EXOTIC MESONS WITH HIDDEN BOTTOM NEAR THRESHOLDS D2 S. OHKODA (RCNP) IN COLLABORATION WITH Y. YAMAGUCHI (RCNP) S. YASUI (KEK) K. SUDOH (NISHOGAKUSHA) A

Heavy quark hadrons 1

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

arXiv:1111.2921 [hep-ph]accepted in PRD


CONTENTS Introduction

What is exotic hadrons? Zb(10610) and Zb(10650)

Potential model

Formalism Numerical results Channel coupling effects

Summary

12/06/21

MOTIVATION

Everything are not forbidden“… while mesons are made out of (qq), (qqqq), etc.”

Gell-Mann, Phys. Lett. 8, 214 (1964)12/06/21


Eichten in QWG 2008 Nara

quarkonium cc

quarkonium cc+ exotic states

C C

s1

s2L

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


12/05/16

Charm2012 5

BB threshold

5s Zb(10650)Zb(10610)

BOTTOMONIUM SPECTRUM

EXOTIC HADRON PROPERTIES

1. Exotic quantum numbers

I(JPC) = 0(0+-), 0(0--), 0(1-+), 0(2+-)… and I=1 states.

Ex) Z(4430)+, Zb(10610)+, Zb(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



OBSERVATION OF Zb(10610) AND Zb(10650)

12/06/21

PRL 108, 122001 (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


Intermediate states appear in Υ(5S) → Υ(nP) π+ π−

PRL 108, 122001 (2012)


LOOK FOR hb AND hb(2P) IN Υ(5S) → π+ π− + ANYTHING

12/06/21


EXOTIC DECAY RATIOS

12/06/21


= for hb(1P)

for hb(2P)

The process with spin-flip is not suppressed !Υ(5S) → hb(mP) π+π- decay is exotic

RESONANT STRUCTURE OF Υ(5S) → hb(mP) π+ π−

〜 BB* threshold

〜 B*B* threshold

Resonance parameters are consistent for hb(1P)ππ and hb(1P)ππ Almost all hb(mP) are produced through Υ(5S) → Zb π → hb ππ12/06/21


12/06/21


MASS AND WIDTH IN EACH MEASUREMENT

M = 10607.2 ± 2.0 MeVΓ = 18.4 ± 2.4 MeV

M = 10652.2 ± 1.7 MeVΓ = 11.5 ± 2.2 MeV

Zb(10610) Zb(10650)


EXOTIC MESONS WITH HIDDEN BOTTOM NEAR THRESHOLDS

12/06/21

ARXIV:1111.2921 [HEP-PH]

SUBMITTED IN PRD

12/06/21


Zb(10610) AND Zb(10650)

• 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

Υ(5S)

Υ(nS), n=1,2,3hb(mP), m=1,2

Zb’s are good candidates of molecule states

Properties

n = 1,2,3 m= 1,2

Υ(5S) Zb π hb(mP) π πΥ(5S) Zb π Υ(nS) π π

Decay processes

± ±x

± ±

10610,10650

By Belle CollaborationarXiv:1110.2251

M(Zb(10610))= 10607.2 ±2.4 MeV

M(Zb(10650))= 10652.2 ±1.5 MeV

The puzzle of Zb Decay width

ϒ(5S) Zb+

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

Sl : spin of light degree of freedom

If Zb is meson molecular states, spin flip problem is solved.

hb π Υ π

ϒ(5S) Zb+

π- hb(kP) π+ π-

12/06/21Heavy quark hadrons 1

6

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?

DO MOLECULE STATES EXIST?

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 spinis suppressed in heavy quark sector mK ∗ − mK ~ 400 MeV

mD ∗ − mD ~ 140 MeV

mB ∗ − mB ~ 45 MeV

12/06/21

Heavy quark hadrons

EFFECT OF MASS DEGENERACY

12/06/21


N N

N N3S1

3S1

3D1

P P

P P1S0

1S0

5D0P* P*

π

π π

π

P=D,B

gDD*π coupling is very strong in heavy quark sector !12/03/14

Seminor in Nagoya Univ. 20

COUPLING STRENGTH HQS VS SU(4)


BB Components

12/06/21

22

LAGRANGIANS FOR HEAVY MESONS

P = D or B P* = 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 ΛN is determined from deuteron• ΛP is determined by the ratio of the size

12/06/21

Model setup

THE COUPLED CHANNEL POTENTIAL

24

We solve numerically the Schrödinger equation

Ex) IG (JPC) = 1+(1+-) : Zb ,Zb’

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 Zb

12/06/21

NUMERICAL RESULTS

12/06/21


B*B*

BB*

45MeV

(10650)

(10604)

Z’b experiment

Zb experiment

BB* bound stateEB = -8.5 MeV

Ere =50.4MeVResonance state

• 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.

Remarks

3 results

THE BB BOUND AND RESONANCE STATES

IG(JPC) 1+(0--) 1+(1+-) 1-(1++) 1+(1--) 1-(2++) 1+(2--) 0+(1-+)

1059410596

10602

10655

10566

1061710621

10606

10649

10622

Zb(10607)

Zb(10652)(10650)B*B*

(10604)BB*

(10559)BB

results

27

12/06/21

Heavy quark hadrons

Heavy quark hadronsIG(JPC) 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, hbπ

Υπ, hbπ Υπ, ηbρ

hbπ, ηbρ, Υπ

hbπ, ηbρ, Υπ

Υπ, ηbπΥρ, Χbπ

Υρ, Χbπ

(10650)B*B*

(10604)BB*

(10559)BB

Decay channel

12/06/21

28

How to produce?

How to decay?

Υπ, ηbπ

NUMERICAL RESULTS

12/06/21


B*B*

BB*

45MeV

(10650)

(10604)

Z’b experiment

Zb experiment



• 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


Total mass shift is 2.4 MeV. Effects of channel coupling are repulsive.

Table: Various coupling constants g = gΥ , ghb and the mass shifts δM of Zb .

Zb

Υ, hb

π

Loop function

Imaginary part of loop function

Mass shiftΛ=600 MeV

NUMERICAL RESULTS

12/06/21


B*B*

BB*

45MeV

(10650)

(10604)

Z’b experiment

Zb experiment



• 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 Zb.

Remarks

results

Push upδM

Γ

Mth

Mth

ϒ(1S) π

5

10

15

2

6

• 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 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


Documents

EXOTIC MESONS WITH HIDDEN BOTTOM NEAR THRESHOLDS D2 S. OHKODA (RCNP) IN COLLABORATION WITH Y. YAMAGUCHI (RCNP) S. YASUI (KEK) K. SUDOH (NISHOGAKUSHA) A