何康林

中科院高能所,hekl@ihep.ac.cn

粲偶素态的实验研究

1

OutlineIntroductionCharm mesons1−− charmonium (above threshold) ISR(Initial State Radiation) correctionCharm production cross section measurement

Below D*D thresholdAbove D*D threshold

Energy dependent charm cross sectionExotic charmonium statesSummary

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What’s charmoniumPotential model

Charmonium spectrumOpen charm threshold

Introduction

3

What is charmoniumBound state of a charm quark and its anti-quark

Quantum number: n, L, S, JParity and charge conjugate: P=(-1)L+1,C=(-1)L+S

Not all JPC are allowed (e.g. 0+-,0--,1-+,2+- forbidden)

rc c

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Potential modelc-quarks are heavy, mc~1.5GeV, velocities small: v/c~1/4, non-relativistic QM can be applied

Ψ=Ψ+Ψ∇− ErVmr

)(2

22

s4V(r) ~ br3 r

α− +

Colombic short distance component

large distance component

5

Charmonium spectrum

DDb threshold

Most of them areNot observed

Observed byexperiment

6

Decay propertyBelow open charm threshold

Only electromagnetic or αs suppressed decay are allowed mostly narrow states Good place to study the light hadron spectrum

Above open charm thresholdDDb decays are allowed mostly board states Ideal charm factory

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Non-DDbar decay

8transition

Measure the quantum numbersProduction

Same JPC (1−−)as photon in e+e− collision

C=+ in two photon (γγ) production

DecayAngular distribution of decay products JP

Prefer to 2-body decays (e.g., γ+X)

Selection rulesConservation of J

Conservation of P and C in strong and EM decays, Isospin in strong decay

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Charmonium spectrum --below DDb threshold

DDb threshold

ψ, ηc, χc, hc10

Open charm thresholds

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D0, D+, Ds mesons

D* mesons

Reconstruction of charm mesons

Charm mesons

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D0 mesonc,u-bar quark

M~(1864.5±0.4)MeV, τ~(410.1±1.5)×10-15 sec

Decay modes

mode fractions

K−π+ 3.80%

K−π+π0 14.1%

Ksπ+π− 2.9%

K−π+π+π− 7.72%

Κ−e+ν 3.51%

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D+ mesonc, d-bar quark

M~(1869.3±0.4)MeV, τ~(1040±7)×10-15 sec

Decay modesmode fractions

Ksπ+ 1.47%

K−π+π+ 9.51%

Ksπ+π0 7.0%

K−π+π+π0 5.5%

Ksπ+π+π− 3.11%

K0e+ν 8.6%

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Ds mesonc, s-bar quark

M~(1968.2±0.5)MeV, τ~(500±7)×10-15 sec

Decay modes mode fractions

K+K0b 4.4%

K+K−π+ 5.2%

φπ+π0 11%

ηπ+ 2.11%

ηρ+ 13.1%

φl+ν 2.4%

μ+νμ 0.6%

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D* mesonD*+ D*0 Ds*

Mass ~2010 MeV ~2007 MeV ~2112 MeV

mode fractions

D*0

D0π0 61.9%

D0γ 38.1%

D*+

D0π+ 67.7%

D+π0 30.7%

D+γ 1.6%

Ds*

Ds+γ 94.2%

Ds+π0 5.8%

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The Q values for D* D transitions

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Q: D momentum in D* rest frame

Reconstruction of charm mesonsReconstruction of D mesons

Lots of decay channels branching ratios smallerHigher multiplicities , low momentum tracks reconstruction efficiencies lower

Reconstruction of D* mesonsHard to reconstruct the soft pions

Reconstruction of charmonium from DDb productionIdentify production procedure by momentum distribution of reconstructed D mesonsExtremely difficult for transition procedure like ψ γχc, χc DDb

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Resonant parameters

ψ(3770)

ψ(4040)

ψ(4160)

ψ(4415)

