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Exotic mesons with heavy flavor

This research delves into exotic mesons with heavy flavor, exploring meson molecules, model setups, state classifications, and experimental results. The study focuses on charm and bottomonium spectra, molecular states, and resonances like Zb(10610) and Zb(10650).

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Exotic mesons with heavy flavor

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  1. Exotic mesons with heavy flavor arXiv:1111.2921[hep-ph] arXiv:1202.0760[hep-ph] D2 S. Ohkoda (RCNP) In collaboration with Y. Yamaguchi (RCNP) S. Yasui (KEK) K. Sudoh (Nishogakusha) A. Hosaka (RCNP) Charm2012

  2. Contents • Introduction • Exotic Hadron? • Meson molecule? • Model setup • Classification of states • One boson exchange potential • Results • DD molecule? • BB molecular states spectrum • Zb(10610) and Zb(10650) Charm2012

  3. charmonium Introduction Y(4630) • Cornell potential well explains the charmonium spectrum Z(4430) Y(4350) s1 quarkoniumcc + exoticstates Z(4250) Y(4260) C C X(4160) Y(4140) L s2 Z(4050) Y(4008) Y(3940) X(3940) X(3872) quarkoniumcc ? Eichten in QWG 2008 Nara Charm2012

  4. Bottomonium spectrum Introduction 5s Zb(10650) Zb(10610) BB threshold Charm2012

  5. Zb(10610) and Zb(10650) Introduction By Belle Collaboration arXiv:1110.2251 Decay processes Υ(5S)Zb πΥ(nS)ππ Υ(5S) Zb πhb(mP)ππ n = 1,2,3 m= 1,2 M(Zb(10610))= 10607.2 ±2.4 MeV M(Zb(10650))= 10652.2 ±1.5 MeV Υ(5S) 10610, 10650 Properties • Exotic quantum numbers • IG (JP) = 1+(1+) • Exotic decay ratios • Γ(Zb → Υ(nS)π) ≈ Γ(Zb → hb(mP)π) • “Exotic twin” resonances • Δm = m(Zb(10650))-m(Zb(10610)) • ≈ 45MeV ± ± ± ±x Υ(nS), n=1,2,3 hb(mP), m=1,2 Zb’s are good candidates of molecule states A.E. Bondar et al. PRD(2011) Charm2012

  6. Can molecule states exist? Introduction B(*) (D) B(*) (D) π, ρ, ω,… • Can the OBEP bind mesons in heavy quark sector? • Could such states explain the exotic states which do not fit into the conventional qq quark model? Charm2012

  7. Why are molecular states studied in heavy quark sectors? Introduction • The kinetic term of Hamiltonian is suppressed Because the reduced mass is larger in heavy mesons Ex) two body systems B and B* are degenerate thanks to HQS The interaction of heavy quark spin is suppressed in heavy quark sector mK∗ − mK ~ 400 MeV mD∗ − mD~ 140 MeV -> The effects of channel-couplings becomes larger mB∗ − mB~ 45 MeV Charm2012

  8. Effect of mass degeneracy Introduction N P P N 3S1 1S0 π π 5D0 3D1 P* P* π π 1S0 3S1 N N P P P=D,B Charm2012

  9. Model setup BB Components

  10. Lagrangians for heavy mesons Model setup Heavy meson field P = D or B P* = D* or B* (D*→ Dπ, radiative decay, loptonicdecay of B) R. Casalbuoni et al, Phys. Rep. 281, 145 (1997) Charm2012

  11. Cutoff Model setup • We employ monopole-type Form factor for each vertex • The cutoff ΛN is determined from deuteron • ΛP is determined by the ratio of the size Charm2012

  12. We obtain the coupled channel potential Model setup Ex) IG (JPC) = 1+(1+-) : Zb,Zb’ • Hamiltonian is derived We solve numerically the Schrödinger equation Charm2012

  13. We solve numerically the coupled-channel Schrödinger equation • We found no DD bound and resonance states • with exotic quantum numbers • But several BB bound and resonance states are obtained • There is novel correspondence of BB states and Zb Charm2012

  14. Numerical results 3 results Resonance state Ere =50.4MeV B*B* Z’bexperiment (10650) Remarks 45MeV • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • OPEP is dominant in this system. • Molecular states in IG (JP) = 1+(1+) are unique property in bottom quark sector. Zbexperiment BB* (10604) BB* bound state EB = -8.5 MeV Charm2012 • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers. • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers. • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers. • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers.

  15. The BB bound and resonance states results B*B* (10650) 10655 10649 Zb(10652) 10622 10621 10617 Zb(10607) 10606 10602 BB* (10604) 10594 10596 10566 BB (10559) IG(JPC) 1+(0--) 1+(1--) 1-(2++) 1+(1+-) 1-(1++) 1+(2--) 0+(1-+) Charm2012

  16. Decay channel 0-(1--) ϒ(5S) (10860) π S-wave B*B* (10650) How to produce? π P-wave γ Υπ, hbπ Υπ, ηbπ Υρ, Χbπ BB* hbπ, ηbρ,Υπ (10604) Υπ, ηbπ Υρ, Χbπ Υπ, hbπ Υπ, ηbρ How to decay? BB (10559) hbπ, ηbρ,Υπ IG(JPC) 1+(0--) 1+(1--) 1-(2++) 1+(1+-) 1-(1++) 1+(2--)

  17. Summary • We have systematically studied the possibility of the BB bound and resonant states having exotic quantum numbers. • IG(JPC)=1+(1+-) states have a bound state with binding energy 8.5 MeV, and a resonant state with the resonance energy 50.4 MeV and the decay width 15.1 MeV. The twin resonances of Zb’s can be interpreted as the BB molecular type states. • The otherpossible BB states are predicted. • The channel mixing plays an important role. • One pion exchange potential is dominant. • Various exotic states would be observed around the thresholds from Υ(5S) decays in accelerator facilities such as Belle. Charm2012

  18. Effects of the coupling to decay channels results Table: Various coupling constants g = gΥ, ghb and the mass shifts δM of Zb . Total mass shift is 5.5 MeV. BB* bound state will get close the BB* threshold. Charm2012 Υ, hb Zb π

  19. Numerical results results Remarks • Total mass shift is 5.5 MeV. • The BB* bound state will get close the threshold, or even become resonance state. Resonance state Ere =50.4MeV B*B* Z’bexperiment (10650) ϒ(1S) π 15 Γ 45MeV 10 5 Zbexperiment Mth BB* (10604) 6 BB* bound state 2 δM EB = -3.3 MeV Push up Mth Charm2012 • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers. • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers. • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers. • We find the twin states in 1+(1+-)near the BB* and B*B* threshold. These states would be interpreted as Zb’s. • In other channels we further predict the BB bound and resonant states. • BB states have decay channels of a quarkonium and a light flavor meson. • OPEP is dominant in this system. • In charm sector, our model does not predict any bound or resonant states which have exotic quantum numbers.

  20. Charm2012

  21. Exotic decay ratios for hb(1P) = for hb(2P) The process with spin-flip is not suppressed ! Charm2012

  22. The puzzle of Zb Decay width ϒ(5S) Zb+ π- ϒ(nS) π+π- ϒ(5S) Zb+ π- hb(kP) π+π- No spin flip Spin flip ! process with spin flip should be suppressed because of large mass of b quark In practice, these process have almost the same probability Sl : spin of light degree of freedom hb π Υ π If Zbis meson molecular states, spin flip problem is solved. Charm2012 A.E. Bondar et al.(2011)

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