Charmonium Spectroscopy: Missing or Unconfirmed States Diego Bettoni INFN – Sezione di Ferrara International Workshop on Physics with Antiprotons at GSI GSI, June 6-8, 2002

Outline Introduction Unconfirmed or missing states –The  c (2 1 S 0 ) –The h c ( 1 P 1 ) –Charmonium states above the D  D threshold Radiative transitions of the  J ( 3 P J ) charmonium states Proton e.m. form factors in the time-like region Conclusions

The charmonium spectrum

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 )

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:

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 

The  c (2 1 S 0 ) E760/E835 limits Upper limits on the product of the branching ratios into the initial and final states can be set by fitting the data to spin 0 resonance + a power law background for different values of the total width. From the combined E760/E835 data we get: In the restricted energy region MeV:

 c (2 1 S 0 ) search in other channels

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

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 ) BELLE candidate

The  c is still waiting to be unambiguously identified. To look for it in the two photon decay channel would 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 . In addition to that, the comparison of the ratios  (  c  )/  (  c  ) and  (  c  pp)/  (  c  pp) could shed light on the possible mixing of the  c with a nearby 0 + glueball. All this is ideally accomplished in direct  pp formation at GSI ! The  c (2 1 S 0 )

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.

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 )

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 candidate

E835 has performed a search for the h c, in the attempt to confirm the E760 results and possibly add new decay channels. So far E835 has been unable to confirm or deny the E760 result, despite the presence of a clear J/  signal in the h c region. The h c ( 1 P 1 ) E835 search

Despite the considerable efforts of E760 and E835, the h c continues to be seen by one experiment in only one channel. It is extremely important to identify this resonance and study its properties. To do so we need: High statistics: the signal could be very tiny Excellent beam resolution: the resonance could be very narrow The ability to detect its hadronic decay modes. Once again, the proposed facility at GSI is the ideal place to find and study this resonance. The h c ( 1 P 1 )

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.

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

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

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 week evidence. This will require high-statistics, small-step scans of the entire energy region accessible at GSI. Charmonium States above the D  D threshold

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:

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

 c1 (1 3 P 1 ) AND  c2 (1 3 P 2 ) ANGULAR DISTRIBUTIONS

2144  c1 events  c1 (1 3 P 1 ) AND  c2 (1 3 P 2 ) ANGULAR DISTRIBUTIONS

6028  c2 events  c1 (1 3 P 1 ) AND  c2 (1 3 P 2 ) ANGULAR DISTRIBUTIONS

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

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

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

Proton e.m. form factors in the time-like region The electromagnetic form factors of the proton in the time-like region can be extracted from the cross section for the process:  pp  e + e - First order QED predicts: Data at high Q 2 are crucial to test the QCD predictions for the asymptotic behavior of the form factors and the spacelike-timelike equality at corresponding values of Q 2.

The dashed line is the PQCD fit: The dot-dashed line represents the dipole behavior of the form factor in the spacelike region for the same values of |q 2 |. At the proposed facility at GSI it will be possible to carry out the proton e.m. form factors at the highest timelike q 2. Proton magnetic form factor PRELIMINARY

Summary (I) Charmonium was discovered in e+e- annihilation: very accurate measurements of the J/  and . The first  pp experiment (R704 at the ISR) demonstrated the feasibility of the technique. E760 and E835 have been very successful in producing a wealth of new measurements: –High precision measurements of  1 and  2 masses and widths –High precision measurements of  2   –Best measurements of  0 mass and width –Best measurements of  1 and  2 angular distributions –First observation of the  c in  pp annihilation, measurement of its mass, total width and partial width to  –Observation of a signal in the h c region –New limits on the  c –Measurement of the proton form factors at the highest timelike q 2.

Still there remains a lot to be done: Improve measurement of  c mass (error still bigger than 2 MeV), width and branching ratios. Detect hadronic decay channels. Identify unambiguously the  c, measure its parameters accurately, detect hadronic decay modes. Confirm/Find the h c ( 1 P 1 ) Find the states above the  DD threshold Improve measurement of  states angular distributions Measure the form factor of the proton at even higher q The proposed experiment at GSI is the ideal facility to carry out all these measurements ! Summary (II)