Charmonium Spectroscopy - GSID. Bettoni - Charmonium 5 Experimental Method The antiproton beam momentum is varied in small steps (≤ 150 KeV/c) around the resonance under study and

Charmonium Spectroscopy

Diego BettoniINFN – Sezione di Ferrara, Italy

JINR-GSI WorkshopJINR, Dubna, November 20-21, 2003

D. Bettoni - Charmonium 2

Outline

• Introduction and experimental method• The ηc(1S)• The ηc(2S)• The hc(1P1)• States above the DD threshold

– The X(3872)• Electromagnetic form factors of the proton in the timelike

region• Conclusions


Introduction

Ever since its discovery in 1974 the charmonium system hasbeen considered a powerful tool for the understanding of thestrong interaction, and this is why it has often been called thepositronium of QCD.

Non relativistic potential models+

relativistic corrections+

perturbative QCDmake it possible to calculate masses, widths and branchingratios to be compared with experiment.

αs ≈ 0.3 β2 ≈ 0.2


Whypp ?In e+e- annihilations only stateswith the quantum numbers ofthe photon JPC = 1-- can beformed directly via the processe+e- → γ* →cc. States withJPC ≠ 1-- are usually studiedfrom radiative decays, e.g.

e+e- → ψ′ → χ + γIn this case the measurementaccuracy ( for masses andwidths ) is limited by thedetector.

In pp annihilations all quantumnumbers are directly accessible.

The resonance parameters aredetermined from the beamparameters and do not dependon the detector energy andmomentum resolution.


Experimental Method

The antiproton beam momentum isvaried in small steps (≤ 150 KeV/c)around the resonance under study and a scan across the resonance ismade. The formation of charmonium isdetected through l+l-, γγ and hadronic final states.The resonanceparameters (MR, ΓR, Bin×Bout) are extracted from the excitationcurve using a maximum likelihood fit.

4)(4

)12(2

2

2

2

R

R

R

outin

BW

ME

BBk

JΓ

+−

Γ+=

πσ ∫ +∆= bckBW EEEdEfL σσεν )(),(0


Experimental Requirements

• Precise knowledge of energy scale to make accurate measurement of masses (calibration at ψ′ mass, now known to better than 10 KeV)

• High beam momentum resolution (charmonium states are narrow) ∆p/p = 10-5÷10-4, in E835 ∆p/p = 2×10-4)

• Precise knowledge of beam momentum distribution• High luminosity !!! (cross sections are small) (maximum

E835 luminosity 5×1031 cm-2s-1).


The charmonium spectrum


The ηc (11S0)

Despite the recent measurements by E835 not much isknown about the ground state of charmonium:• the error on the mass is still bigger than 1 Mev• recent measurements give larger widths thanpreviously expectedA large value of the ηc width is difficult to explain interms of simple quark models. Also unusually largebranching ratios into channels involving multiple kaonsand pions have been reported.A precision measurements of the ηc mass, width andbranching ratios is of the utmost importance, and it can only be done in by direct formation in pp.


The ηc(11S0)

M(ηc) = 2979.9 ± 1.0 MeV Γ(ηc) = 25.5 ± 3.3 MeVT. Skwarnicki – Lepton Photon 2003


• Two photon channel ηc → γγ (weak branching ratioBR(ηc→γγ)=3×10-4).

• Hadronic decay channels, with branching ratios which are larger by several orders of magnitude.– ηc →π+π-K+K-

– ηc →2(K+K-)– ηc →2(π+π-)– ηc →KKπ– ηc → ηππ– ...

• ηc → pp

The ηc (11S0)


• The mass difference ∆′ between the η′c and the ψ′ can be related to the mass difference ∆ between the ηc and the J/ψ :

• Various theoretical predictions of the η′c mass have been reported:– M(η′c) = 3.57 GeV/c2 [Bhaduri, Cohler, Nogami, Nuovo Cimento A,

65(1981)376].– M(η′c) = 3.62 GeV/c2 [Godfrey and Isgur, Phys. Rev. D 32(1985)189].– M(η′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:Γ (η′c) ≈ 5 ÷ 25 MeV

• Decay channels similar to ηc.

