Study of $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions in $I=1$ and relationship to the $Z_b(10610)$, $Z_b(10650)$ states

Abstract

We use the local hidden gauge approach in order to study the $B{\bar{B}}^{\ast }$ and $B^{\ast }{\bar{B}}^{\ast }$ interactions for isospin I=1. We show that both interactions via one light meson exchange are not allowed by OZI rule and, for that reason, we calculate the contributions due to the exchange of two pions, interacting and noninteracting among themselves, and also due to the heavy vector mesons. Then, to compare all these contributions, we use the potential related to the heavy vector exchange as an effective potential corrected by a factor which takes into account the contribution of the others light mesons exchange. In order to look for poles, this effective potential is used as the kernel of the Bethe-Salpeter equation. As a result, for the $B{\bar{B}}^{\ast }$ interaction we find a loosely bound state with mass in the range $10587-10601$ MeV, very close to the experimental value of the $Z_b(10610)$ reported by Belle Collaboration. For the $B^{\ast }{\bar{B}}^{\ast }$ case, we find a cusp at $10650$ MeV for all spin $J=0,1,2$ cases.

23 pages, 20 figures

References in corpus (11)

• Heavy quarkonium: progress, puzzles, and opportunities
• Prediction of narrow $N^{\ast }$ and ${\Lambda }^{\ast }$ resonances with hidden charm above 4 GeV
• X(3872) and Other Possible Heavy Molecular States
• Is X(3872) {\sl Really} a Molecular State?
• Axial Resonances in the Open and Hidden Charm Sectors
• The Vector and Axial-Vector Charmonium-like States
• New Hadron States
• Confirming the molecular nature of the $Z_b(10610)$ and the $Z_b(10650)$
• Decays of Zb(+) and Zb'(+) as hadronic molecules
• The radiative decay of $\psi (3770)$ into the predicted scalar state X(3700)
• Is $Z_b(10610)$ a Molecular State?

Cited by in corpus (25)

• Pentaquark and Tetraquark states
• Exotics: Heavy Pentaquarks and Tetraquarks
• Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?
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• ${\bar{B}}^{(\ast )}{\bar{B}}^{(\ast )}$ interactions in chiral effective field theory
• $Z_b(10610)$ and $Z_b^{\prime }(10650)$ decays in a covariant quark model
• Photoproduction of strange hidden-charm and hidden-bottom states
• Tetraquark systems $\bar{b}b\bar{d}u$ in the static limit and lattice QCD
• $P$-wave coupled channel effects in electron-positron annihilation
• Magnetic dipole moment of $Z_b(10610)$ in light-cone QCD
• Insights into $Z_b(10610)$ and $Z_b(10650)$ from dipion transitions from ${\rm Y}(10860)$
• Photo- and electro-production of narrow exotic states: from light quarks to charm and up to bottom
• The $Z_b$ structures in a constituent quark model coupled-channels calculation
• Investigations on the light hadron decays of $Z_b(10610)$ and $Z_b(10650)$
• Bottomonium-like tetraquarks in a chiral quark model
• Two-pion exchange for coupled-channel scattering of two heavy mesons
• Composite nature of $Z_b$ states from data analysis
• $D$ wave bottomonia production from $Z_b^{(\prime )}$ decay
• Spin Partners of the $B^{(\ast )}{\bar{B}}^{(\ast )}$ resonances with a different approach than the Breit-Wigner parameterization
• Pole analysis for the $D^{\ast }\bar{K}$-$D\overline{K^{\ast }}$ coupled-channel system
• Production of the bottomonium-like states $Z_b$ states at $e$-$h$ and ultraperipheral $h$-$h$ collisions
• Quarkonium interactions with (hot) hadronic matter
• Exotic hadrons associated with $b$-quark
• The dynamically generated $h_1$ state by the $K^{\ast }{\bar{K}}^{\ast }$ interaction and its $K_1(1270)\bar{K}$ and $b_1(1235)\pi$ decays
• An analysis on doubly bottom molecular tetraquarks composed of $H_{(s)}$ and $T_{(s)}$ doublets