Spin Partners of the $B^{(*)}\bar{B}^{(*)}$ resonances with a different approach than the Breit-Wigner parameterization

TL;DR

This paper proposes an alternative to the Breit-Wigner parameterization, called the Sill, to better analyze near-threshold resonances like the Z_b states, predicting their heavy quark spin symmetry partners as bound states.

Contribution

It introduces the Sill distribution as a new method for analyzing near-threshold resonances, improving upon Breit-Wigner limitations, and predicts heavy quark spin symmetry partners as bound states.

Findings

All predicted partners are bound states.

The Sill approach effectively captures threshold effects.

Heavy quark spin symmetry partners are identified as bound states.

Abstract

In general, resonances are obtained by the Breit-Wigner parameterization. However, it is not entirely appropriate to use this parameterization with near-threshold resonances such as the $Z_b(10610)$ and the $Z_b(10650)$, as Breit-Wigner does not contain the threshold effect. To eliminate this defect, a recently proposed alternative distribution, the Sill, is used to predict possible heavy quark spin symmetry partners of the $Z_b(10610)$ and the $Z_b(10650)$. With the Sill values of the $Z_b(10650)$ and the $Z_b(10610)$ states, assuming these exotics generate molecular states consisting of contact and a pion exchange potential, heavy quark spin symmetry partners are examined with $S$ and $D$-wave contributions. In the light of the Sill type resonance approach, all the partners are found as bound states.