1207.3301 (R. Giachetti et al.)

Unified treatment of hyperfine splittings in $b\bar{b}$, $c\bar{c}$ and
$s\bar{s}$    [PDF]

R. Giachetti, E. Sorace

We present a relativistic potential model for $b\bar{b}$, $c\bar{c}$ and $s\bar{s}$ using the Cornell potential to extend a two fermion wave equation determined for the study of the hyperfine structure of hydrogen atom and positronium. The hyperfine splitting is obtained by the first perturbation order of the appropriate Breit term. The excellent agreement of the numerical with the experimental results for such a simple potential shows the fundamental importance of relativity in potential quark models. Only three parameters are used for each system. Moreover the same value for the string tension parameter has been used for fitting both the $b\bar{b}$ and $c\bar{c}$ spectra. The numerical results for the $s\bar{s}$ system show the large influence of the hyperfine splitting on the spectrum and are in agreement also with some of the not assigned states.

View original: http://arxiv.org/abs/1207.3301