EXOTIC MESONS WITH HIDDEN BOTTOM NEAR THRESHOLDS D2 S. OHKODA (RCNP) IN COLLABORATION WITH Y. YAMAGUCHI (RCNP) S. YASUI (KEK) K. SUDOH (NISHOGAKUSHA) A. HOSAKA (RCNP) 12/06/21 Heavy quark hadron s 1 arXiv: [hep-ph] accepted in PRD

CONTENTS  Introduction  What is exotic hadrons?  Z b (10610) and Z b (10650)  Potential model  Formalism  Numerical results  Channel coupling effects  Summary 12/06/21 Heavy quark hadrons 2

MOTIVATION Everything are not forbidden “… while mesons are made out of (qq), (qqqq), etc.” Gell-Mann, Phys. Lett. 8, 214 (1964) 12/06/21 Heavy quark hadrons 3

Eichten in QWG 2008 Nara quarkonium cc + exotic states CC s1s1 s2s2 L CHARMONIUM Cornell potential well explains the charmonium spectrum Z(4250) X(3940) X(4160) Y(4260) Y(4008) Y(4350) Y(4630) X(3872) Y(3940) Z(4050) Z(4430) Y(4140) ? 12/06/21 Heavy quark hadrons 4

12/05/16 Charm BB threshold 5s Z b (10650) Z b (10610) BOTTOMONIUM SPECTRUM

EXOTIC HADRON PROPERTIES 1.Exotic quantum numbers I(J PC ) = 0(0 +- ), 0(0 -- ), 0(1 -+ ), 0(2 +- )… and I=1 states. Ex) Z(4430) +, Z b (10610) +, Z b (10650) + 2.Decay width is quite narrow Some exotic hadrons have the “narrow” decay width. Open charm decays seem to be suppressed. Ex) Γ(Y(4140)) = 11.6 MeV 3.Unexpected decay channel and ratio Isospin breaking? Exotic spin structure? 4.Mass position do not fit into usual quark model prediction Exotic hadrons do not fit into the conventional qq quark model 12/06/21 Heavy quark hadrons 6

OBSERVATION OF Z b (10610) AND Z b (10650) 12/06/21 Heavy quark hadrons 7 PRL 108, (2012) BY BELLE COLLABOALTION

Υ(5S) HAS ANOMALOUSLY HIGH RATES TO Υ(1S), Υ(2S) AND Υ(3S) What is the origin ? 12/06/21 Heavy quark hadrons 8

Intermediate states appear in Υ(5S) → Υ(nP) π + π − PRL 108, (2012) Heavy quark hadrons 9

LOOK FOR h b AND h b (2P) IN Υ(5S) → π + π − + ANYTHING 12/06/21 Heavy quark hadrons 10

EXOTIC DECAY RATIOS 12/06/21 Heavy quark hadrons 11 = for h b (1P) for h b (2P) The process with spin-flip is not suppressed ! Υ(5S) → h b (mP) π + π - decay is exotic

RESONANT STRUCTURE OF Υ(5S) → h b (mP) π + π − 〜 BB* threshold 〜 B*B* threshold Resonance parameters are consistent for h b (1P)ππ and h b (1P)ππ Almost all h b (mP) are produced through Υ(5S) → Z b π → h b ππ 12/06/21 Heavy quark hadrons 12

12/06/21 Heavy quark hadrons 13 MASS AND WIDTH IN EACH MEASUREMENT M = ± 2.0 MeV Γ = 18.4 ± 2.4 MeV M = ± 1.7 MeV Γ = 11.5 ± 2.2 MeV Z b (10610) Z b (10650)

EXOTIC MESONS WITH HIDDEN BOTTOM NEAR THRESHOLDS 12/06/21 Heavy quark hadrons 14 ARXIV: [HEP-PH] SUBMITTED IN PRD

12/06/21 Heavy quark hadrons 15 Z b (10610) AND Z b (10650) Exotic quantum numbers I G (J P ) = 1 + (1 + ) Exotic decay ratios Γ(Z b → Υ(nS)π) ≈ Γ(Z b → h b (mP)π) “Exotic twin” resonances Δm = m(Z b (10650))-m(Z b (10610)) ≈ 45MeV Υ(5S) Υ(nS), n=1,2,3 h b (mP), m=1,2 Z b ’s are good candidates of molecule states Properties n = 1,2,3 m= 1,2 Υ(5S)  Z b π  h b (mP) π π Υ(5S)  Z b π  Υ(nS) π π Decay processes ± ±x±x ± ± 10610, By Belle Collaboration arXiv: M(Z b (10610))= ±2.4 MeV M(Z b (10650))= ±1.5 MeV

The puzzle of Z b Decay width ϒ (5S)  Z b + π -  ϒ (nS) π + π - A.E. Bondar et al. PRD(2011) Spin flip ! No 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 S l : spin of light degree of freedom If Z b is meson molecular states, spin flip problem is solved. h b π Υ π ϒ (5S)  Z b + π -  h b (kP) π + π - 12/06/21 Heavy quark hadrons 16

