The Charmonium Spectrum

1
The Charmonium Spectrum
Spectroscopic Notation
n2S1LJ
2
The J/?(13S0) and the ??(23S0)

• The masses of the triplet S states have
• been measured very precisely in ee-
• collision (using resonant depolarization)
• and in ?pp annihilation at Fermilab (E760)
• Accuracy of 11 keV/c2 for the J/? and of
• 34 keV/c2 for the ??.

• The widths of these states were determined by the
  early ee- experiments
• by measuring the areas under the resonance
  curves.
• Direct measurement by E760 at Fermilab, which
  found larger values.

PDG92 PDG04
J/? 68?10 91.0 ? 3.2
?? 243 ? 43 277 ? 22
Triplet S states total widths (keV)
3
The ??? puzzle

• Within the framework of PQCD the decay widths for
  both 3S1 ? ee-
• and 3S1 ? 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 3S1 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??lt0.0023. Many explanations have been proposed
  (vector glueball,
• intrinsic charm, ...) the ?-? puzzle must still
  be understood.

4
The ?c(11S0)

• It is the ground state of charmonium, with
  quantum numbers JPC0-.
• 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 ee-
  annihilations
• Can be produced in M1 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.

5
The ?c(11S0) Mass and Total Width
M(?c) 2979.6 ? 1.2 MeV/c2
?(?c) 17.3 ? 2.6 MeV
6
?c???
In PQCD the ? ? BR can be used to calculate ?s
Using ?s0.32 (PDG) and the measured values for
the widths
???(?c) 7.0 ? 1.0 keV
7
Expected properties of the ?c(21S0)

• 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/c2 Bhaduri, Cohler, Nogami,
  Nuovo Cimento A, 65(1981)376.
• M(??c) 3.62 GeV/c2 Godfrey and Isgur, Phys.
  Rev. D 32(1985)189.
• M(??c) 3.67 GeV/c2 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.

8
The ?c(21S0)Crystal Ball Candidate

• The first ?c candidate was
• observed by the Crystal
• Ball experiment
• By measuring the recoil ?
• they found

9
The ?c(21S0)E760/E835 search
?2???

• Both E760 and E835
• searched for the ??c in the
• energy region
• using the process
• but no evidence of a signal
• was found.

Crystal Ball
10
?c(21S0) search in?? collisions at LEP

• 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

11
The ?c(21S0) 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.

12
?? ? ?c(21S0)
BaBar
M(??c) 3637.7 ? 4.4 MeV/c2
BaBar ?(??c) 17.0 ? 8.3 ? 2.5 MeV
13
Effect of Coupled Channel on the Mass Spectrum
Estia Eichten BaBar workshop on heavy quark and
exotic spectroscopy
14
The ?cJ(13PJ) States

• First observed by the early ee- 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 (R704, E760, E835).
• ?1 width measured only by E760, most precise
• measurement of ?0 width by E835.

0
?0
Mass (MeV/c2) Width (MeV)
?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
1
2
15
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 ?cJ 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 ee-
  have been eliminated.

16
?cJ ? ?pp
The ?pp decay of the ?cJ states has been
measured both in ee- 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 ?cJ data
carried out by the PDG.
The ?c0??pp BR is almost 4 times as large as that
of the ?c1 and ?c2!!!
17
Two-Photon Decay of ?c0 and ?c2
?c0
?c2
???(?c0) 2.6 ? 0.5 keV
???(?c2) 0.49 ? 0.05 keV
18
Radiative transitions of the ?cJ(3PJ) 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

19
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,
  a3?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.

20
?c1(13P1) AND ?c2(13P2) ANGULAR DISTRIBUTIONS
21
?c1(13P1) AND ?c2(13P2) ANGULAR DISTRIBUTIONS
Interesting physics. Good test for models
Predicted to be 0 or negligibly small
22
?c1(13P1) and ?c2(13P2) Angular Distributions
McClary and Byers (1983) predict that ratio is
independent of c-quark mass and anomalous
magnetic moment
23
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 E835.
• While the value of a2(?2) agrees well with the
  predictions of
• a simple theoretical model, the value of a2(?1)
  is lower than
• expected (for ?c0) 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.

24
The hc(11P1)

• 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 ?cJ 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.

25
Expected properties of the hc(1P1)

• Quantum numbers JPC1-.
• The mass is predicted to be within a few MeV of
  the center of gravity of the ?c(3P0,1,2) states
• The width is expected to be small ?(hc) ? 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

26
The hc(1P1) E760 observation

• A signal in the hc 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

27
The hc(1P1) E835 search

• E835 took the following data in 2 running
  periods
• 90 pb-1 in the ?cJ 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 ?c1
  and ?c2 stacks taken in E835 have been
  preliminarly analyzed, to find ?(Ecm)run/run
  better then 100 keV in both data taking periods.
• Not just a cross check new measurements of the
  ?cJ parameters

?c1 E835(PRELIM) E760
M(MeV/c2) 3510.64 ? 0.10 ? 0.07 3510.53 ? 0.10 ? 0.07
?(MeV) 0.88 ? 0.09 0.88 ? 0.14
B(p?p)?(J/??)(eV) 18.8 ? 0.7 ? 0.6 21.8 ? 2.7 ? 1.2
?c2 E835(PRELIM) E760
M(MeV/c2) 3556.10 ? 0.15 ? 0.07 3556.15 ? 0.11 ? 0.07
?(MeV) 1.93 ? 0.22 1.98 ? 0.18
B(p?p)?(J/??)(eV) 25.8 ? 1.9 ? 0.8 28.2 ? 2.9 ? 1.5
28
E835 Preliminary results for hc ? J/??0
Claudia Patrignani BEACH 04 Chicago 6/28-7/3
PRELIMINARY conclusion no evidence for hc ?
J/??0.
29
E835 Preliminary results for hc ? ?c?

