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arXiv · hep-ph/0406113

Momentum Representation of Coulomb Wave Functions and Level Shifts in Bottomonium due to Charm Effects

Hai-bin Wang·York-Peng Yao
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Abstract

Since effective potentials derived from Feynman diagrams are naturally given in momentum space, we formulate the non-relativistic Coulomb problem entirely in momentum representation. We give momentum wave functions for all quantum numbers in one-dimensional integrals, even though they can be evaluated. Angular momentum decomposed Green's functions are then compactly represented. We apply this formalism to investigate the next to next leading order charm effects on 1S bottomonium level shift. Our one insertion results are given completely in analytic form and numerically agree with previous results. Our two insertion results are also in agreement. The net effect of finite charm mass is to decrease the bottom mass by 33 MeV, as determined through the measured 1S energy.

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Hai-bin Wang, York-Peng Yao. 2004-09-02. Momentum Representation of Coulomb Wave Functions and Level Shifts in Bottomonium due to Charm Effects. https://doi.org/10.1103/physrevd.70.094046

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