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Topological and differentiable rigidity of submanifolds in space forms
Let be an -dimensional simply connected space form with
nonnegative constant curvature . We prove that if is a compact
submanifold in , and if where is the mean
curvature of , then is homeomorphic to a sphere. We also show that the
pinching condition above is sharp. Moreover, we obtain a new differentiable
sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page
"Hard-scattering" approach to very hindered magnetic-dipole transitions in quarkonium
For a class of hindered magnetic dipole () transition processes, such as
(the discovery channel of the 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 rather well, and can also reasonably
account for other recently measured hindered transition rates. The
branching fractions of are also
predicted.Comment: v3; 5 pages, 1 figure and 1 table; title changed, presentation
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