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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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.