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We present two methods for computing dimensionally-regulated NRQCDheavy-quarkonium matrix elements that are related to the second derivative ofthe heavy-quarkonium wave function at the origin. The first method makes use ofa hard-cutoff regulator as an intermediate step and requires knowledge only ofthe heavy-quarkonium wave function. It involves a significant cancellation thatis an obstacle to achieving high numerical accuracy. The second method is moredirect and yields a result that is identical to the Gremm-Kapustin relation,but it is limited to use in potential models. It can be generalized to thecomputation of matrix elements of higher order in the heavy-quark velocity andcan be used to resum the contributions to decay and production rates that areassociated with those matrix elements. We apply these methods to the Cornellpotential model and compute a matrix element for the J/psi state that appearsin the leading relativistic correction to the production and decay of thatstate through the color-singlet quark-antiquark channel.Comment: 26 pages, 3 figures, Sec. IV completely re-written, published version  in Phys. Rev.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Potential-model calculation of an order-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>v</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:math>nonrelativistic QCD matrix element

Potential-model calculation of an order-v2nonrelativistic QCD matrix element