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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). Contents.
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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
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
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
Bottomonium spectrum Introduction 5s Zb(10650) Zb(10610) BB threshold Charm2012
Zb(10610) and Zb(10650) Introduction By Belle Collaboration arXiv:1110.2251 Decay processes Υ(5S)Zb πΥ(nS)ππ Υ(5S) Zb πhb(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
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
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
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
Model setup BB Components
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
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
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
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
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.
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
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--)
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
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
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.
Exotic decay ratios for hb(1P) = for hb(2P) The process with spin-flip is not suppressed ! Charm2012
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)