1. D. Bettoni - The Panda experiment 1 Charmonium Spectroscopy The charmonium system has often been called the positronium of QCD. Non relativistic potential models (with relativistic corrections) and PQCD make it possible to calculate masses, widths and branching ratios to be compared with experiment. In  pp annihilations states with all quantum numbers can be formed directly: the resonace parameters are determined from the beam parameters, and do not depend on energy and momentum resolution of the detector.

2. D. Bettoni - The Panda experiment 2 The  c (1 1 S 0 ) Despite the recent measurements by E835 not much is known about the ground state of charmonium: the error on the mass is still bigger than 1 Mev recent measurements give larger widths than previously expected A large value of the  c width is difficult to explain in terms of simple quark models. Also unusually large branching ratios into channels involving multiple kaons and pions have been reported. A precision measurements of the  c mass, width and branching ratios is of the utmost importance, and it can only be done in by direct formation in  pp.

3. D. Bettoni - The Panda experiment 3 The  c (1 1 S 0 ) M(  c ) = 2979.9  1.0 MeV  (  c ) = 25.5  3.3 MeV T. Skwarnicki – Lepton Photon 2003

4. D. Bettoni - The Panda experiment 4 Two photon channel  c   (weak branching ratio BR(  c  )=3  10 -4 ). Hadronic decay channels, with branching ratios which are larger by several orders of magnitude. –  c  +  - K + K - –  c  2(K + K - ) –  c  2(  +  - ) –  c  K  K  –  c   –...  c  p  p The  c (1 1 S 0 )

5. D. Bettoni - The Panda experiment 5 The mass difference  between the  c and the  can be related to the mass difference  between the  c and the J/  : Various theoretical predictions of the  c mass have been reported: –M(  c ) = 3.57 GeV/c 2 [Bhaduri, Cohler, Nogami, Nuovo Cimento A, 65(1981)376]. –M(  c ) = 3.62 GeV/c 2 [Godfrey and Isgur, Phys. Rev. D 32(1985)189]. –M(  c ) = 3.67 GeV/c 2 [Resag and Münz, Nucl. Phys. A 590(1995)735]. Total width ranging from a few MeV to a few tens of MeV:  (  c )  5  25 MeV Decay channels similar to  c. Expected properties of the  c (2 1 S 0 )

6. D. Bettoni - The Panda experiment 6 The  c (2 1 S 0 ) Crystal Ball Candidate The first  ´ c candidate was observed by the Crystal Ball experiment: By measuring the recoil  they found:

7. D. Bettoni - The Panda experiment 7 Both E760 and E835 searched for the  c in the energy region: using the process: but no evidence of a signal was found The  c (2 1 S 0 ) E760/E835 search Crystal Ball  2 

8. D. Bettoni - The Panda experiment 8 The  c has been looked for by the LEP experiments via the process: L3 sets a limit of 2 KeV (95 %C.L.) for the partial width  (  c  ). DELPHI data (shown on the right) yield:  c (2 1 S 0 ) search in  collisions at LEP

9. D. Bettoni - The Panda experiment 9 The Belle collaboration has recently presented a 6  signal for B  KK S K  which they interpret as evidence for  c production and decay via the process: with: in disagreement with the Crystal Ball result, but reasonably consistent with potential model expectations. (DPF 2002). The  c (2 1 S 0 ) discovery by BELLE

10. D. Bettoni - The Panda experiment 10    c (2 1 S 0 ) BaBar 88 fb -1 Preliminary Log-scale M(  c ) = 3637.7  4.4 MeV  (  c ) = 19  10 MeV T. Skwarnicki – Lepton Photon 2003

11. D. Bettoni - The Panda experiment 11 In PANDA we will be able to identify the  c in the following channels: two photon decay channel  c  .This will require a substantial increase in statistics and reduction in background with respect to E760/E835: lower energy threshold, better angular and energy resolution, increased geometric acceptance. The real step forward will be to detect the  c through its hadronic decays, such as K + K - and .  c  p  p The  c (2 1 S 0 )

12. D. Bettoni - The Panda experiment 12 The h c ( 1 P 1 ) Precise measurements of the parameters of the h c are of extreme importance in resolving a number of open questions: Spin-dependent component of the q  q confinement potential. A comparison of the h c mass with the masses of the triplet P states measures the deviation of the vector part of the q  q interaction from pure one-gluon exchange. Total width and partial width to  c +  will provide an estimate of the partial width to gluons. Branching ratios for hadronic decays to lower c  c states.

