Study of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:math> bottomonium bound states and resonances in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>P</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi></mml:math> waves with lattice QCD static-static-light-light potentials
Pedro Bicudo, Nuno Cardoso, Lasse Mueller, Marc Wagner
Abstract
In this paper we study $I=0$ bottomonium in $S$, $P$, $D$ and $F$ waves considering five coupled channels, one confined quarkonium and four open ${B}^{(*)}{\overline{B}}^{(*)}$ and ${B}_{s}^{(*)}{\overline{B}}_{s}^{(*)}$ meson-meson channels. To this end we use and extend a recently developed novel approach utilizing lattice QCD string breaking potentials for the study of quarkonium bound states and resonances. This approach is based on the Born-Oppenheimer approximation and the unitary emergent wave method and allows to compute the poles of the $\mathrm{T}$ matrix. We compare our results to existing experimental results for $I=0$ bottomonium and discuss masses, decay widths and the assignment of angular momentum quantum numbers. Moreover, we determine the quarkonium and meson-meson composition of these states to clarify, which of them are ordinary quarkonium, and which of them should rather be interpreted as tetraquarks.