New Results onCharmonium and Charmonium(-like) Statesfrom Belle
Jens Sören LangeJustus-Liebig-Universität Gießen
hadron2011XIV International Conference on Hadron Spectroscopy06/16/2011Künstlerhaus, München
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
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3Sören Lange | Charmonium(-like) States at Belle
Is the Charmonium Potential Modelappropriate for explaining XYZ states?
confinement(scalar ?)
QCD vacuum is 3P0
(„Lamb shift“ of c0 ?)
S > 1 at large radiusnon-perturbative?
asymptotic free?(why annihilation branching so high?)contact term (spin-spin)
string breaking regimestill bound state?
2-gluon exchange?3 gluon vertex in hadronic decays?molecular potential?[cc]8 + gluon hybrid?(color octet)
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4Sören Lange | Charmonium(-like) States at Belle
Outline
c and c´ mass width
X(3872) mass width quantum numbers
c2 production in B decays
c and c´
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6Sören Lange | Charmonium(-like) States at Belle
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 shownat this conference)
In → c and B decays: Breit-Wigner line shape is appropriate approximation
c
J/
BaBar, 469/fbPhys. Rev. D81(2010)052010
c
c0c2
Belle, 395/fbEur. Phys. J. C53(2008)1
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7Sören Lange | Charmonium(-like) States at Belle
PDG2010
' 15 MeV in J/ and ´radiative decays' 30 MeV in B decays and
Mass Width
LEES et al., BaBar, Phys. Rev. D81(2010)052010
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8Sören Lange | Charmonium(-like) States at Belle
New mass and width measurement for c in B decays
2-dim fit of angle(K+ KS) vs. M(KSK )
M = 2985.4 ± 1.5 −2.0+0.2 MeV
= 35.1 ± 3.1 −1.6+1.0 MeV
Agreement with BaBar resultin c
B+ K+ c, c KS K± ¨
arXiv: 1105.0978 submitted to PLB
Agreement with Bes-III resultin ´ cshown at this conference
non-resonantcharmlessB decays
c(2S)1st radial excited stateJPC=0−+, 21S0
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10Sören Lange | Charmonium(-like) States at Belle
New mass and width measurement of c(2S) in B decays
Interference of signal and non-resonant background importantfit with interference = 6.6−5.1
+8.4(stat.+model)−0.9+2.6(syst.) MeV
fit w/o interference = 41.1 ± 12.0(stat.)−10.9+6.4(syst.) MeV
B+ K+ c(2S) , c(2S) KS K± ¨
arXiv: 1105.0978 submitted to PLB
´
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11Sören Lange | Charmonium(-like) States at Belle
c(2S)
New Belle measurementMass 3636.1−4.1
+3.9(stat.+model)−2.0+0.5(syst.) MeV
Width 6.6−5.1+8.4(stat.+model)−0.9
+2.6(syst.) MeV
Error on widthimproved by factor ' 2
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12Sören Lange | Charmonium(-like) States at Belle
Hadronic width of c(2S) must be smaller than c(1S)
3 gluon decay not possible(parity)
c(1S)
c(2S)Potential model for c(2S)width prediction not reliable, because close toDD threshold would be nice test for Lattice QCD
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)
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14Sören Lange | Charmonium(-like) States at Belle
Reference Analysis: BK´, ´ J/ +−
3-dim fit in beam constrained mass, J/ + − mass and Eat first, fit reference signal ´ fix core Gaussian and tail Gaussian for resolution parameters
MBC /GeV M(J/ + − )/GeV E/GeV
MBC /GeV M(J/ + − )/GeV E/GeV
B+
B0
Preliminary
Preliminary
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15Sören Lange | Charmonium(-like) States at Belle