17 B ( * ) (D) π, ρ, ω,… B ( * ) (D) 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? 12/06/21 Heavy quark hadrons

WHY ARE MOLECULAR STATES STUDIED IN HEAVY QUARK SECTORS? 18 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 effects of channel-couplings becomes larger The interaction of heavy quark spin is suppressed in heavy quark sector m K ∗ − m K ~ 400 MeV m D ∗ − m D ~ 140 MeV m B ∗ − m B ~ 45 MeV 12/06/21 Heavy quark hadrons

EFFECT OF MASS DEGENERACY 12/06/21 Heavy quark hadrons 19 NN N N 3S13S1 3S13S1 3D13D1 PP P P 1S01S0 1S01S0 5D05D0 P*P* P*P* π π π π P=D,B

g DD*π coupling is very strong in heavy quark sector ! 12/03/14 Seminor in Nagoya Univ. 20 COUPLING STRENGTH HQS VS SU(4)

21 BB Components 12/06/21 Heavy quark hadrons

22 LAGRANGIANS FOR HEAVY MESONS P = D or BP* = D* or B* Heavy meson field R. Casalbuoni et al, Phys. Rep. 281, 145 (1997) 12/06/21 Heavy quark hadrons (D* → Dπ, radiative decay, loptonic decay of B) Model setup

CUTOFF We employ monopole-type Form factor for each vertex The cutoff Λ N is determined from deuteron Λ P is determined by the ratio of the size 12/06/21 Heavy quark hadrons 23 Model setup

THE COUPLED CHANNEL POTENTIAL 24 We solve numerically the Schrödinger equation Ex) I G (J PC ) = 1 + (1 +- ) : Z b,Z b ’ 12/06/21 Heavy quark hadrons Model setup HAMILTONIAN

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 Z b 12/06/21 Heavy quark hadrons 25

NUMERICAL RESULTS 12/06/21 Heavy quark hadrons 26 B*B* BB* 45MeV (10650) (10604) Z ’ b experiment Z b experiment BB* bound state E B = -8.5 MeV E re =50.4MeV Resonance state We find the twin states in 1 + (1 +- ) near the BB* and B*B* threshold. These states would be interpreted as Z b ’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 Z b ’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 Z b ’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 Z b ’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 Z b ’s. OPEP is dominant in this system. Molecular states in I G (J P ) = 1 + (1 + ) are unique property in bottom quark sector. Remarks 3 results

THE BB BOUND AND RESONANCE STATES I G (J PC ) 1 + (0 -- ) 1 + (1 +- )1 - (1 ++ ) 1 + (1 -- )1 - (2 ++ ) 1 + (2 -- ) 0 + (1 -+ ) Z b (10607) Z b (10652) (10650) B*B* (10604) BB* (10559) BB results 27 12/06/21 Heavy quark hadrons

I G (J PC ) 1 + (0 -- ) 1 + (1 +- )1 - (1 ++ ) 1 + (1 -- )1 - (2 ++ ) 1 + (2 -- ) ϒ (5S) 0 - (1 -- ) (10860) π S-wave π P-wave γ Υπ, h b π Υπ, η b ρ h b π, η b ρ, Υπ Υπ, η b π Υρ, Χ b π (10650) B*B* (10604) BB* (10559) BB Decay channel 12/06/21 28 How to produce? How to decay? Υπ, η b π Heavy quark hadrons

NUMERICAL RESULTS 12/06/21 Heavy quark hadrons 29 B*B* BB* 45MeV (10650) (10604) Z ’ b experiment Z b experiment BB* bound state E B = -8.5 MeV E re =50.4MeV Resonance state We find the twin states in 1 + (1 +- ) near the BB* and B*B* threshold. These states would be interpreted as Z b ’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 Z b ’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 Z b ’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 Z b ’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. Observed Zb’s are resonance states. But our model predict BB* bound state. What will happen if our prediction includes channel coupling effect ? Remarks 3 results

EFFECTS OF THE COUPLING TO DECAY CHANNELS 12/06/21 Heavy quark hadrons 30 Total mass shift is 2.4 MeV. Effects of channel coupling are repulsive. Table: Various coupling constants g = g Υ, g hb and the mass shifts δM of Z b. ZbZb Υ, h b π Loop function Imaginary part of loop function Mass shift Λ=600 MeV

NUMERICAL RESULTS 12/06/21 Heavy quark hadrons 31 B*B* BB* 45MeV (10650) (10604) Z ’ b experiment Z b experiment BB* bound state E B = -6.1 MeV E re =50.4MeV Resonance state We find the twin states in 1 + (1 +- ) near the BB* and B*B* threshold. These states would be interpreted as Z b ’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 Z b ’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 Z b ’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 Z b ’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. Channel coupling effects push up BB* bound state to 6.1MeV. If we use Λ=520 MeV, BB* bound state corresponds the mass position of Z b. Remarks results Push up δM Γ M th ϒ (1S) π

We have systematically studied the possibility of the BB bound and resonant states having exotic quantum numbers. I G (J PC )=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 Z b ’s can be interpreted as the BB molecular type states. The other possible 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. SUMMARY 12/06/21 Heavy quark hadrons 32