Bottomonium vector resonances and threshold effects

TL;DR

This paper reviews experimental and theoretical analyses of bottomonium vector resonances, highlighting the potential existence of unlisted $^{3}D_1$ states below the $Bar{B}$ threshold and questioning the nature of the $
0580$ resonance.

Contribution

It introduces evidence for two unlisted $^{3}D_1$ bottomonium states and revisits empirical models of vector $bar{b}$ resonances using the Resonance-Spectrum-Expansion formalism.

Findings

Indications of two unlisted $^{3}D_1$ states below the $Bar{B}$ threshold.

Reassessment of the $
0580$ as a non-resonant state.

Application of the Resonance-Spectrum-Expansion formalism to bottomonium data.

Abstract

The bottomonium spectrum is the perfect testing ground for the confining potential and unitarisation effects. The bottom quark is about three times heavier than the charm quark, so that $b\bar{b}$ systems probe primarily the short-range part of that potential. Also, the much smaller colour-hyperfine interaction in the $B$ mesons make the $B\bar{B}$ threshold lie significantly higher than the $D\bar{D}$ threshold in charmonium, on a relative scale of course. A further complicating circumstance is that none of the experimentally observed vector $b\bar{b}$ mesons has been positively identified as a $^{3\!}D_1$ state, contrary to the situation in charmonium. This makes definite conclusions about level splittings very problematic. Finally, there are compelling indications that the $\Upsilon(10580)$ is not the $\Upsilon(4S)$ state, as is generally assumed. Here we review an analysis of experimental bottomonium data which show indications of the two lowest and so far unlisted $^{3\!}D_1$ states below the $B\bar{B}$ threshold. Next an empirical modelling of vector $b\bar{b}$ resonances above the open-bottom threshold is revisited, based on the Resonance-Spectrum-Expansion production formalism applied to other experimental data. A recent effective-Lagrangian study supporting our non-resonant assignment of the $\Upsilon(10580)$ is briefly discussed as well.