Analysis of X(3872) J/ +−
MBC /GeV M(J/ + − )/GeV E/GeV
MBC /GeV M(J/ + − )/GeV E/GeV
B+
B0
3-dim fitwith fixed resolution parameters from ´Mass MC/data shift +0.92§0.06 MeV, measured and fixed from ´ mass
151§15 events
21.0§5.7 events
Preliminary
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16Sören Lange | Charmonium(-like) States at Belle
Experiment X mass
CDF 2 3871.61 ± 0.16 ± 0.19 MeV
BaBar (B+) 3871.4 ± 0.6 ± 0.1 MeV
BaBar (B0) 3868.7 ± 1.5 ± 0.4 MeV
D0 3871.8 ± 3.1 ± 3.0 MeV
Belle (This result) 3871.84 ± 0.27 ± 0.19 MeV
World Average 3871.62 ± 0.19 MeV
LHCb (new) 3871.96 ± 0.46 ± 0.10 MeV
World Average again
3871.67 ± 0.17 MeV
M(D0)+M(D*0) PDG2010
3871.79 ± 0.30 MeV
X(3872) mass in J/ channel only
“Binding Energy”m(X)−m(D*0)−m(D0) becomes smaller:
Old: m = −0.32 ± 0.35 MeVNew: m = −0.17 ± 0.36 MeV
Reminder: m(deuteron) = −2.2 MeV
New w/ LHCb: m = −0.12 ± 0.35 MeV
<MX>prev_WA= 3871.46 ± 0.19 MeV
Here former Belle measurement3872.0 ± 0.6 ± 0.5 MeVnot considered anymore(superseded by new measurement)
Belle result contains MC/data shift 0.92 § 0.006 MeV, fixed from reference channel ´
Preliminary
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17Sören Lange | Charmonium(-like) States at Belle
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 MeVbecause 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 fixednsignal and npeaking BG floating calculate likelihood
X(3872) < 0.95 MeV + bias
(input) / MeV
(o
utpu
t) / M
eV MC
90%
1.2 MeV
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18Sören Lange | Charmonium(-like) States at Belle
X(3872) possible Charmonium Assignment 1++
c1´ 3P1 predicted mass 3953 MeVn=2favoured by angular analysisCDF-II, PRL98(2007)132002 Belle, hep-ex/0505037
2−+c2 1D2predicted mass 3837 MeVn=1(would be a L=2 meson)favoured by X(3872) J/ analysis BaBar, Phys. Rev. D82(2010)011101
Mass predictions by Barnes, Godfrey, SwansonPhys. Rev. D72(2005)054026
2−+
1++
r / fm
/
fm−
3/2
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19Sören Lange | Charmonium(-like) States at Belle
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 amplitudesL=1, S=1 or S=2
22 sinsincoscos
)1(
ddd
J. Rosner PRD 70(2004)092023
B11
B 11 B12
1
1 B12B11
only normalizationfloating in fit
normalization and (complex)floating in the fit
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20Sören Lange | Charmonium(-like) States at Belle
XX
XX
X
dd
dd
flatdd
2
2
sincos
:0
cos31cos
:1
2
cos:1
Angular Variables
X
X(3872) rest frame
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21Sören Lange | Charmonium(-like) States at Belle
1++ Hypothesis vs. 2−+ Hypothesis
2/dof =1.76/4 CL=0.78
2/dof =0.56/4 CL=0.97
2/dof =3.82/4 CL=0.51
2/dof =4.60/4 CL=0.33
2/dof =5.24/4 CL=0.26
2/dof =4.72/4 CL=0.32
=0.69 e23° i, only value which gives >10% CL in all three plots
| cos |
| cos lep | | cos lep |
| cos |
| cos X | | cos X |
c2 in B Decays
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23Sören Lange | Charmonium(-like) States at Belle
B§K§ c1,2 with c1,2→ J/
First Evidence for B§! c2 K§B+ → K+ c232.8+10.9
−10.2 events3.6 (stat. and syst.)
B0 → K0 c22.8+4.7
−3.9 events0.7 (stat. and syst.)
B+
c1
c1c2
c2
B0
L=1
Control signal for X(3872) J/ , Belle, arXiv:1105.0177 [hep-ex], subm. PRL
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24Sören Lange | Charmonium(-like) States at Belle
Same Analysis, but reference signal c1,2→ J/
First Evidence for B§! c2 K§
B+ → K+ c232.8+10.9
−10.2 events3.6 (stat. and syst.)
B0 → K0 c22.8+4.7
−3.9 events0.7 (stat. and syst.)
