1. Zb states (All Results from Belle)
Jin Li
New Hadron Workshop

2. Anomalies in (5S) decay
hb(2P)
hb(1P)
(2S)
(1S)
b(2S)
b(1S)
(4S)
(10860)
(11020)
JPC = 0 + - 1+ 1 --
9.50
9.75
10.00
10.25
10.50
10.75
11.00
Mass, GeV/c2
2M(B)
+–
260
430
290
190
330 6 2
partial (keV)
Belle PRL100,112001(2008)
100
[(5S) (1,2,3S) +–] >> [(4,3,2S) (1S) +–] _
 Rescattering of on-shell B(*)B(*) ?
Meng and Chao PRD77, (2008)
Chen et al., PRD84, (2011)
Belle PRL108,032001(2012)
(5S)  hb(1,2P) +– are not suppressed
expect suppression QCD/mb
spin-flip
Heavy Quark Symmetry Violation

3. Anomalies in (5S) decay
hb(2P)
hb(1P)
(2S)
(1S)
b(2S)
b(1S)
(4S)
(10860)
(11020)
JPC = 0 + - 1+ 1 --
9.50
9.75
10.00
10.25
10.50
10.75
11.00
Mass, GeV/c2
2M(B)
260
430
290 6 2
partial (keV)
hb production
 via intermediate charged states Zb – + + Zb
Belle PRL108,032001(2012)
(5S)  hb(1,2P) +– are not suppressed
expect suppression QCD/mb
spin-flip
Heavy Quark Symmetry Violation

4. The analysis of hb(nP)π+π−
Studying the decay (5S)  hb(nP) +-: led to observation of Zb
Look at the missing mass of a single pion π−, MM(π−) = M(hb π+).
Then fit MM(π +π− ) in bins of MM(π−).
Fit Function:
Significances with systematic:
1 resonance v.s. 0: 6.6 σ
2 resonances v.s. 0: 16 σ

5. Resonant structure of (5S)  (bb) +–_
(5S)  hb(1P)+-
(5S)  hb(2P)+-
Belle PRL108,122001(2012)
no non-res.
contribution
Two peaks in all modes
phsp
Minimal quark content _
 bbud 
phsp
flavor-exotic states
M[ hb(1P) π ]
M[ hb(2P) π ]
Dalitz plot analysis
(5S) (1S)+-
(5S) (2S)+-
(5S) (3S)+-
note different scales

6. Angular analyses for Zb+
arxiv:
Example :
(5S)  Zb+(10610) -  [(2S)+] -
i (i,e+), [plane(1,e+), plane(1, 2)]
cos1
cos2
, rad
non-resonant
combinatorial
Color coding: JP=
(0 is forbidden by parity conservation)
All angular distributions are consistent with JP=1+ , with other JP disfavored at 3  level.

7. Zb results Angular analysis  both states are JP = 1+’
Average over 5 channels
M1 =  2.0 MeV
1 = 18.4  2.4 MeV
MZb – (MB+MB*) =  2.1 MeV
M2 =  1.5 MeV
2 =  2.2 MeV
MZb’ – 2MB* =  1.7 MeV
Angular analysis  both states are JP = 1+
Decays  IG = 1+ (C= –)
Angular plot
Phase btw Zb and Zb amplitudes is 0o for (nS) and 180o for hb(mP) ’

8. Zb amplitudes
Properties of Zb amplitudes and phases are consistent with molecular structure.
 = 180o
 = 0o hb
(2S)
M(hb), GeV/c2
hb(1P) yield / 10MeV
Dip due to destructive interference with non-resonant amplitude in the whole Dalitz plane.
 Information on JP of Zb .

9. Molecule explanation of Zb
Wave func. at large distance – B(*)B*
 B*B*  =  
 B B*  =   + –
Bondar et al, PRD84,054010(2011)
Proximity to thresholds
favors molecule over tetraquark
Zb 
hb(mP)
S-wave
Zb’ 
not suppressed
Explains
Why hb is unsuppressed relative to 
Relative phase ~0 for  and ~1800 for hb
Production rates of Zb(10610) and Zb(10650) are similar Widths .

