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

For a class of hindered magnetic dipole ($M1$) transition processes, such as $\Upsilon(3S)\to \eta_b+\gamma$ (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 Schr\"odinger 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 $\Upsilon(3S)\to \eta_b+\gamma$ rather well, and can also reasonably account for other recently measured hindered $M1$ transition rates. The branching fractions of $\Upsilon(4S)\to \eta_b^{(\prime)}+\gamma$ are also predicted.Comment: v3; 5 pages, 1 figure and 1 table; title changed, presentation improve

Exclusive Decay of 1−−1^{--} Quarkonia and BcB_c Meson into a Lepton Pair Combined with Two Pions

We study the exclusive decay of $J/\Psi$, $\Upsilon$ and $B_c$ into a lepton pair combined with two pions in the two kinematic regions. One is specified by the two pions having large momenta, but a small invariant mass. The other is specified by the two pions having small momenta. In both cases we find that in the heavy quark limit the decay amplitude takes a factorized form, in which the nonperturbative effect related to heavy meson is represented by a NRQCD matrix element. The nonperturbative effects related to the two pions are represented by some universal functions characterizing the conversion of gluons into the pions. Using models for these universal functions and chiral perturbative theory we are able to obtain numerical predictions for the decay widths. Our numerical results show that the decay of \jpsi is at order of $10^{-5}$ with reasonable cuts and can be observed at BES II and the proposed BES III and CLEO-C. For other decays the branching ratio may be too small to be measured.Comment: 19 pages, Latex 2e file, 12 EPS figures (included). Replaced with version to appear in Eur. Phys. J. C,published online: 8 May 200