1. Quarkonium Spectroscopy
2nd International Workshop on Heavy Quarkonium
Steve Godfrey
Carleton University
Wealth of new results in past year!
Overview of Quark Potential Models
Tests
Puzzles and Problems
Future Opportunities
S. Godfrey, Carleton University

2. 1. Potential Models: Spin independent potentials
Relativistic corrections
Spin dependent effects
Coupled channel effects
Reviews:
Kwong and Rosner, Ann. Rev. Nucl. Part. Sci. 37, 325 (1987)
Buchmuller and Cooper, Adv.Ser.Direct.High Energy Phys. 1, 412 (1988)
Konigsmann, Phys. Rept. 139, 243 (1986).
Thomas as has recent review and maybe quigg?
S. Godfrey, Carleton University

3. Spin independent potentials
Meson quantum numbers characterized by given JPC:
For given spin and orbital angular momentum configurations
& radial excitations generates meson spectra
1-gluon exchange at short
distance + linear confining
potential
S. Godfrey, Carleton University

4. Quark potential models are strongly supported by emperical
From Buchmuller & Tye
PR D24, 132 (1981)
Quark potential models are strongly supported by emperical
agreement with quarkonium spectroscopy and with lattice QCD
S. Godfrey, Carleton University

5. Spin-dependent potentials:
Spin-dependent interactions are (v/c)2 corrections
Lorentz structure of confining potential:
scalar? vector? pseudoscalar? …
Mif =
1. Lorentz vector 1-gluon exchange + scalar confinement
2. If the confining interaction couples to the colour charge
density so interaction is
Gives rise to spin-dependent interactions
S. Godfrey, Carleton University

6. Systematic treatment starts with Wilson loop
Expanding in 1/mQ write spin-dependent Hamiltonian in terms
of static potential and correlation functions of colour
electric and magnetic fields
With some assumptions one obtains:
Which corresponds to short range vector and long range
scalar exchange
Observation of 1P1 states is important test
Eichten and Feinberg, PR D23, 2724 (1981)
Gromes, Yukon Advanced Study Inst.
S. Godfrey, Carleton University

7. Lorentz vector 1-gluon exchange + scalar confinementy hc
Spin-spin interactions:
Spin-orbit interactions: 1P
c2(13P2)
c1(13P1)
c0(13P0)
S. Godfrey, Carleton University

8. But numerous variations exist:
eg. Ebert Faustov & Galkin introduce Lorentz vector piece
of confining potential: Phys.Rev. D67, (2003); D62, (2000)
also include anomalous chromomagnetic moment of the quark
in VV:
Long range magnetic contributions vanish from choice of
Parameters (which is equivalent to scalar confinement)
Also included spin independent relativistic effects
S. Godfrey, Carleton University

9. Coupled Channel effects
Eichten et al, Phys Rev D17, 3090 (1978); D21, 203 (1980).
Expected to be most important for states near threshold
Induces splittings of states of different J with same L
Mechanism induces strong 23S1 -13D1 mixing in charmonium:
Shifts DM( 23S1)=mass –118 MeV vs DM(13S1)=-48 MeV
explains large 13D1 leptonic width
No work on this important subject since!
S. Godfrey, Carleton University

10. bottomonium
charmonium
S. Godfrey, Carleton University

11. Bc
S. Godfrey, Carleton University

12. 1P1 vs 3Pcog mass – distinguish models
2. Tests:
1P1 vs 3Pcog mass – distinguish models
In QM triplet-singlet splittings test
the Lorentz nature of the confining potential
Relativistic effects
important validation of
lattice QCD calculations
NRQCD calculations
Observation of 1P1 states is an important test of theory
S. Godfrey, Carleton University

13. Wide variation of theoretical predictions:QM QM QM
PQCD
lattice
wide variation in predictions indicates need for
experimental data
S. Godfrey, Carleton University

14. 3DJ masses – test spin dependent splittings
CESR/CLEO has just completed high statistics run at U(3S)
Expect very rich spectroscopy
S. Godfrey, Carleton University