1−− charmonnium

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1−− charmonium states

ψe+

e-

Important BES contribution to R

( hadrons)( )e eRe e

σσ μ μ

+ −

+ − + −

→=

→

DDb thresholdCharmonium spectrum from potential model20

σ(e+e− hadrons)Non-resonance contribution

e+e− γ* hadrons (u, d, s quark anti-quark pairs)

Resonance contributione+e− γ* Res hadrons

N L σ ε= ⋅ ⋅Monte Carlo

Luminosity

Cross section21

Resonant parametersBorn order σ(e+e− Res hadrons) is described by a Breit-Wigner formula

ee2 2 2

12πΓ( )( - M )+M Γ

ss

σ Γ=

M: central mass of resonanceΓ: total decay width of resonanceΓee: partial width of resonance decay to e+e− pair√s: energy of center-of-mass system

eepeak 2

12πM

σ Γ= ×

Γ

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Resonant parameters of 1−− charmoniumstate M Γ Γee

J/ψ 1S ~3096.9 MeV ~93.4 keV ~5.55 keV

ψ(2S) 2S ~3686 MeV ~337 keV ~2.48 keV

ψ(3770) 1D ~3771 MeV ~23.0 MeV ~0.242 keV

ψ(4040) 3S ~4039 MeV ~80 MeV ~0.86 keV

ψ(4160) 2D ~4153 MeV ~103 MeV ~0.83 keV

ψ(4415) 4S ~4421 MeV ~62 MeV ~0.58 keV

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The decay width of 1-- charmonium

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Theory model can not predict decay width to D*D,D*D* very well The experiment results need improvingGood opportunity at BESIII

Charm cross section predicted bycoupled-channel model

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ψ(3770): a 13D1--23S1 mixing state

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Generally, ψ(3370) is assumed to be the 13D1 state, perhaps with a significant 23S1 component

3 31 1(3770) cos 1 D sin 2 Sψ = θ + θ

Γexp~23 MeV θ~−17º

ee

ee

0.10 0.03(thy)( (3770))0.12 0.02(exp)( (3686))

±⎧Γ ψ= ⎨ ±Γ ψ ⎩

ψ(3770): decay and production X- sec

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Almost 100% decay to DDb, small fractions (<5%) to non-DDb (e. g. π+π− J/ψ)

Isospin conservation and P-wave phase space

0

30 0

D

D

p( (3770) D D ) 1.45( (3770) D D ) p +

+ −

⎛ ⎞σ ψ →= =⎜ ⎟⎜ ⎟σ ψ → ⎝ ⎠

~1.3—1.4

Suppressed by a 3D1 form factor

ψ(3770): decay angle

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(3770) DDψ →

JPC

ψ(3770) 1−−

D 0−+

2P(cos ) sinθ = θ

a vector resonance decay to a pair of pseudoscalars, they should be produced with the angular distribution P(cosθ)=sin2θ, θ is the polarangle

ψ(4040) and ψ(4160)

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DDb production is much smaller

D*D dominate at ψ(4040), D*D* dominate at ψ(4160)

σ(Ds*Ds) at ψ(4160) ~ 3 σ(DsDs) at ψ(4040)

ψ(4040): a D*D* molecule?

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*0 *0 *0 0 0 0B(D D : D D : D D ) ~ 1:1.2 : 0.09

*0 *0 *0 0 03

0B (D D : D D : D D ) ~ 128p

: 5 : 0.15

*0 *0 *0 0 0 0D D D D D D>> >>ψ(4040) might be a D*D* molecule

ψ(4040)

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ISR (Initial State Radiation)

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Radiation correction

ISR and FSRInterference between ISR and FSRRadiation correction in Particle decays ( DR)

Important to electron-contained final state PHOTOS

CEEX(Coherent Exclusive Exponentiation)

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Observed cross section

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In e+e− collision, the observed cross section for a certain physics procedure is the contribution of

