Model-independent Study on Magnetic Dipole Transition in Heavy Quarkonium

Some new results on magnetic dipole (M1) transitions in heavy quarkonium from nonrelativistic effective field theories of QCD are briefly reported. This model-independent approach not only facilitates a systematic and lucid way to investigate the relativistic corrections, it also clarifies some inconsistent treatment in previous potential model approach. The impact of our formalism on J/Psi -> eta_c gamma, Upsilon(Upsilon') -> eta_b gamma and h_c -> chi_{c0} gamma are discussed.Comment: 7 pages and 3 figures. Talk presented at QCD@Work 2005, Conversano, June 16-20, 2005 and QCD05, Montpellier, July 4-8, 200

Which hadronic decay modes are good for ηb\eta_b searching: double J/ψJ/\psi or something else?

It has been controversial whether $\eta_b$ can be discovered in Tevatron Run 2 through the decay $\eta_b\to J/\psi J/\psi$ followed by $J/\psi\to \mu^+\mu^-$. We clear this controversy by an explicit calculation which predicts ${\rm Br}[\eta_b\to J/\psi J/\psi]$ to be of order $10^{-8}$. It is concluded that observing eta_b through this decay mode in Tevatron Run 2 is rather unrealistic. The eta_b may be observed in the forthcoming LHC experiments through the 4-lepton channel, if the background events can be significantly reduced by imposing some kinematical cuts. By some rough but plausible considerations, we find that the analogous decay processes eta_b to VV, D^*\bar{D}^* also have very suppressed branching ratios, nevertheless it may be worth looking for \eta_b at LHC and Super B factory through the decay modes \eta_b \to K_S K^{\pm}\pi^{\mp}, D^*\bar{D}.Comment: v2; 28 pages, 2 figures. References added, presentation improved. Discussion on possible nonperturbative mechanism for eta_b->VV added, analysis for eta_b->VP updated by incoprating the U-spin violation effec

"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

A local construction of the Smith normal form of a matrix polynomial

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular row and column operations to the original matrix. The performance of the algorithm in exact arithmetic is reported for several test cases.Comment: 26 pages, 6 figures; introduction expanded, 10 references added, two additional tests performe