The Charmonium Spectroscopic Notation n 2 S1 LJ

The Charmonium Spectroscopic Notation n 2 S+1 LJ Diego Bettoni Charmonium 1

The J/ (13 S 0) and the (23 S 0) • The masses of the triplet S states have been measured very precisely in e+ecollision (using resonant depolarization) and in pp annihilation at Fermilab (E 760) Accuracy of 11 ke. V/c 2 for the J/ and of 34 ke. V/c 2 for the . • The widths of these states were determined by the early e+e- experiments by measuring the areas under the resonance curves. Direct measurement by E 760 at Fermilab, which found larger values. Triplet S states total widths (ke. V) Diego Bettoni PDG 92 PDG 04 J/ 68 10 91. 0 3. 2 243 43 277 22 Charmonium 2

The puzzle Within the framework of PQCD the decay widths for both 3 S 1 e+eand 3 S 1 hadrons are proportional to the square of the wavefunction at the origin | (0)|2. If this is true for each individual hadronic channel one finds the following universal ratio (12 % rule): This holds experimentally for many hadronic decays of the 3 S 1 states, but it is badly violated for several final states. The first violation to be observed was for the decay, for which the latest result by BES is R <0. 0023. Many explanations have been proposed (vector glueball, intrinsic charm, . . . ): the - puzzle must still be understood. Diego Bettoni Charmonium 3

The c(11 S 0) • It is the ground state of charmonium, with quantum numbers JPC=0 -+. • Knowledge of its parameters is crucial. Potential models rely heavily on the mass difference M(J/ )-M( c) to fit the charmonium spectrum. • The c cannot be formed directly in e+e- annihilations: – Can be produced in M 1 radiative decays from the J/ and (small BR). – Can be produced in photon-photon fusion. – Can be produced in B-meson decay. • The c can be formed directly in pp annihilation. • Many measurements of mass and c width (6 new measurements in the last 2 years). However errors are still relatively large and internal consistency of measurements is rather poor. • Large value of c width difficult to explain in simple quark models. • Decay to two photons provides estimate of s. Diego Bettoni Charmonium 4

The c(11 S 0) Mass and Total Width M( c) = 2979. 6 1. 2 Me. V/c 2 Diego Bettoni Charmonium ( c) = 17. 3 2. 6 Me. V 5

c In PQCD the BR can be used to calculate s: Using s=0. 32 (PDG) and the measured values for the widths: ( c) = 7. 0 1. 0 ke. V Diego Bettoni Charmonium 6

Expected properties of the c(21 S 0) • 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 Ge. V/c 2 [Bhaduri, Cohler, Nogami, Nuovo Cimento A, 65(1981)376]. – M( c) = 3. 62 Ge. V/c 2 [Godfrey and Isgur, Phys. Rev. D 32(1985)189]. – M( c) = 3. 67 Ge. V/c 2 [Resag and Münz, Nucl. Phys. A 590(1995)735]. • Total width ranging from a few Me. V to a few tens of Me. V: – ( c) 5 25 Me. V • Decay channels similar to c. Diego Bettoni Charmonium 7

The c(21 S 0) Crystal Ball Candidate The first ´c candidate was observed by the Crystal Ball experiment: By measuring the recoil they found: Diego Bettoni Charmonium 8

The c(21 S 0) E 760/E 835 search Both E 760 and E 835 searched for the c in the energy region: 2 Crystal Ball using the process: but no evidence of a signal was found. Diego Bettoni Charmonium 9

c(21 S 0) search in collisions at LEP The c has been looked for by the LEP experiments via the process: L 3 sets a limit of 2 Ke. V (95 %C. L. ) for the partial width ( c ). DELPHI data (shown on the right) yield: Diego Bettoni Charmonium 10

The c(21 S 0) discovery by BELLE The Belle collaboration has recently presented a 6 signal for B KKSK which they interpret as evidence for c production and decay via the process: with: in disagreement with the Crystal Ball result. Diego Bettoni Charmonium 11

c(21 S 0) Ba. Bar M( c) = 3637. 7 4. 4 Me. V/c 2 Ba. Bar: ( c) = 17. 0 8. 3 2. 5 Me. V Diego Bettoni Charmonium 12

Effect of Coupled Channel on the Mass Spectrum Estia Eichten – Ba. Bar workshop on heavy quark and exotic spectroscopy Diego Bettoni Charmonium 13

