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

TL;DR

This paper investigates the hyperfine splitting in the $bar{b}$ system, demonstrating that a specific relativistic potential model can accurately reproduce the observed large splitting.

Contribution

The authors present a relativistic potential model that successfully accounts for the large hyperfine splitting in the $bar{b}$ system by retaining delta function terms in the hyperfine potential.

Findings

Calculated hyperfine splitting of 67.5 MeV closely matches experimental value.

Model includes relativistic kinetic energy, scalar confining potential, and one-loop QCD corrections.

Softening delta function terms reduces the predicted hyperfine splitting, failing to match observations.

Abstract

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.