1. New Results on Charmonium and Charmonium(-like) States from Belle
Jens Sören Lange Justus-Liebig-Universität Gießen
hadron2011 XIV International Conference on Hadron Spectroscopy
06/16/2011 Künstlerhaus, München

2. Are the Charmonium(-like) States („XYZ“) Charmonium States, or not
Are the Charmonium(-like) States („XYZ“) Charmonium States, or not? (see plenary talks by De Fazio, Eidelman, Gao, Springer, Patriagni, and several parallel talks)
Here: charmonium mass region only

3. Is the Charmonium Potential Model appropriate for explaining XYZ states?
S > 1 at large radius non-perturbative?
string breaking regime still bound state?
confinement (scalar ?)
QCD vacuum is 3P0 („Lamb shift“ of c0 ?)
2-gluon exchange?
3 gluon vertex in hadronic decays?
molecular potential?
[cc]8 + gluon hybrid? (color octet)
asymptotic free? (why annihilation branching so high?)
contact term (spin-spin)

4. Outline c and c´ mass width X(3872) quantum numbers
c2 production in B decays

5. c and c´

6. c Ground state of Charmonium JPC=0−+, 11S0
Observed e.g. in J/ and ´ radiative decays, but cross section varies according to Ea, a=3…7 → modifies lineshape → width determination non-trivial (new Bes-III result shown at this conference)
In   → c and B decays: Breit-Wigner line shape is appropriate approximation
Belle, 395/fb
Eur. Phys. J. C53(2008)1
BaBar, 469/fb Phys. Rev. D81(2010)052010 c
c0
c2
J/ c

7. PDG2010 Width Mass  ' 15 MeV in J/ and ´radiative decays
LEES et al., BaBar, Phys. Rev. D81(2010)052010
PDG2010
Width
Mass
 ' 15 MeV in J/ and ´radiative decays
 ' 30 MeV in B decays and 

8. New mass and width measurement for c in B decays
arXiv: submitted to PLB
New mass and width measurement for c in B decays
B+  K+ c, c  KS K± ¨
non-resonant charmless B decays
Agreement with BaBar result in   c
2-dim fit of angle(K+ KS) vs. M(KSK  )
M = ± 1.5 − MeV
 = 35.1 ± 3.1 − MeV
Agreement with Bes-III result in ´  c shown at this conference

9. 1st radial excited state JPC=0−+, 21S0

10. New mass and width measurement of c(2S) in B decays
arXiv: submitted to PLB
New mass and width measurement of c(2S) in B decays
B+  K+ c(2S) , c(2S) KS K± ¨
Interference of signal and non-resonant background important
fit with interference  = 6.6− (stat.+model)− (syst.) MeV
fit w/o interference  = 41.1 ± 12.0(stat.)− (syst.) MeV

11. Error on width improved by factor ' 2
c(2S)
Error on width improved by factor ' 2
New Belle measurement
Mass − (stat.+model)− (syst.) MeV
Width 6.6− (stat.+model)− (syst.) MeV

12. Hadronic width of c(2S) must be smaller than c(1S)
Potential model for c(2S) width prediction not reliable, because close toDD threshold
 would be nice test for Lattice QCD
3 gluon decay not possible (parity)

13. full data set 711/fb on Y(4S)
New results on X(3872)
full data set 711/fb on Y(4S)
re-processed data (improved low momentum tracking, reconstruction efficiency in some channels ¸20% increased)

14. Reference Analysis: BK´, ´  J/ +−
MBC /GeV M(J/ + − )/GeV E/GeV B+ B0
Preliminary
Preliminary
3-dim fit in beam constrained mass, J/ + − mass and E
at first, fit reference signal ´  fix core Gaussian and tail Gaussian for resolution parameters

15. Analysis of X(3872)  J/ +−
Preliminary B+
151§15 events
MBC /GeV M(J/ + − )/GeV E/GeV B0
21.0§5.7 events
MBC /GeV M(J/ + − )/GeV E/GeV
3-dim fit
with fixed resolution parameters from ´
Mass MC/data shift +0.92§0.06 MeV, measured and fixed from ´ mass