Expected properties of the ηc(21S0)

MeV65)ee/J(

)ee(M

M)M()M(

2/J

2

/Js

s ≈∆→Γ

→′Γ=∆′

−+

−+′′

ψψ

αα

ψ

ψ

ψ

ψ


ηc(21S0) History

• Crystal Ball candidate

• Not seen by E760/E835 in pp annihilation

2c c/MeV)53594()(M ±=′η

.)L.C%95(MeV8)( c ≤′Γ η

• Not seen by LEP in γγ collisions


The Belle collaboration has recentlypresented a 6σ signal for B→KKSKπwhich they interpret as evidence forη′c production and decay via the process:

with:

in disagreement with the Crystal Ballresult, but reasonably consistent withpotential model expectations.(DPF 2002).

The ηc(21S0) discovery by BELLE

MeV)stat(2022MeV)stat(22978M

±=Γ±=

MeV)stat(2415MeV)stat(63654M

±=Γ±=

−+→′′→ πηη KK;KB Scc

2c

2c

c/MeV55)(

c/MeV863654)(M

<′Γ

±±=′

η

η


γγ → ηc(21S0)

BaBar 88 fb-1

Preliminary

Log-

scal

e

M(ηc) = 3637.7 ± 4.4 MeVΓ(ηc) = 19 ± 10 MeV

T. Skwarnicki – Lepton Photon 2003


The ηc(21S0) mass

M(ηc) = 3637.7 ± 4.4 MeV

Is there a problem?

1. Quark models predict M(ψ’)- M(ηc’)~50-90 MeV(GI model predicts 53 MeV ⇒ M(ηc’)=3633 MeV)

2. Coupled channel mechanism shifts ∆M( 23S1)=mass –118 MeV vs ∆M(13S1)=-48 MeV

⇒ ⇒ need more precise measurementsneed to include coupled channel effects

S. Godfrey – QWG03


In PANDA we will be able to identify the η′c in the followingchannels:• two photon decay channel η′c → γγ.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 η′c through its hadronic decays, such as K+K- and ΦΦ.

• η′c → pp

The ηc(21S0)


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 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 ηc+γ 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 χc(3P0,1,2) states

• The width is expected to be small Γ(hc) ≤ 1 MeV.• The dominant decay mode is expected to be ηc+γ, which should

account for ≈ 50 % of the total width.• It can also decay to J/ψ:

J/ψ + π0 violates isospinJ/ψ + π+π- suppressed by phase space

and angular momentum barrier

Expected properties of the hc(1P1)

9)(M5)(M3)(M

M 210cog

χχχ ++=


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 massof this structure and to put an upperlimit on the width:

The hc(1P1) E760 observation

0c /Jhpp πψ +→→

)%90(1.1)(/2.015.02.3526)( 2

CLMeVhcMeVhM

c

c

<Γ±±=


E835 has performed a search forthe hc, in the attempt to confirmthe E760 results and possiblyadd new decay channels. Data analysis is still under wayin various decay channels• hc → ηc + γ → (γγ)+γ• hc → ηc + γ → (ΦΦ)+γ → (4K)+ γ• hc → J/ψ+π0 → (e+e-)+(γγ)

The hc(1P1) E835 search


The hc(1P1)

11PP11 vsvs 33PPcog cog mass mass –– distinguish modelsdistinguish models•In QM triplet-singlet splittings test

•the Lorentz nature of the confining potential•Relativistic effects

•important validation of •lattice QCD calculations•NRQCD calculations

•Observation of 1P1 states is an important test of theoryS. Godfrey – QWG03

S. Godfrey, Carleton University 22

latticePQCD

QM

QM

QM

Wide variation of theoretical predictions:

wide variation in predictions indicates need for experimental data


It is extremely important to identify this resonance and study itsproperties. 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 hThe search and study of the hcc is a central part of the experimental is a central part of the experimental program of the PANDA experiment at GSI.program of the PANDA experiment at GSI.