13. D. Bettoni - The Panda experiment 13 Quantum numbers J PC =1 +-. The mass is predicted to be within a few MeV of the center of gravity of the  c ( 3 P 0,1,2 ) states The width is expected to be small  (h c )  1 MeV. The dominant decay mode is expected to be  c + , which should account for  50 % of the total width. It can also decay to J/  : J/  +  0 violates isospin J/  +  +  - suppressed by phase space and angular momentum barrier Expected properties of the h c ( 1 P 1 )

14. D. Bettoni - The Panda experiment 14 A signal in the h c region was seen by E760 in the process: Due to the limited statistics E760 was only able to determine the mass of this structure and to put an upper limit on the width: The h c ( 1 P 1 ) E760 observation

15. D. Bettoni - The Panda experiment 15 E835 has performed a search for the h c, in the attempt to confirm the E760 results and possibly add new decay channels. Data analysis is still under way in various decay channels h c   c +   (  )+  h c   c +   (  )+   (4K)+  h c  J/  +  0  (e + e - )+(  ) The h c ( 1 P 1 ) E835 search

16. D. Bettoni - The Panda experiment 16 It is extremely important to identify this resonance and study its properties. To do so we need: High statistics: the signal will be very tiny Excellent beam resolution: the resonance is very narrow The ability to detect its hadronic decay modes. The search and study of the h c is a central part of the experimental program of the PANDA experiment at GSI. The h c ( 1 P 1 )

17. D. Bettoni - The Panda experiment 17 Charmonium States above the D  D threshold The energy region above the D  D threshold at 3.73 GeV is very poorly known. Yet this region is rich in new physics. The structures and the higher vector states (  (3S),  (4S),  (5S)...) observed by the early e+e- experiments have not all been confirmed by the latest, much more accurate measurements by BES. It is extremely important to confirm the existence of these states, which would be rich in D  D decays. This is the region where the first radial excitations of the singlet and triplet P states are expected to exist. It is in this region that the narrow D-states occur.

18. D. Bettoni - The Panda experiment 18 The D wave states The charmonium “D states” are above the open charm threshold (3730 MeV ) but the widths of the J= 2 states and are expected to be small: forbidden by parity conservation forbidden by energy conservation Only the, considered to be largely state, has been clearly observed

19. D. Bettoni - The Panda experiment 19 The D wave states The only evidence of another D state has been observed at Fermilab by experiment E705 at an energy of 3836 MeV, in the reaction: This evidence was not confirmed by the same experiment in the reaction and more recently by BES

20. D. Bettoni - The Panda experiment 20 New State Observed by Belle B   K  (J/  +  - ), J/  µ + µ - or e + e - M = 3872.0  0.6  0.5 MeV  2.3 MeV (90 % C.L.) Possible Interpretations D 0  D 0 * molecule  (1 3 D 2 ) state Charmonium hybrid...

21. D. Bettoni - The Panda experiment 21 It is extremely important to identify all missing states above the open charm threshold and to confirm the ones for which we only have a weak evidence. This will require high-statistics, small-step scans of the entire energy region accessible at GSI. Charmonium States above the D  D threshold

22. D. Bettoni - The Panda experiment 22 Radiative transitions of the  J ( 3 P J ) charmonium states The measurement of the angular distributions in the radiative decays of the  c states provides insight into the dynamics of the formation process, the multipole structure of the radiative decay and the properties of the c  c bound state. Dominated by the dipole term E1. M2 and E3 terms arise in the relativistic treatment of the interaction between the electromagnetic field and the quarkonium system. They contribute to the radiative width at the few percent level. The angular distributions of the  2 and  2 are described by 4 independent parameters:

23. D. Bettoni - The Panda experiment 23 The coupling between the set of  states and  pp is described by four independent helicity amplitudes: –  0 is formed only through the helicity 0 channel –  1 is formed only through the helicity 1 channel –  2 can couple to both The fractional electric octupole amplitude, a 3  E3/E1, can contribute only to the  2 decays, and is predicted to vanish in the single quark radiation model if the J/  is pure S wave. For the fractional M2 amplitude a relativistic calculation yields: where  c is the anomalous magnetic moment of the c-quark. Angular Distributions of the  c states

24. D. Bettoni - The Panda experiment 24  c1 (1 3 P 1 ) AND  c2 (1 3 P 2 ) ANGULAR DISTRIBUTIONS

25. D. Bettoni - The Panda experiment 25 Predicted to be 0 or negligibly small Interesting physics. Good test for models  c1 (1 3 P 1 ) AND  c2 (1 3 P 2 ) ANGULAR DISTRIBUTIONS

26. D. Bettoni - The Panda experiment 26 McClary and Byers (1983) predict that ratio is independent of c-quark mass and anomalous magnetic moment  c1 (1 3 P 1 ) AND  c2 (1 3 P 2 ) ANGULAR DISTRIBUTIONS

27. D. Bettoni - The Panda experiment 27 The angular distributions in the radiative decay of the  1 and  2 charmonium states have been measured for the first time by the same experiment in E835. While the value of a 2 (  2 ) agrees well with the predictions of a simple theoretical model, the value of a 2 (  1 ) is lower than expected (for  c =0) and the ratio between the two, which is independent of  c, is  2  away from the prediction. This could indicate the presence of competing mechanisms, lowering the value of the M2 amplitude at the  1. Further, high-statistics measurements of these angular distributions are clearly needed to settle this question. Angular Distributions of the  c states