"Hard-scattering" approach to very hindered magnetic-dipole transitions in quarkonium

Abstract

For a class of hindered magnetic dipole ($M1$) transition processes, such as ${\rm Y}(3S)\to {\eta }_b+\gamma$ (the discovery channel of the ${\eta }_b$ meson), the emitted photon is rather energetic so that the traditional approaches based on multipole expansion may be invalidated. We propose that a "hard-scattering" picture, somewhat analogous to the pion electromagnetic form factor at large momentum transfer, may be more plausible to describe such types of transition processes. We work out a simple factorization formula at lowest order in the strong coupling constant, which involves convolution of the Schrödinger wave functions of quarkonia with a perturbatively calculable part induced by exchange of one semihard gluon between quark and antiquark. This formula, without any freely adjustable parameters, is found to agree with the measured rate of ${\rm Y}(3S)\to {\eta }_b+\gamma$ rather well, and can also reasonably account for other recently measured hindered $M1$ transition rates. The branching fractions of ${\rm Y}(4S)\to {\eta }_b^{(\prime )}+\gamma$ are also predicted.

v3; 5 pages, 1 figure and 1 table; title changed, presentation improved

References in corpus (7)

• Quarkonia and their transitions
• Radiative Transitions in Charmonium from Lattice QCD
• Observation of the bottomonium ground state in the decay Upsilon(3S) -> gamma eta_b
• Model-independent Study of Magnetic Dipole Transitions in Quarkonium
• J/psi and psi(2S) Radiative Transitions to eta_c
• Hadronic loop contributions to $J/\psi$ and ${\psi }^{\prime }$ radiative decays into $\gamma {\eta }_c$ or $\gamma {\eta }_c^{\prime }$
• Which hadronic decay modes are good for ${\eta }_b$ searching: double $J/\psi$ or something else?

Cited by in corpus (1)

• Re-Study on the wave functions of ${\rm Y}(nS)$ states in LFQM and the radiative decays of ${\rm Y}(nS)\to {\eta }_b+\gamma$