The hc(1P1)


Charmonium States abovethe DD threshold

The energy region above the DD threshold at 3.73 GeV is very poorlyknown. Yet this region is rich in new physics.• The structures and the higher vector states (ψ(3S), ψ(4S), ψ(5S) ...)

observed by the early e+e- experiments have not all been confirmedby 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 states

• 3DJ masses – test spin dependent splittings• There is still some question about the Lorentz structure of the potential

– Vector 1-gluon exchange + scalar confinement– Vector 1-gluon exchange + colour electric confinement– + more complicated structures

• Because the D waves are larger they will feel the long-range spin-dependent potential more than the P waves.

• Observation of 3DJ would be important in understanding the Lorentz structure of the confining potential

S. Godfrey – QWG03


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:

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(ψ1

3D


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:

XJLi +→ −+πψππ /

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

XJpLi +→ −+πψπ/


The X(3872)

New state discovered by Belle inB±→K± (J/ψπ+π-), J/ψ→µ+µ- or e+e-

M = 3872.0 ± 0.6 ± 0.5 MeVΓ< 2.3 MeV (90 % C.L.)

X(3872) seen also by CDF

M = 3871.4 ± 0.7 ± 0.4 MeV


What is the X(3872) ?The mass of the state is right at the D0D0* threshold, this suggests aloosely bound D0D0* molecule. “Molecular Charmonium”

13D2 state. Because D-states have negative parity, spin 2 states cannot decay to DD. They are narrow as long as below the DD* threshold.

32

32

( (1 ) / )~ 3

( (1 ) / )BR D J

BR D Jψ

ψπψ πψγγ

+ −

→→

BR XBR X J

c( ( ) )( ( ) / )

.3872

38720 891→

→<+ −

γχπ π ψ

(90% CL) Bellehep-ex/0309032

Predict

BUT

Most models predict the ψ(13D2) mass ~70 MeV lower than X(3872) mass.At the same time they reproduce the Υ(13D2) very well. No models canaccomodate ψ(3770) and X(3872) in the same 13DJ triplet.Can coupled channel effects and ψ(13D1)- ψ(23S1) mixing change this ?

A Charmonium Hybrid

1.

2.

3. S. Godfrey – QWG03


It is extremely important to identify all missing states abovethe open charm threshold and to confirm the ones for whichwe only have a weak evidence.This will require high-statistics, small-step scans of theentire energy region accessible at GSI.

Charmonium States abovethe DD threshold


Proton Timelike E.M. Form Factors

The electromagnetic form factors of the proton in the time-like regioncan 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 theasymptotic behavior of the form factors and the spacelike-timelikeequality at corresponding values of Q2.

( ) ( ) ( )

−++= *22

2*22

222

* cos14

cos12cos

θθπαθ

σE

pM G

s

mG

xsc

dd h


Predictions of nucleon form factors are applicable up to high Q2 in both the spacelike and timelike regions.• Perturbative QCD and analyticity relate timelike and spacelike form factors,

predicting a continuous transition and spacelike-timelike equality at high Q2.• At high Q2 PQCD predicts:

F1 and F2 are the Dirac and Pauli form factors respectively.• PQCD and analyticity predict:

There are several unexpected features in the existing data which deserve further experimental investigation:• Threshold Q2 dependence.• High Q2 predictions.• Resonant structures.