The c. J(13 PJ) States • First observed by the early e+e- experiments, which measured radiative decay widths, directly for 1 and 2, indirectly for 0. Radiative decay important for relativistic corrections and coupled channel effects. • Precision measurements of masses and widths in pp experiments (R 704, E 760, E 835). • 1 width measured only by E 760, most precise measurement of 0 width by E 835. Mass (Me. V/c 2) Width (Me. V) 0 3415. 19 0. 34 10. 2 0. 9 1 3510. 59 0. 12 0. 88 0. 14 2 3556. 26 0. 11 2. 00 0. 18 Diego Bettoni 1++ Charmonium 0 0++ 2++ 14

PDG Global Fit Following a method proposed by Patrignani, the Particle Data Group has carried out a global fit to all available data for the and c. J decays using each experimentally measured quantity (e. g. product of branching ratios) to extract individual branching ratios and partial widths. This method minimized the propagation of systematic effects from one measurement to the other. The results of the global fit have been implemented in the PDG 2002 and 2004 Reviews of Particle Properties. As a result of this new procedure, many values of branching ratios and partial widths have changed, and some of the discrepancies between different measurements in pp and e+e- have been eliminated. Diego Bettoni Charmonium 15

c. J pp The pp decay of the c. J states has been measured both in e+e- collisions and in pp annihilation. Historically the two methods gave results which were barely compatible with each other. The situation has changed drastically after the global fit to all and c. J data carried out by the PDG. The c 0 pp BR is almost 4 times as large as that of the c 1 and c 2!!! Diego Bettoni Charmonium 16

Two-Photon Decay of c 0 and c 2 c 0 c 2 ( c 0) = 2. 6 0. 5 ke. V Diego Bettoni Charmonium ( c 2) = 0. 49 0. 05 ke. V 17

Radiative transitions of the c. J(3 PJ) 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 E 1. M 2 and E 3 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: Diego Bettoni Charmonium 18

Angular Distributions of the c States • 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 E 3/E 1, 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 M 2 amplitude a relativistic calculation yields: where c is the anomalous magnetic moment of the c-quark. Diego Bettoni Charmonium 19

c 1(13 P 1) AND c 2(13 P 2) ANGULAR DISTRIBUTIONS Diego Bettoni Charmonium 20

c 1(13 P 1) AND c 2(13 P 2) ANGULAR DISTRIBUTIONS Interesting physics. Good test for models Predicted to be 0 or negligibly small Diego Bettoni Charmonium 21

c 1(13 P 1) and c 2(13 P 2) Angular Distributions Mc. Clary and Byers (1983) predict that ratio is independent of cquark mass and anomalous magnetic moment Diego Bettoni Charmonium 22

Angular Distributions of the c states 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 E 835. 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 M 2 amplitude at the 1. Further, high-statistics measurements of these angular distributions are clearly needed to settle this question. Diego Bettoni Charmonium 23

The hc(11 P 1) Precise measurements of the parameters of the hc give extremely important information on the spin-dependent component of the q q confinement potential. The splitting between triplet and singlet is given by the spin-spin interaction (hyperfine structure). If the vector potential is 1/r (one gluon exchange) than the expectation value of the spin-spin interaction for P states (whose wave function vanishes at the origin) should be zero. In this case the hc should be degenerate in mass with the center-of-gravity of the c. J states. A comparison of the hc 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. Diego Bettoni Charmonium 24

Expected properties of the hc(1 P 1) • • Quantum numbers JPC=1+-. The mass is predicted to be within a few Me. V of the center of gravity of the c(3 P 0, 1, 2) states • • The width is expected to be small (hc) 1 Me. V. 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 • Diego Bettoni Charmonium 25

The hc(1 P 1) E 760 observation A signal in the hc region was seen by E 760 in the process: Due to the limited statistics E 760 was only able to determine the mass of this structure and to put an upper limit on the width: Diego Bettoni Charmonium 26