10. More states can be predicted
Sbb
Sqq 1
States IG(JP)
Zb,Zb’ (1+)
Wb0,Wb0’ 1−(0+)
Wb −(1+)
Wb −(2+)

11. Molecular bottomiums Wb0 Xb Wb1 Wb2 Zb U(?S)
Voloshin, PRD 84, (2011)
U(6S) h
U(5S) r w g r r p g w
B*B* w
Up hbphbr Ur
Ur hbp
Uh hbw
Uw hbh g Uw g
BB* Ur Uw BB Zb
Wb0 Xb
Wb1
Wb2 11
0-(1+)
1+(1+)
0+(0+)
1-(0+)
0+(1+)
1-(1+)
0+(2+)
1-(2+)
0-(1-)
IG(JP)

12. Other explanations
1. Threshold effect due to initial pion emission
Chen Liu PRD84,094003(2011)   Zb
Zb’
B(*)
B(*)
(5S)
(2S)
B(*) _
S-wave
M [(2S)π]
Danilkin Orlovsky Simonov PRD85,034012(2012)
2. Coupled-channel resonance multiple re-scatterings  pole Zb   
B(*)
B(*) 
B(*) 
Zb’ +
+ ...
(5S)
B(*) _
B(*) _
B(*) _
(2S)
(2S)
(2S)

13. Systematic study of B(*)B(*) bound states 
3. Deuteron-like molecule
B(*)
,,, exchange
(5S) 
B(*) _
(2S)
Ohkoda et al PRD86, (2012)

14. Study of Zb→B*B(*) _ For the ϒ(5S) →B*B(*) + channel: _
Fully reconstruct one B meson in five exclusive decay modes.
Look at recoil mass of B (for missing B) rM(B) and of the pion (for two B combination) rM(). _

15. Clear BB* and B*B* signals_ _
Select two peaks
Full reconstruction of one B in 5 modes
recoil mass _
BB*
M(B)
Mmiss(B) _
BB _
B*B*
BF[ (5S)  B(*)B(*) ] _
preliminary
PRD81,112003(2010)
Belle fb-1
significance
Belle 23.6 fb-1 _ BB
BB* + BB*
B*B*
<0.60 % at 90% C.L.
(4.25  0.44  0.69) % (2.12  0.29  0.36) %
(0  1.2) %
(7.3  2.3) %
(1.0  1.4) % _ _ _ _
9.3
5.7 _

16. Observation of ZbBB* and Zb’B*B*_
Zb’  BB* is suppressed w.r.t. B*B* despite larger PHSP _
M (BB*) Zb
preliminary 8
arXiv:
Zb’ ?
Challenging for tetraquark
Molecule  admixture of BB* in Zb’ is small _
phsp
Assuming Zb decays are saturated by these channels:
recoil mass of  _
M (B*B*)
Zb’
6.8
phsp
Crucial input for the models

17. Absolute branching fractions (3 body)
Br((10860)→ (1S) π+π- )= [4.45 ± 0.16(stat.) ± 0.35(syst.)] x 10-3
Br((10860)→ (2S) π+π- )= [7.97 ± 0.31(stat.) ± 0.96(syst.)] x 10-3
Br((10860)→ (3S) π+π- )= [2.88 ± 0.19(stat.) ± 0.36(syst.)] x 10-3
c.f. PRD 81, (2010)
f(BB* )=(7.3 ± 2.2 ±0.8) %
f(B*B* )=(1.0±1.4 ±0.4) %
Br((10860)→ BB* ) = [28.3 ± 2.9± 4.6] x 10-3
Br((10860)→ B*B*π) = [14.1 ± 1.9 ± 2.4] x 10-3
Fractions of sub-modes:

18. Study of e+e−  (5S)  (nS)00
preliminary
BF[(5S)(1S)00] = (2.250.110.20) 10-3
BF[(5S)(2S)00] = (3.790.240.49) 10-3
(2S)
in agreement with isospin relations
(1S)
(1S)π+π-
(nS)π+π− fit curve
(nS)π0π0 data points
(BG subtracted)
M miss (0 0)
Is there a neutral Zb partner?
(2S)π+π-

19. Fit (2S)00 structure Clear Zbs signals are seen in (2S)π0π0
arXiv:
Dalitz plot analysis
with Zbs
without
Clear Zbs signals are seen in (2S)π0π0
Significance of Zb(10610) is 5.3σ (4.9σ with systematics)
Zb(10650) is less significant (~2σ)
Fit gives M(Zb0(10610) ) =10609±8±6 MeV
cf: M(Zb+)= ±2.0 MeV
Belle PRELIMINARY

20. Search for partners of X(3872)
C-odd neutral partner search
Charged partner X+ search
J/ψ+0 channel
J/ψη channel
χc1γ channel
Preliminary
PRD 84, (2011)

21. Summary
Zb+ explanation as molecular states and in (nS)+ and hb(nP) + decays.
Observation of Zb+ decays to BB* and B*B* final states in the (5S) B*B(*) + decay study.
Zb(10610) decays dominantly to BB*, and Zb(10650) decays dominantly to B*B*. Supporting the molecule explanation.
Observation of the neutral partner Zb0(10610) in (5S)(nS)00 decay. Mass of Zb0(10610)= ± 8 ± 6 MeV .
Direct charmonium partner not found.
Other recent progress on bottomonium, such as hb(nP), ηb(nS), χb(3P) not covered.