B+
c1
c1c2
c2
B0
Production of J=
2, Parity=+
Charmonium in B Meson Decays
0− ! 0− 2+
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25Sören Lange | Charmonium(-like) States at Belle
Radiative Transition from c1,2 to J/
Photon energies of transitionscomparable (E ' 414 MeV ' 459 MeV)but dynamics different
Lattice QCDDudek, Edwards, ThomasPhys. Rev. D79(2009)094504( c1 ! J/ ) = 270(70) keV ( c2 ! J/ ) = 380(50) keV
Transistion Formfactors
E1
M2
E1
M2
E3
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26Sören Lange | Charmonium(-like) States at Belle
B§K§ c2
J=0 or J=1 preferredParity + 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
Jq=½ Jq=½
Vector oraxial-vector
Jq=½ JW=1
forbidden in naïve factorization additional soft gluon required
Bauer, Stech, WirbelZ. Phys. C34(1987)103
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27Sören Lange | Charmonium(-like) States at Belle
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* thresholdm=−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 MeVfactor 2 narrower than before
further improvement <1 MeV feasiblebut 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)
Backup
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29Sören Lange | Charmonium(-like) States at Belle
Charmonium Excited States n · 3, L · 4
Terra Novan2S+1 L J
JPC
Barnes, Godfrey, Swanson, Phys. Rev. D72(2005)054026
Mass / GeV
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30Sören Lange | Charmonium(-like) States at Belle
B Factories
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31Sören Lange | Charmonium(-like) States at Belle
~952 /fbOn-resonance samples:Y(4S): 711 /fbY(5S): 121 /fbY(3S): 3.0 /fbY(2S): 24 /fbY(1S): 5.7 /fbOff-resonance: 87 /fb
~553 /fbOn-resonance samples:Y(4S): 433 /fbY(3S): 30 /fbY(2S): 14 /fbOff-resonance: 54 /fb
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32Sören Lange | Charmonium(-like) States at Belle
Production of Charmonium
in 2-body B decays,JPC=0− +, 1− −, 1++ in factorization limit
B Decays Double CharmoniumProduction
Initial State Radiation
C=+1
JPC=0++,0−+, 2++JPC=1− −
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33Sören Lange | Charmonium(-like) States at Belle
Decays of Charmonium States
EM
Annihilation1-
J=0,1,2
Strong
Do(*)
Do(*)
e.g. J/! + - 0
OZI suppressed
Strong~1/S
2
EMradiativeL=1
e.g. /! cJ
Strongspectatorisospin transition ?(if ()=)~1/S
2
e.g. ´! J/ + -
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34Sören Lange | Charmonium(-like) States at Belle
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35Sören Lange | Charmonium(-like) States at Belle
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36Sören Lange | Charmonium(-like) States at Belle
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37Sören Lange | Charmonium(-like) States at Belle
Braaten, Kusunoki, Phys. Rev. D71(2005)074005
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38Sören Lange | Charmonium(-like) States at Belle
B+ vs. B0 decays: mixing angle
Diquark – anti-diquark modelMaiani, Piccinini, PolosaPhys. Rev. D71(2005)014028
Mixing occurs by gluon annihilationuu gluon dd
Xu (Xd) populates B+ (B0) decay
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39Sören Lange | Charmonium(-like) States at Belle
Helicity amplitudes for X J/ D are Wigner functions
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40Sören Lange | Charmonium(-like) States at Belle
B+ and B0 decays are quite different.
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
B+ = BuB0 = Bd
Swanson, Phys. Rept. 429(2006)243
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41Sören Lange | Charmonium(-like) States at Belle
PRELIMINARY X(3872) in B+ vs. B0 decays
BaBar 0.41±0.24±0.05 04.014.050.0
))3872(())3872(()(
00
XKBBXKBBXR
MeVfromMfromMM XX 13.097.069.0)B ()B ( 0
BaBar (2.7 ± 1.6 ±0.4) MeV
B(B+K+ X(3872)) x B(X(3872) J/ + −)) = (8.61±0.82±0.78) x 10−6
B(B0K0 X(3872)) x B(X(3872) J/ + −)) = (4.3±1.2±0.4) x 10−6
Small mass difference disfavours Diquark-Antidiquark Model
Maiani, Piccinini, PolosaPhys. Rev. D71(2005)014028
for molecule expected R(X) ' 1Braaten, Kusunoki, Phys. Rev. D71(2005)074005
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42Sören Lange | Charmonium(-like) States at Belle
c fit function
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43Sören Lange | Charmonium(-like) States at Belle
c fit function
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44Sören Lange | Charmonium(-like) States at Belle
X(3872) mass measurement syst. errors
Width is upper limit no syst. error to be given.