6

222

24

222

1

)()(

)()(

QQ

QFQ

QQF ss αα

∝∝

25.022

=

≈

u

dp

M

nM

qq

GG


E835 Backgrounds

The main background sources for the form factor analysis come from the following reactions:• J/ψ + X inclusive events, with J/ψ→e+e- and X

undetected σ′J/ψX<1.6×10-2 pb• Photon conversions and πº Dalitz decays from:

– pp → πºπº– pp → πºγ– pp → γ γ

σp<3.1×10-3 pb• Hadronic two-body final states, mainly pp → π+π-

σh<4.3×10-3 pb


E835 measurement ofσ(pp→e+e-)

<1.5×10-23450.5012.43

<2.3×10-23232.8611.63

σback

(pb)σacc

(pb)NL

(pb-1)s

(GeV2)17.034.010.029.061.1 ++

−−

12.023.007.019.011.1 ++

−−


Measurement of the Form Factor

+=

Ω= ∫∫

+

−

22

22

*cos

*cos

2

0

4

2

)*(cosmax

max

Ep

Mp

acc

GBs

mGA

s

ddd

d

βπα

θσ

φσθ

θ

π

E835 statistics not sufficient to measure the angular distribution (andthus determine GE and GM separately. Calculate GM under two hypotheses:• (a) GE = GM• (b) GE contribution negligible


The dashed line is the PQCD fit:

Λ

=

222 ln

ss

CG

p

M

µ

E835 Form Factor Measurement

12.4311.63

102× |GM|(b)

102×|GM|(a)

s(GeV2)

11.018.007.016.074.1 ++

−−12.020.008.017.094.1 ++

−−08.015.005.013.048.1 ++

−−09.017.005.014.063.1 ++

−−

•(a) GE = GM•(b) GE contribution negligible


Form Factor Measurement in Panda

In Panda we will be able to measure the proton timelike form factorsover the widest q2 range ever covered by a single experiment, fromthreshold up to q2=30 GeV2, and reach the highest q2.• At low q2 (near threshold) we will be able to measure the form

factors with high statistics, measure the angular distribution (and thus GM and GE separately) and confirm the sharp rise of the FF.

• At the other end of our energy region we will be able to measure the FF at the highest values of q2 ever reached, 30 GeV2, which is 2.5 larger than the maximum value measure by E835. Since the FF decrease ~1/s5, to get comparable precision to E835 we will need ~80 times more data.

• In the E835 region we need to gain a factor of at least 10-20 in data size to be able to measure the electric and magnetic FF separately.


Form Factor Measurement in Panda

4104100?0.01482301651650?0.034332555550?0.100112015150?0.3703155500.0151.11112.43

days∫Ldt(pb-1)

σbck

(pb)σ

(pb)factors

(GeV2)

•Values of cross sections at various energies assuming 1/s5 scaling.•The same angular acceptance as E835 is assumed.•Integrated luminosities and running times required to achieve the sameaccuracy as E835-II.

•Backgrounds need to be evaluated at the higher energies. The majorbackground component, J/ψ+X, increases with energy !


Summary

The measurement of the e.m. form factors of the proton inthe timelike region has considerable physics interest. In order to make the measurement in Panda we need:• High statistics, in order to measure GE and GM

separately, and in order to be able to carry out the measurement at the highest q2 values.

• excellent electron ID capability (at least as good as E835)

• Excellent background rejection (mainly from π0π0, π0γ, γγand π+π-).


Conclusions

• The B-factories have proven very effective in providing new results in charmonium (and bottomonium).

• Over the next few years more data will come from BaBar, Belle, Cleo-C, BES.

• Charmonium production from Tevatron, DESY, LHC.• Still pp annihilation is unbeatable for

– high-precision measurements, in particular of narrow resonances (e.g. hc(1P1))

– systematic scans of extended energy regions (e.g. region above DD threshold)

• Measurement of the proton time-like form factors over the widest q2 range ever covered by a single experiment

Documents

Charmonium Spectroscopy - GSID. Bettoni - Charmonium 5 Experimental Method The antiproton beam momentum is varied in small steps (≤ 150 KeV/c) around the resonance under study and