Charmonium Spectroscopy

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
The ?c (11S0)

• 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
The ?c(11S0)
M(?c) 2979.9 ? 1.0 MeV
?(?c) 25.5 ? 3.3 MeV
T. Skwarnicki Lepton Photon 2003
4
The ?c (11S0)

• 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 ???-KK-
• ?c ?2(KK-)
• ?c ?2(??-)
• ?c ?K?K?
• ?c ? ???
• ...
• ?c ? p?p

5
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.

6
The ?c(21S0)Crystal Ball Candidate

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

7
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
8
?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

9
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, but reasonably consistent with
• potential model expectations.
• (DPF 2002).

10
?? ? ?c(21S0)
M(?c) 3637.7 ? 4.4 MeV ?(?c) 19 ? 10 MeV
T. Skwarnicki Lepton Photon 2003
11
The ?c(21S0)

• 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 KK- and ??.
  
• ?c ? p?p

12
The hc(1P1)

• Precise measurements of the parameters of the hc
  are of
• extreme importance in resolving a number of open
  questions
• Spin-dependent component of the q?q confinement
  potential. 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.
• Branching ratios for hadronic decays to lower c?c
  states.

13
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

14
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

15
The hc(1P1) E835 search

• E835 has performed a search for
• the hc, in the attempt to confirm
• the E760 results and possibly
• add new decay channels.
• Data analysis is still under way
• in various decay channels
• hc ? ?c ? ? (??)?
• hc ? ?c ? ? (??)? ? (4K) ?
• hc ? J/??0 ? (ee-)(??)

16
The hc(1P1)

• 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 hc is a central part
  of the experimental
• program of the PANDA experiment at GSI.

17
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. 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
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
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
New State Observed by Belle
B??K? (J/???-), J/??µµ- or ee-

• Possible Interpretations
• D0?D0 molecule
• ?(13D2) state
• Charmonium hybrid
• ...

M 3872.0 ? 0.6 ? 0.5 MeV ?? 2.3 MeV (90
C.L.)
21
Charmonium States abovethe D?D threshold

• 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.

22
Radiative transitions of the ?J(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

23
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.

24
?c1(13P1) AND ?c2(13P2) ANGULAR DISTRIBUTIONS
25
?c1(13P1) AND ?c2(13P2) ANGULAR DISTRIBUTIONS
Interesting physics. Good test for models
Predicted to be 0 or negligibly small
26
?c1(13P1) AND ?c2(13P2) ANGULAR DISTRIBUTIONS
McClary and Byers (1983) predict that ratio is
independent of c-quark mass and anomalous
magnetic moment
27
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.