• We observe a total of 23 ?c? candidates
• 13 of them in 30 pb-1 within 0.5 MeV/c2 of
• the ?cJ 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
30
Other hc(1P1) Searches

• The E705 experiment at Fermilab observed an
  enhancement in the J/??0 mass spectrum at 3527
  MeV/c2 in ??-Li interactions at 300 GeV/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 E705 interpreted this signal as due to the
  production of the hc and its decay to J/??0.
• The BaBar collaboration has recently reported on
  a search for the hc in the B decay process B ?
  Khc ? KJ/???-. The absence of a signal
  allowed the collaboration to set the following
  upper limit on the product of branching ratios
  (at 90 C.L.)

31
Charmonium States abovethe 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
  ee- experiments 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 D-states
  occur.

32
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 ?(3770), considered to be largely 3D1
state, has been clearly observed. It is a wide
resonance (?(?(3770)) 25.3 ? 2.9 MeV)
decaying predominantly to D?D. A recent
observation by BES of the J/???- decay mode was
not confirmed by CLEO-c.
33
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/c2, in the reaction

• This evidence was not confirmed
• by the same experiment in the
• reaction
• and more recently by BES

34
The X(3872)
New state discovered by Belle in the
hadronic decays of the B-meson B??K?
(J/???-), J/??µµ- or ee-
M 3872.0 ? 0.6 ? 0.5 MeV/c2 ?? 2.3 MeV (90
C.L.)
35
The X(3872)
BaBar
CDF
D0
36
Experimental Evidence on the X(3872) - I

• The mass (3871.9 ? 0.5 MeV/c2) is very close to
  the D0?D0 threshold (3871.1 ? 1.0 MeV/c2). This
  value differs from the simplest prediction for
  the 3D2 mass, however coupled channel effects
  might change masses considerably. In a
  calculation by Eichten et al the 3D3 state falls
  very close to 3872.
• The state is very narrow. The present limit by
  Belle is 2.3 MeV, compatible with a possible
  interpretation as 3D2 or 1D2.With a mass of 3872
  MeV/c2 both could decay to D0?D0 , but the
  widths would still be very narrow. The 3D3 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.

37
Experimental Evidence on the X(3872) - II

• The decays X(3872) ???c1 and X(3872) ???c2 have
  been unsuccessfully looked for by Belle. This
  makes the 3D2 and 3D3 interpretations
  problematic.
• The decay X(3872)?J/?? has been unsuccessfully
  looked for by BaBar. This is a problem for the
  charmonium hybrid interpretation.
• CLEO did not find this state in Initial State
  Radiation, which rules out the assignment
  JPC1--. Results from BaBar expected in the
  summer.
• Angular distribution measured by Belle
  incompatible with the JPC1- assignment for this
  state.

38
Possible X(3872) Interpretations

• If X(3872) is a charmonium state, the most
  natural hypotheses are the 13D2 and 13D3 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 D0?D0 threshold the
  X(3872) could be a D0?D0 molecule. In this case
  decay modes such as D0?D0?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 MeV/c2) 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.

39
Outlook

• All 8 states below threshold have been observed,
  but only 7 of them 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.

40
The Future

• For the near future, new results in charmonium
  spectroscopy will come from existing ee-
  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.
• BaBar 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.

41
The GSI p Facility

• HESR High Energy Storage Ring
• Production rate 2x107/sec
• Pbeam 1 - 15 GeV/c
• Nstored 5x1010 p
• High luminosity mode
• Luminosity 2x1032 cm-2s-1
• dp/p10-4 (stochastic cooling)
• High resolution mode
• dp/p10-5 (el. cooling lt 8 GeV/c)
• Luminosity 1031 cm-2s-1

42
The detector

• Detector Requirements
• (Nearly) 4? solid angle coverage (partial wave
  analysis)
• High-rate capability (2107 annihilations/s)
• Good PID (?, e, µ, ?, K, p)
• Momentum resolution (? 1 )
• Vertex reconstruction for D, K0s, ?
• Efficient trigger
• Modular design
• For Charmonium
• Pointlike interaction region
• Lepton identification
• Excellent calorimetry
• Energy resolution
• sensitivity to low-energy photons

43
Panda Detector Concept
forward spectrometer
target spectrometer
straw tubetracker
mini driftchambers
muon counter
DIRC
iron yoke
Solenoidal magnet
micro vertexdetector
electromagneticcalorimeter