Born order cross sectionFor resonance, a Breit-Wigner

Radiation effectsBeam energy spread

Gaussian appoximateImportant for narrow resonance

Effective CMS energy

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Only ψ

(3770)D

Db

is considered

CMS energy shift

ISR effects to physics analysis

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reso

lutio

nsef

ficie

ncie

s

ISR tails

Special function needed when Fitting the mass plot

The feature of ISR photons

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Distributed around beam direction

might be more than one ISR photons, most of them are not detectable (low energies)

Small probability for large ISR photons

Special trigger and large coverage solid angle detector provide a opportunity to study 1– charmonium states at high energy region, e.g. B-factories

Charm production cross section from Belle (ISR measurements)

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Resonance Generation at BESIII

1. ρ, ω, φ2. ρ', ω', ρ", φ' (Γee is not well measured)3. J/ψ, ψ(2S), ψ(3770), ψ(4030), ψ(4160), ψ(4415)

1. Beam energy spread2. ISR and FSR return3. Generate μ-pair, τ-

pair and hadron events according to their cross section

4. For hadron events:• Quark and anti-

quark pairs• Resonances

5. Generated particles are send to programs to handle particle decays or to simulation programs

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Below D*D threshold

Above D*D threshold

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Measurements of charm production cross section

Event display for charmonium to DDb

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0 0(3770) D Dψ → *s s(4160) D D+ −ψ →

Charm tag

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Single tag: charm mesons are pair produced, fully reconstructing a D decay from a subset of tracks in an event therefore guarantees that the remaining tracks originated from the recoiling Dbar.

The reconstructed D is referred to as the tagged D or simply the tagEverything not associated with the tag is referred to as recoil.Once a tag has been obtained, the recoil track can be analyzed for the decay modes of interest

Double tag: both D and Dbar are fully reconstructedFlavor tag, CP tag, semi-leptonic tag, etc.

Charm tag below D*D threshold

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( ) ( )2 2

2 2

E

= −

= −Δ = −

∑ ∑inv i i

bc b

D

D

b

M E p

EM E

Ep

Since the D's are pair produced and the Laboratory frame is also the rest frame of the DD system, each D is produced with an energy equal to that of the beamin the laboratory frame.

Cross section measurement

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i i iDDS 2 N B= × × ×ε

i j ijDDij 2

i iiDD

2 N B B i jD

N B i j× × × × ≠⎧

= ⎨ × × =⎩

εε

2i j i j i jDDS S 4 N B B× = × × × × ×ε ε

i j ij

ij i jDD 2

i ii2

ii i

S S1 i j2 D

NS1 i j

4 D

×⎧× × ≠⎪ ×⎪= ⎨

⎪ × × =⎪⎩

εε ε

εε

~1

0 0

0 0

0 0 0

D K , K , K

D K , K ,K

D K , K

− + − + − + + −

+ − + + + + + −

+ + − + +

→ π π π π π π

→ π π π π π π

→ π π π π π

Cabibbo favored hadronicdecay modes, with large branching ratios, are selected to be as tags.

Lots of systematic cancelledWhen applying double tagtechnique

BESII measurement: σψ(3770)

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0 0D D

D D

DD

(3.44 0.24 0.16)nb

(2.37 0.29 0.14)nb

(5.81 0.38 0.22)nb+ −

σ = ± ±

σ = ± ±

σ = ± ±Single tags

Double tags

CLEOc measurement: σψ(3770)

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0 0

0.070.05D D0.100.04D D

0.170.08DD

(3.60 0.07 )nb

(2.79 0.07 )nb

(6.39 0.10 )nb

+ −

+−

+−

+−

σ = ±

σ = ±

σ = ±

Charm tag above D*D threshold

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The low Q value of the hadronic decay modes of the D* provides a clean method to identify charm.

To determine charmed meson cross sections above the D* production threshold, requires the D* branching ratios.

