charmonium spectroscopy: missing or unconfirmed states

Charmonium Spectroscopy:Charmonium Spectroscopy:Missing or UnconfirmedMissing or Unconfirmed

StatesStates

Diego Bettoni

INFN – Sezione di Ferrara

International Workshop on Physics with

Antiprotons at GSI

GSI, June 6-8, 2002

OutlineOutline

• Introduction

• Unconfirmed or missing states– The c(21S0)

– The hc(1P1)

– Charmonium states above the DD threshold

• Radiative transitions of the J(3PJ) charmonium states

• Proton e.m. form factors in the time-like region

• Conclusions

The charmonium spectrumThe 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/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.

Expected properties Expected properties of the of the cc(2(211SS00))

MeV65)ee/J(

)ee(

M

M

)M(

)M(2

/J

2

/Js

s

The The cc(2(211SS00))Crystal Ball CandidateCrystal Ball Candidate

The first ´c candidate was

observed by the Crystal

Ball experiment:

By measuring the recoil

they found:

Xee

2

c c/MeV)53594()(M .)L.C%95(MeV8)( c

Both E760 and E835

searched for the c in the

energy region:

using the process:

but no evidence of a signal

was found

The The cc(2(211SS00))E760/E835 searchE760/E835 search

Crystal Ball

cpp

2

MeV)36603570(Ecm

The The cc(2(211SS00))E760/E835 limitsE760/E835 limits

)MeV8(107.3).(R.B)pp.(R.B

)MeV5(106.5).(R.B)pp.(R.B

'c

'c

8'c

'c

8'c

'c

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:

)MeV15(105.4).(R.B)pp.(R.B

)MeV10(100.5).(R.B)pp.(R.B

)MeV5(100.8).(R.B)pp.(R.B

'c

'c

'c

8'c

'c

8'c

'c

8'c

'c

In the restricted energy region 3589-3599 MeV:

0c /J /Jc

cc(2(211SS00) search in) search inother channelsother 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:

cc(2(211SS00) search in) search in collisions at LEP collisions at LEP

c)(eeee

.)L.C%90(34.0)()(

c

c

The Belle collaboration has recently

presented a 6 signal for BKKSK

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 The cc(2(211SS00) ) BELLE candidateBELLE candidate

MeV)stat(2022

MeV)stat(22978M

MeV)stat(2415

MeV)stat(63654M

KK;KB Scc

2c

2c

c/MeV55)(

c/MeV863654)(M

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 (cpp)/(cpp)

could shed light on the possible mixing of the c with a nearby

0+ glueball.

All this is ideally accomplished in direct All this is ideally accomplished in direct pp formation at GSI !pp formation at GSI !

The The cc(2(211SS00))

The hThe hcc((11PP11))

Precise measurements of the parameters of the hc are of

extreme importance in resolving a number of open questions:

• Spin-dependent component of the qq 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 qq 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 cc states.

• Quantum numbers JPC=1+-.

• 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

Expected properties of the hExpected properties of the hcc((11PP11))

9)(M5)(M3)(M

M 210cog

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:


E760 candidateE760 candidate

0c /Jhpp

)%90(1.1)(

/2.015.02.3526)( 2

CLMeVh

cMeVhM

c

c

E835 has performed a search for

the hc, 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 hc region.


E835 searchE835 search

Despite the considerable efforts of E760 and E835, the hc

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 toOnce again, the proposed facility at GSI is the ideal place to

find and study this resonance.find and study this resonance.


Charmonium States aboveCharmonium States abovethe Dthe DD thresholdD threshold

The energy region above the DD 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 DD 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 statesThe 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:

DDD 23,1

forbidden by parity conservation*

23,1 DDD forbidden by energy conservation

21D2

3D

• Only the , considered to be largely state, has been clearly observed

)3770(1

3D

The D wave statesThe 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:

XJLi /

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

XJpLi /

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 aboveCharmonium States abovethe Dthe DD thresholdD threshold

Radiative transitions of the Radiative transitions of the JJ((33PPJJ) )

charmonium statescharmonium statesThe 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

cc 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:

ee/Jpp c

)(a),(B),(a),(a 2c32c202c21c2

• 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, a3E3/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 Angular Distributions of the cc states states

)1(065.0)1(m4

E)(a cc

c1c2

)1(096.0)1(m4

E

53

)(a ccc

2c2

c1c1(1(133PP11) AND ) AND c2c2(1(133PP22) ANGULAR DISTRIBUTIONS) ANGULAR DISTRIBUTIONS

eeJpp /1c

2

0

:amplitudesDecay

0 :amplitudes Production

a

B

eeJpp /2c

32

20

:amplitudesDecay

:amplitudes Production

a,a

B

2144 c1 events 95.0cos


6028 c2 events 95.0cos


01.008.013.0)pp(B

)0J,pp(BB

2c

z2c20

50

)0,(

)( therefore

2

0

zJppB

ppB

009.002.0a 055.0044.0-3

Predicted to be 0 or negligibly small

Interesting physics. Good test for models


004.0032.0002.0)(a 1c2

006.0093.0)(a 039.0041.02c2

34.002.0)(

)(

835E22

12

c

c

a

a

McClary and Byers (1983) predict that ratio is independent of c-quark mass and anomalous magnetic moment

676.0)/(

)/(

35

)(

)(

2

1

theory22

12

JE

JE

a

a

c

c

c

c


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 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 Angular Distributions of the cc states states

Proton e.m. form factorsProton e.m. form factorsin the time-like regionin 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 Q2 are crucial to test the QCD predictions for the asymptotic

behavior of the form factors and the spacelike-timelike equality at

corresponding values of Q2.

*22

2*22

222

* cos14

cos12cos

E

pM G

s

mG

xs

c

d

d

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 |q2|.

At the proposed facility at GSI it will

be possible to carry out the proton e.m.

form factors at the highest timelike q2.

Proton magnetic form factorProton magnetic form factorPRELIMINARYPRELIMINARY

222 ln

ss

CG

p

M

Summary (I)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 hc region

– New limits on the c

– Measurement of the proton form factors at the highest timelike q2.

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 hc(1P1)

• Find the states above the DD threshold

• Improve measurement of states angular distributions

• Measure the form factor of the proton at even higher q2.

• ..............

The proposed experiment at GSI is the ideal facility to carryThe proposed experiment at GSI is the ideal facility to carry

out all these measurements !out all these measurements !

Summary (II)Summary (II)

charmonium spectroscopy: missing or unconfirmed states

Documents

partial width c

c candidate

lepthe c

total width

hc mass

c21s0the mass difference

final states

tens of mev