Hyperfine splittings in the $b\bar{b}$ system

Details Hyperfine splittings in the $b\bar{b}$ system Hyperfine splittings in the $b\bar{b}$ system

2009-12-11

arxiv.org/abs/0912.2259v4

Nucl.Phys.A865:69-75,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

5 pages, 3 tables, text revisions

Scientific paper

10.1016/j.nuclphysa.2011.06.032

Recent measurements of the $\eta_b(1S)$, the ground state of the $b\bar{b}$ system, show the splitting between it and the $\Up(1S)$ to be 69.5$\pm$3.2 MeV, considerably larger than lattice QCD and potential model predictions, including recent calculations published by us. The models are unable to incorporate such a large hyperfine splitting within the context of a consistent description of the energy spectrum and decays. We demonstrate that in our model, which incorporates a relativistic kinetic energy term, a linear confining term including its scalar-exchange relativistic corrections, and the complete one-loop QCD short distance potential, such a consistent description, including the measured hyperfine splitting, can be obtained by not softening the delta function terms in the hyperfine potential. We calculate the hyperfine splitting to be 67.5 MeV.

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