A Accepted version

References in corpus (4)

• Observation of the eta_c(2S) in exclusive B-->K KsK-pi+ decays
• Tests of Power Corrections for Event Shapes in e+e- Annihilation
• Pion Rescattering in Two-Pion Decay of Heavy Quarkonia
• The Coupling of eta Mesons to Quarks and Baryons from D_s^* -> D_s pi^0 Decay

Cited by in corpus (32)

• Heavy quarkonium: progress, puzzles, and opportunities
• Exotics: Heavy Pentaquarks and Tetraquarks
• Quarkonia and their transitions
• Evidence for the decay $X(3872)\to \psi (2S)\gamma$
• Model-independent Study of Magnetic Dipole Transitions in Quarkonium
• Quark structure of the $X(3872)$ and ${\chi }_b(3P)$ resonances
• Photon transitions in Upsilon(2S) and Upsilon(3S)
• Study of open-charm decays and radiative transitions of the X(3872)
• Leptonic universality breaking in Upsilon decays as a probe of new physics
• Hadronic loop contributions to $J/\psi$ and ${\psi }^{\prime }$ radiative decays into $\gamma {\eta }_c$ or $\gamma {\eta }_c^{\prime }$
• The ratio of decay widths of X(3872) to ${\psi }^{\prime }\gamma$ and $J/\psi \gamma$ as a test of the X(3872) dynamical structure
• Magnetic properties of ground-state mesons
• $X(3872)$, $X_b$, and the ${\chi }_{b1}(3P)$ state
• Two-Photon, Two-gluon and Radiative Decays of Heavy Flavoured Mesons
• Electromagnetic form factors of the $B_c$-like tetraquarks: molecular and diquark-antidiquark pictures
• Study of radiative bottomonium transitions using converted photons
• The electromagnetic form factors of heavy-light pseudo-scalar and vector mesons
• The $c\bar{c}$ interaction above threshold and the radiative decay $X(3872)\to J/\psi \gamma$
• Search for psi(2S) -> gamma eta_c(2S) via fully reconstructed eta_c(2S) decays
• Study of the electromagnetic Dalitz decays $\psi ({\rm Y})\to {\eta }_c({\eta }_b)l^{+}{l}^{-}$
• Decay rates and electromagnetic transitions of heavy quarkonia
• Self-consistent $M1$ radiative transitions of excited $B_c$ and heavy quarkonia with different polarizations in the light-front quark model
• Measurements of branching fractions for electromagnetic transitions involving the ${\chi }_{bJ}(1P)$ states
• Study of $B_c$$\to$$J/\psi V$ and $B_c^{\ast }$$\to$${\eta }_{c}V$ decays within the QCD factorization
• Observation of chi-b(1PJ,2PJ) decays to light hadrons
• Study of $B_c^{\ast }$ $\to$ $\psi (1S,2S)P$, ${\eta }_c(1S,2S)P$ weak decays
• The role of electromagnetic interaction in the $X(3872)$ and its analogs
• Multipole Moments of Heavy Vector and Axial-Vector Mesons in QCD
• $B_c^{\ast }$ meson parameters and radiative decay width within the covariant confined quark model
• Line shape of the $J\psi \to \gamma {\eta }_c$ decay
• Radiative and Dalitz decays of ${\rm Y}(1S)$ in the light of the ATOMKI X17 anomaly
• Electromagnetic probes revealing the inner structure of the ${\Lambda }_c(2940)$