16. X(3872) mass in p+p-J/y channel only
Belle result contains MC/data shift 0.92 § MeV, fixed from reference channel ´
<MX>prev_WA= ± 0.19 MeV
Experiment
X mass
CDF 2
± 0.16 ± 0.19 MeV
BaBar (B+)
± 0.6 ± 0.1 MeV
BaBar (B0)
± 1.5 ± 0.4 MeV D0
± 3.1 ± 3.0 MeV
Belle (This result)
± 0.27 ± 0.19 MeV
World Average
± MeV
LHCb (new)
± 0.46 ± 0.10 MeV
World Average again
± MeV
M(D0)+M(D*0) PDG2010
± MeV
Here former Belle measurement ± 0.6 ± 0.5 MeV not considered anymore (superseded by new measurement)
“Binding Energy” m(X)−m(D*0)−m(D0) becomes smaller:
Old: m = −0.32 ± 0.35 MeV
New: m = −0.17 ± 0.36 MeV
Preliminary
New w/ LHCb: m = −0.12 ± 0.35 MeV
Reminder: m(deuteron) = −2.2 MeV

17. New measurement of width of X(3872)
Previous best limit X(3872) < 2.3 MeV (90% CL)
3-dim fits are sensitive to natural widths narrower than resolution <>'4 MeV because of constraints (mBC, E)
Method validated with ´width ´=0.52§0.11 MeV (PDG 0.304§0.009 MeV)  bias 0.23 § 0.11 MeV
procedure for upper limit: width in 3-dim fit fixed nsignal and npeaking BG floating  calculate likelihood
X(3872) < 0.95 MeV + bias MC
 (output) / MeV
 (input) / MeV
90%
1.2 MeV

18. X(3872) possible Charmonium Assignment
1++ c1´ 3P1 predicted mass 3953 MeV n=2 favoured by angular analysis CDF-II, PRL98(2007) Belle, hep-ex/
2−+ c2 1D2 predicted mass 3837 MeV n=1 (would be a L=2 meson) favoured by X(3872)  J/  analysis BaBar, Phys. Rev. D82(2010)011101
1++
 / fm−3/2
2−+
r / fm
Mass predictions by Barnes, Godfrey, Swanson Phys. Rev. D72(2005)054026

19. Angular Variables
Assume X(3872)  J/  in kinematic limit: both particles at rest in X(3872) rest frame mX ' m+mJ/  higher partial waves can be neglected
1++ 1 amplitude L=0, S=1
2−+ 2 amplitudes L=1, S=1 or S=2
J. Rosner
PRD 70(2004)092023
only normalization floating in fit
normalization and  (complex) floating in the fit

20. Angular Variables X
X(3872) rest frame

21. 1++ Hypothesis vs. 2−+ Hypothesis
=0.69 e23° i, only value which gives >10% CL in all three plots
c2/dof =1.76/4
CL=0.78
c2/dof =4.60/4 CL=0.33
| cos  |
| cos  |
c2/dof =0.56/4
CL=0.97
c2/dof =5.24/4 CL=0.26
| cos lep |
| cos lep |
c2/dof =3.82/4 CL=0.51
c2/dof =4.72/4 CL=0.32
| cos X |
| cos X | 21

22. c2 in B Decays

23. B§K§ c1,2 with c1,2 → J/  First Evidence for B§! c2 K§ c2 c1
Control signal for X(3872)  J/ , Belle, arXiv: [hep-ex], subm. PRL
B§K§ c1,2 with c1,2 → J/ 
First Evidence for B§! c2 K§ B+
c2
c1
B+ → K+ c −10.2 events 3.6 (stat. and syst.)
B0 → K0 c −3.9 events 0.7 (stat. and syst.) B0
c2
c1
 L=1

24. Same Analysis, but reference signal c1,2 → J/
First Evidence for B§! c2 K§ B+
c2
c1
Production of J=2, Parity=+
Charmonium in B Meson Decays 0− ! 0− 2+
B+ → K+ c −10.2 events 3.6 (stat. and syst.)
B0 → K0 c −3.9 events 0.7 (stat. and syst.) B0
c2
c1

25. Radiative Transition from c1,2 to J/
Photon energies of transitions comparable (E ' 414 MeV ' 459 MeV) but dynamics different
Lattice QCD Dudek, Edwards, Thomas Phys. Rev. D79(2009) ( c1 ! J/  ) = 270(70) keV ( c2 ! J/  ) = 380(50) keV
Transistion Formfactors E1 E1 E3 M2 M2

