Abstract
Two hadrons with exotic quark content ${Z}_{b}^{+}\ensuremath{\simeq}\overline{b}b\overline{d}u$ were discovered by Belle. We present a lattice study of the $\overline{b}b\overline{d}u$ systems with various quantum numbers using static bottom quarks. Only one set of quantum numbers that couples to ${Z}_{b}$ and $\mathrm{\ensuremath{\Upsilon}}\ensuremath{\pi}$ was explored on the lattice before; these studies found an attractive potential between $B$ and ${\overline{B}}^{*}$ resulting in a bound state below the threshold. The present study considers the other three sets of quantum numbers. Eigenenergies of the $\overline{b}b\overline{d}u$ system are extracted as a function of separation between $b$ and $\overline{b}$. The resulting eigenenergies do not show any sizable deviation from noninteracting energies of the systems $\overline{b}b+\overline{d}u$ and $\overline{b}u+\overline{d}b$, so no significant attraction or repulsion is found. A slight exception is a small attraction between $B$ and ${\overline{B}}^{*}$ at small distance for the quantum number that couples to ${Z}_{b}$ and ${\ensuremath{\eta}}_{b}\ensuremath{\rho}$.
Highlights
The Belle experiment discovered two tetraquarksZbð10610Þ and Zbð10650Þ with JP 1⁄4 1þ and I 1⁄4 1 in 2011 [1,2]
We present a lattice study of the bbdu systems with various quantum numbers using static bottom quarks
One set of quantum numbers that couples to Zb and Υπ was explored on the lattice before; these studies found an attractive potential between B and B Ã resulting in a bound state below the threshold
Summary
Zbð10610Þ and Zbð10650Þ with JP 1⁄4 1þ and I 1⁄4 1 in 2011 [1,2]. Both resonances were first observed in decays to ZÆb → ΥðnSÞπÆ and ZÆb → hbðmPÞπÆ, which indicates the exotic flavor content Zþb ∼ bbdu. The eigenenergies represent lattice input to study this system within the Born-Oppenheimer approximation via static potentials, according to the general strategy outlined in [19,20,21,22,23,24] This approximation is valuable when the b-quark mass is much larger than the energy scale of the light degrees of freedom. Throughout this paper we refer to any combination of BðÃÞBðÃÞ as BB Ã.2 Both available studies found that the eigenstate dominated by BB à has energy significantly below mB þ mBà at small r. The Schrödinger equation for BB à leads to a bound state below the BB à threshold, which could be related to Zb. The present lattice study considers another three sets of quantum numbers for the bbqq system. Numbers which do not couple to BB à but only to 1⁄2bb1⁄2qq in the explored energy region
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.