The hc(1 P 1) E 835 search • E 835 took the following data in 2 running periods: – 90 pb-1 in the c. J c. o. g. region. – data taken outside this energy region for background studies, providing 120 pb-1 for the c mode and 80 pb-1 for the J/ 0 mode. • • Very careful beam energy studies. All single c 1 and c 2 stacks taken in E 835 have been preliminarly analyzed, to find (Ecm)run/run better then 100 ke. V in both data taking periods. Not just a cross check: new measurements of the c. J parameters: Diego Bettoni c 1 E 835(PRELIM) E 760 M(Me. V/c 2) 3510. 64 0. 10 0. 07 3510. 53 0. 10 0. 07 (Me. V) 0. 88 0. 09 0. 88 0. 14 B(p p) (J/ )(e. V) 18. 8 0. 7 0. 6 21. 8 2. 7 1. 2 c 2 E 835(PRELIM) E 760 M(Me. V/c 2) 3556. 10 0. 15 0. 07 3556. 15 0. 11 0. 07 (Me. V) 1. 93 0. 22 1. 98 0. 18 B(p p) (J/ )(e. V) 25. 8 1. 9 0. 8 28. 2 2. 9 1. 5 Charmonium 27

E 835 Preliminary results for hc J/ 0 Claudia Patrignani – BEACH 04 – Chicago 6/28 -7/3 PRELIMINARY conclusion: no evidence for hc J/ 0. Diego Bettoni Charmonium 28

E 835 Preliminary results for hc c • We observe a total of 23 c candidates 13 of them in 30 pb-1 within 0. 5 Me. V/c 2 of the c. J c. o. g. • The statistical significance is ~ 0. 001 • If interpreted as hc c the best fit resonance parameters are: Claudia Patrignani – BEACH 04 – Chicago 6/28 -7/3 Diego Bettoni Charmonium 29

Other hc(1 P 1) Searches • The E 705 experiment at Fermilab observed an enhancement in the J/ 0 mass spectrum at 3527 Me. V/c 2 in -Li interactions at 300 Ge. V/c incident momentum. The magnitude of this effect is 42 17 events above background, corresponding to a 2. 5 significance. Due to its vicinity to Mcog E 705 interpreted this signal as due to the production of the hc and its decay to J/ 0. • The Ba. Bar collaboration has recently reported on a search for the hc in the B decay process B K+hc K+J/ + ++ -. The absence of a signal allowed the collaboration to set the following upper limit on the product of branching ratios (at 90 % C. L. ): Diego Bettoni Charmonium 30

Charmonium States above the D D threshold The energy region above the D D threshold at 3. 73 Ge. V is very poorly known. Yet this region is rich in new physics. • The structures and the higher vector states ( (3 S), (4 S), (5 S). . . ) observed by the early e+eexperiments have not all been confirmed by the latest, much more accurate measurements by BES. • 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 Dstates occur. Diego Bettoni Charmonium 31

The D wave states • The charmonium “D states” are above the open charm threshold (3730 Me. V ) but the widths of the J= 2 states and are expected to be small: forbidden by parity conservation forbidden by energy conservation Only the (3770), considered to be largely 3 D 1 state, has been clearly observed. It is a wide resonance ( ( (3770)) = 25. 3 2. 9 Me. V) decaying predominantly to D D. A recent observation by BES of the J/ + - decay mode was not confirmed by CLEO-c. Diego Bettoni Charmonium 32

The D wave states • The only evidence of another D state has been observed at Fermilab by experiment E 705 at an energy of 3836 Me. V/c 2, in the reaction: • This evidence was not confirmed by the same experiment in the reaction and more recently by BES Diego Bettoni Charmonium 33

The X(3872) New state discovered by Belle in the hadronic decays of the B-meson: B K (J/ + -), J/ µ+µ- or e+e. M = 3872. 0 0. 6 0. 5 Me. V/c 2 2. 3 Me. V (90 % C. L. ) Diego Bettoni Charmonium 34

The X(3872) Ba. Bar CDF D 0 Diego Bettoni Charmonium 35

Experimental Evidence on the X(3872) - I • The mass (3871. 9 0. 5 Me. V/c 2) is very close to the D 0 D*0 threshold (3871. 1 1. 0 Me. V/c 2). This value differs from the simplest prediction for the 3 D 2 mass, however coupled channel effects might change masses considerably. In a calculation by Eichten et al the 3 D 3 state falls very close to 3872. • The state is very narrow. The present limit by Belle is 2. 3 Me. V, compatible with a possible interpretation as 3 D 2 or 1 D 2. With a mass of 3872 Me. V/c 2 both could decay to D 0 D*0 , but the widths would still be very narrow. The 3 D 3 could decay to D D, but its f-wave decay would be strongly suppressed. • In the only decay mode detected so far, J/ + -, the + - mass distribution peaks at the kinematic limit, which corresponds to the mass. The decay to J/ would violate isospin and should therefore be suppressed. Diego Bettoni Charmonium 36