26. B§K§ c2 Jq=½ Jq=½ Jq=½ JW=1 but J=2 difficult to be generated
Vector or axial-vector
J=0 or J=1 preferred
Parity + or parity − allowed
JP=1+ possible (e.g. B+! K+c1 BR 4.6§0.4 x 10−4)
but J=2 difficult to be generated
forbidden in naïve factorization
additional soft gluon required Bauer, Stech, Wirbel Z. Phys. C34(1987)103

27. Summary
New measurement of c´width in B decays (undistorted lineshape)
New measurements of X(3872), full data set, re-processed data
New world average mass of X(3872) moves closer to DD* threshold m=−0.12±0.35 MeV (but still negative)
X(3872) never seen in radiative decays (e.g. (4040))  mass measurement by Bes-III could provide important cross-check with independant method
New upper limit on X(3872) < 1.2 MeV factor 2 narrower than before
further improvement  <1 MeV feasible but only way to reach  ·100 keV  cooled antiproton beam
PANDA experiment >2017
More Belle Results:
XYZ States, Simon Eidelman (plenary, Thursday morning)
Bottomonium, Alex Kuzmin (parallel, Tuesday afternoon) Belle-II, Boris Shwartz (plenary, Friday afternoon)

28. Backup

29. Charmonium Excited States n · 3, L · 4
Barnes, Godfrey, Swanson, Phys. Rev. D72(2005)054026
n2S+1 L J
Terra Nova
Mass / GeV
JPC

30. B Factories

31. ~952 /fb On-resonance samples: Y(4S): 711 /fb Y(5S): 121 /fb Y(3S): 3
~952 /fb On-resonance samples: Y(4S): 711 /fb Y(5S): 121 /fb Y(3S): 3.0 /fb Y(2S): 24 /fb Y(1S): 5.7 /fb Off-resonance: 87 /fb
~553 /fb
On-resonance samples:
Y(4S): 433 /fb
Y(3S): 30 /fb
Y(2S): 14 /fb
Off-resonance: 54 /fb

32. Production of Charmonium
B Decays
Double Charmonium Production
in 2-body B decays,
JPC=0− +, 1− −, 1++ in factorization limit
C=+1
Initial State Radiation
JPC=0++,0−+, 2++
JPC=1− −
 

33. Decays of Charmonium States1-
Annihilation EM
e.g. J/! + - 0
OZI suppressed
 J=0,1,2
Do(*)
Strong
~1/S2
Do(*)
Strong
Strong
spectator isospin transition ? (if ()=)
~1/S2
e.g.  ´! J/ + - EM
radiative
 L=1
e.g. /! cJ 

37. Braaten, Kusunoki, Phys. Rev. D71(2005)074005

38. B+ vs. B0 decays: mixing angle
Diquark – anti-diquark model Maiani, Piccinini, Polosa Phys. Rev. D71(2005)014028
Mixing occurs by gluon annihilation uu  gluon  dd
Xu (Xd) populates B+ (B0) decay

39. Helicity amplitudes for X  J/  D are Wigner functions

40. B+ and B0 decays are quite different.
Swanson, Phys. Rept. 429(2006)243
B+ = Bu B0 = Bd
B+ ! K+ B0 ! K0 (charge sign changes by W§, and changes back,
! same charge for B and K)
color suppressed (color is locked by spectator quark)
B0 ! K+
B0 ! K0
B+ ! K+
B+ ! K0
any combination possible
color enhanced

41. X(3872) in B+ vs. B0 decays BaBar 0.41±0.24±0.05
PRELIMINARY
X(3872) in B+ vs. B0 decays
B(B+K+ X(3872)) x B(X(3872)  J/ + −)) = (8.61±0.82±0.78) x 10−6
B(B0K0 X(3872)) x B(X(3872)  J/ + −)) = (4.3±1.2±0.4) x 10−6
BaBar 0.41±0.24±0.05
for molecule expected R(X) ' 1
Braaten, Kusunoki, Phys. Rev. D71(2005)074005
BaBar (2.7 ± 1.6 ±0.4) MeV
Small mass difference disfavours Diquark-Antidiquark Model
Maiani, Piccinini, Polosa Phys. Rev. D71(2005)014028

42. c fit function

43. c fit function

44. X(3872) mass measurement syst. errors
Width is upper limit  no syst. error to be given.