22. BACKUP

23. The bottomonium family
(1S)
(2S)
(3S)
(4S)
2M(B)
BaBar, CLEO collected large ϒ(3S) data because its rich decay trees.

24. Results of +− missing mass study
hb(1P)
hb(2P)
(1S)
(2S)
(3S)
121.4 fb-1
2S1S
residuals
PRL
hb(1,2P) JPC=1+-
1st observations
3S1S

25. (2) (nS)ππ production shape
Belle,Phys.Rev.,D82,091106R(2010) Rb
Energy scan  mean of shapes of () and hadronic cross section Rb shapes differ by 2.0


26. CLEO-c’s e+e− → +− hc cross section
(hc +–)  (J/ +–)
Γ(Y(4260) → J/ψπ+π−)>508 90% C.L.  Large!! X. H. Mo et al., Phys. Lett. B 640 (2006) 182
An interesting comparison!
PRL107, (2011)
arXiv:
+−hc production is enhanced at Y(4260)
+−hb may be enhanced at Yb
Substructure of +− hc in Y(4260) has not been studied.
Original Motivation for hb search
Substructure of +− hb : Enough statistics in Belle’s ϒ(5S) data.

27. Observation of hb(1P,2P) b(1S) 
(5S)hb(nP) +–
 b(1S) 
Fit Mmiss(+-) spectra [ hb yield] in bins of Mmiss(+-)
arxiv:
MHF(1S)
(11020)
Belle : 57.9  2.3 MeV 3
11.00
(10860)
hb(1P)
PDG’12 : 69.3  2.8 MeV
b(1S)
10.75
+-
BaBar (3S)
(4S)
2M(B)
10.50
BaBar (2S)
b(3S)
(3S)
hb(2P)
b(2P)
hb(2P)
b(1S)
10.25
CLEO (3S)
b(2S)
(2S)
10.00
hb(1P)
b(1P)
pNRQCD
LQCD 
9.75
Kniehl et al, PRL92,242001(2004)
Mmiss (+-)
(n)
Meinel, PRD82,114502(2010)
(1S)
9.50
b(1S)
MHF(1S)
Belle result decreases tension with theory
JPC = 0 + - 1 --
1 + -
(0,1,2)++
First measurement  = MeV
–3.7
–2.0
as expected

28. First evidence for b(2S)
e+e-(5S)hb(2P) +–
 b(2S) 
MHF(2S) = MeV
–4.5
First measurement
arxiv: PRL
pNRQCD
LQCD
b(2S)
Belle
4.2 w/ syst
In agreement with theory
Mmiss (+-)
(2)
(2S) = 4  8 MeV, < 90% C.L.
expect 4MeV
Branching fractions
Expectations
BF[hb(1P)  b(1S) ] = 49.2 %
BF[hb(2P)  b(1S) ] = 22.3 %
BF[hb(2P)  b(2S) ] = 47.5 %
41%
13%
19%
–3.3
–3.3
Godfrey Rosner PRD66,014012(2002)
–7.7
c.f. BESIII BF[hc(1P)  c(1S) ] = 54.38.5 %
39%

29. Observation of Y(5S)gY(1D)p+p-
Y(1S)[m+m-]p+p-gg final state
Three peaks in MM(p+p-):
Y(2S) p+p-
Y(1D) p+p-
Y(2S)[Yp+p-]h[gg] reflection
After cb(1P)gYg selection
preliminary
statistical significance 9s
B[Y(5S)gY(2S)p+p-] = (7.51.10.8) 10-3 (cross check)
B[Y(5S)gY(1D)p+p-] B[Y(1D)gcb(1P)ggY(1S)gg] = (2.00.40.3) ×10-4
P.S. : An evidence of Y(1D) was seen in inclusive MM(p+p-) spectra 29

30. Angular Analysis JP = 1+, 1−, 2+, 2−
Zb velocity is very small ( β<0.02)  measure all pion momenta in the c.m. frame.
(5S)→Zb((nS),hb+ π1)π2
1= (π1,e+)
2= (π2,e+)
= (plane(π1,e+)),plane(π1, π2))
JP = 1+, 1−, 2+, 2−
Example: (5S)→ Zb(10610) π2 → (2S)π1 π2
Non-resonant

31. Angular Analysis (hb final state)
JP = 1+, 1−, 2+, 2−
Example: (5S)→ Zb(10610) π2 → hb(1P)π1 π2
Probabilities at which other JP hypotheses are disfavored with respect to 1+