Experimental Evidence on the X(3872) - II • The decays X(3872) c 1 and X(3872) c 2 have been unsuccessfully looked for by Belle. This makes the 3 D 2 and 3 D 3 interpretations problematic. • The decay X(3872) J/ has been unsuccessfully looked for by Ba. Bar. This is a problem for the charmonium hybrid interpretation. • CLEO did not find this state in Initial State Radiation, which rules out the assignment JPC=1 --. Results from Ba. Bar expected in the summer. • Angular distribution measured by Belle incompatible with the JPC=1+assignment for this state. Diego Bettoni Charmonium 37

Possible X(3872) Interpretations • If X(3872) is a charmonium state, the most natural hypotheses are the 13 D 2 and 13 D 3 states. In this case the non-observation of the expected radiative transitions is a potential problem, but the present experimental limits are still compatible with these hypotheses. • Due to its closeness to the D 0 D*0 threshold the X(3872) could be a D 0 D*0 molecule. In this case decay modes such as D 0 0 might be enhanced. • The charmonium hybrid (c cg) interpretation has been proposed by Close and Godfrey. However present calculations indicate higher mass values (around 4100 Me. V/c 2) for the ground state. Absence of J/ mode a potential problem. Further experimental evidence is needed to establish the nature of the X(3872): spin-parity, search for charged partners, search for further decay modes, in particular the radiative decay modes. Diego Bettoni Charmonium 38

Outlook • All 8 states below threshold have been observed, but only 7 of them are supported by strong experimental evidence. The study of the hc remains a very high priority in charmonium physics. • The agreement between the various measurements of the c mass and width is not satisfactory. New, high-precision measurments are needed. The large value of the total width needs to be understood. • The study of the c has just started. Small splitting from the must be understood. Width and decay modes must be measured. • The angular distributions in the radiative decay of the triplet P states must be measured with higher accuracy. • The entire region above open charm threshold must be explored in great detail, in particular the missing D states must be found. • Decay modes of all charmonium states must be studied in greater detail: new modes must be found, existing puzzles must be solved (e. g. - ), radiative decays must be measured with higher precision. Diego Bettoni Charmonium 39

The Future • For the near future, new results in charmonium spectroscopy will come from existing e+e- machines: – BES at BEPC in Beijing will collect data at the (3770) resonance – CLEO-c at Cornell will run for at least 5 years at the and especially above threshold. – Ba. Bar and Belle at the existing B-factories will continue to provide first rate results in charmonium spectroscopy. • For the future beyond 2010 it will be again the turn of pp annihilation to take the lead in charmonium physics: the PANDA experiment at the FAIR facility in GSI will take data with a rich program of hadron spectroscopy, of which the study of charmonium will be a major part. Diego Bettoni Charmonium 40

The GSI p Facility HESR = High Energy Storage Ring • Production rate 2 x 107/sec • Pbeam = 1 - 15 Ge. V/c • Nstored = 5 x 1010 p High luminosity mode • Luminosity = 2 x 1032 cm-2 s-1 • dp/p~10 -4 (stochastic cooling) High resolution mode • dp/p~10 -5 (el. cooling < 8 Ge. V/c) • Luminosity = 1031 cm-2 s-1 D. Bettoni - Charmonium at GSI 41

The detector • Detector Requirements: – – – – (Nearly) 4 solid angle coverage (partial wave analysis) High-rate capability (2× 107 annihilations/s) Good PID ( , e, µ, , K, p) Momentum resolution ( 1 %) Vertex reconstruction for D, K 0 s, Efficient trigger Modular design • For Charmonium: – Pointlike interaction region – Lepton identification – Excellent calorimetry • Energy resolution • sensitivity to low-energy photons D. Bettoni - Charmonium at GSI 42

Panda Detector Concept target spectrometer straw tube tracker mini drift chambers forward spectrometer muon counter DIRC iron yoke Solenoidal magnet electromagnetic calorimeter micro vertex detector D. Bettoni - Charmonium at GSI 43