15. There is still some question about the Lorentz
structure of the qq potential
vector 1-gluon exchange + scalar confinement
vector 1-gluon exchange + colour electric confinement
+ more complicated structures
because the D-waves are
larger they will feel the long
range spin-dependent potential
more than the P-waves
observation of 3DJ would
be important in understanding
the Lorentz structure of the
confining potential
see Eichten & Feinberg PRL 43, 1205 (1979)
Pantaleone Tye & Ng PR D33, 777 (1986);
Buchmuller Ng & Tye PR D24, 3003 (1981)
Gupta Radford & Repko PR D26, 3305 (1982);
Gromes, Z. Phys C22, 265 (1984)…..
S. Godfrey, Carleton University

16. Use angular distributions in E1 transitions to probe
internal structure
eg mixing in charmonium
SG, G. Karl, P.O’Donnell, Z. Phys. C31, 77 (1986)
For q and q’ the angles between the photon and either lepton in the y or y’ rest frame the angular distributions are of the form:
Where q is the mixing angle
x=+1 for
x=-1 for
One could make a quantitative determination of the Mixing angle with new, more precise, measurements.
S. Godfrey, Carleton University

17. 3. Puzzles and Challenges in Quarkonium Spectroscopy
Puzzle 1. hc’ mass
Is there a problem?
1. Quark models predict M(y’)- M(hc’)~50-90 MeV
(GI model predicts 53 MeV Þ M(hc’)=3633 MeV)
2. Coupled channel mechanism
shifts DM( 23S1)=mass –118 MeV vs DM(13S1)=-48 MeV
Þ need more precise measurements
need to include coupled channel effects
3637.7±4.4 MeV
From Tomasz Skwarnicki
Lepton-Photon’03
S. Godfrey, Carleton University

18. Puzzle 2. New state observed by Belle: X(3871)
hep-ex/
seeTomasz Skwarnicki Lepton-Photon’03
M= ± 0.6 ± 0.5 MeV
1. The mass of the state is right at the D0D*0 threshold!
This suggests a loosely bound D0D*0 molecule, right below the
dissociation energy
“Molecular Charmonium” discussed in literature since 1975
Belle
S. Godfrey, Carleton University

19. Should easily see y(13D2) → gg J/ y BUT:
2. 13D2 state?
Because D-states have negative parity, spin-2 states cannot decay to DD
They are narrow as long as below the DD* threshold
Predict:
Should easily see y(13D2) → gg J/ y
BUT:
Most models predict y(13D2) mass to be ~70 MeV lower than
the measured X(3872) mass.
At the same time they reproduce the U(13D2) mass very well.
No models appear to accommodate y(3770) and X(3872) in the
same 13DJ triplet!
Can coupled channel effects and y(13D1)- y(23S1) mixing change this?
3. A charmonium hybrid?
seeTomasz Skwarnicki Lepton-Photon’03
Belle
hep-ex/
S. Godfrey, Carleton University

20. U(nS)®h(n’S) + g Puzzle 3: M1 transitions: production of hb(nS) states
S.G + J. Rosner, Phys Rev D64, (2001)
Proceeds via magnetic dipole (M1)
transitions:
U(nS)®h(n’S) + g
Hindered transitions have large phase space
Relativistic corrections resulting in differences in
3S1 and 1S0 wavefunctions due to hyperfine interaction
S. Godfrey, Carleton University

21. But no signal found! Is there a problem?
Ebert Faustov Galkin
Is there a problem?
Most likely due to poorly understood relativistic effects:
S. Godfrey, Carleton University

22. 4. Future Opportunities 1. More charmonium results at Belle and BaBar:
Find 1D2 and hc in B-decay
2. Charmonium results from BES-III and CLEO-c
3. PANDA at GSI: charmonium in pp annihilation
4. More Upsilon runs at CESR?
5. Upsilon runs at SLAC and KEK?
6. Quarkonium at LHC?
S. Godfrey, Carleton University