D mesons can be produced either directly or as decay products of D*‘s through DD, D*D, D*D*

The recoil mass squared spectrum will provide clean information to identify the production procedure

2 2D Du ( s E ) p= − −

D tagging above D*D threshold

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D meson from D*D*,D*D and DD can be Clean identified by Momentum CUT

BES I√s=4.03 data

D0 KπD

*D*

DD

D*D

Monte Carlo simulation at BESIII

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*(4040) D Dψ →

production Original D

D*0D0 direct D

D*0D0 D*0 π0D0

D*0D0 D*0 γD0

D*+D− D*+ π+D0

D*+D− direct D

D*+D− D*+ π0D+

D*+D− D*+ γD+

D momentum distributions are obtained byMC simulation, ISR, ψ(4040) lineshape, beamEnergy spread are taken into account

Sim

ulta

neou

sly fi

t

Tag reconstruction(√s=4.14GeV)

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Recoil mass fitting(√s=4.14GeV)

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Xsec measurement with double tag method above D*D threshold

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Single tag reconstruction

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D0 Kπ

D0 Kπππ

D+ Kππ

D*D D*D*

Double tag reconstruction(D*D)

53

Double tag reconstruction (D*D*)

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Results

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measure measure

2 2measure predict measure predict2

2 2

( ) ( )

i ij

i i ij ij

i ijS D

S S D Dχ

σ σ− −

= +∑ ∑

0

0

* 0

Br( ) (3.95 0.58 0.26)%Br( ) (8.24 1.12 0.57)%Br( ) (9.6 2.9 1.4)%Br( ) (51 11 5)%

D KD KD KD D

ππ π π

π ππ

− +

− + + −

+ − + +

+ +

→ = ± ±→ = ± ±

→ = ± ±→ = ± ±

Replace by a likelihoodfor low statistics double tagχ2=−2logL

0 *0

*

*0 *0

* *

( ) (2.46 0.51)nb( ) (2.31 0.65)nb

( ) (2.07 0.37)nb( ) (0.87 0.22)nb

D DD D

D DD D

σ

σ

σ

σ

±

±

= ±

= ±

= ±

= ±

∓

∓

Lower than world average value(~68%), it hints there might be a DDπ(γ) moleculeat ψ(4040), but not confirmed by experiment

Around ψ(3770) (BESII)

3.97--4.26GeV (CLEO-c)

cross section using initial-state radiation (BELLE)

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Energy dependedcharm cross section

Energy dependent production cross section

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The observed cross section is the total contribution of born order cross section, the ISR kernel function and beam energy spread

A correction factor is needed for a certain energy point. The typical values of ISR correction factors are between 0.7—0.8 for ψ(3770), ψ(4030), ψ(4160), etc

How to get energy dependent cross sectionEnergy scan experimentISR in high energy region

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D0 K−π+

D+ K−π+ π+

Energy dependent cross section around ψ(3770) from BESII

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Get # of events in each energy point

Calculate luminosity in each energy point

σ(E)’s are normalized by the σpeak

ISR effects to D tag reconstruction efficiencies are taken into account

σ(ψ

D0 D

0 bar

)σ(

ψD

+D

− )

Open Charm Production in e+e-Annihilations ECM = 3970-4260 GeV

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Primary CLEO-c motivations:Determine optimal energy for Ds studiesAssess capabilities for D physics above y(3770)

Additional Objectives: Detailed study of “intricate behavior” of hadronic cross section in the region above open-charm threshold. Y(4260): confirmation

Scan Data Sample:12 energies, 60 pb-1

20pb-1 around 4.17 GeV

Tag reconstruction

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DD

DD*

D*D*

DsDs

DsDs*

MC Ds φπ Ecm = 4160 MeV

Cut on ΔE, use Mbc toextract yields

Cut on Mbc, use invariantmass to extract yields

σ(D*D*, D*D, DD)

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Plateau in D*D*

Very little DD

D*D Enhancement at D*D* threshold

σ(DsDs, Ds*Ds, Ds*Ds*)

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Location that maximizes the Ds

+ yield.

Peak structure in DsDs

Charm cross section using initial-stateradiation (e+e− γ + D(*)+D*−)

64

ISR photon is required

D0 candidates are reconstructed using five decay modes

D+ candidates are reconstructed using the decay modes

D*+ candidates are selected via D*+ π+D0

Recoiling mass of

will appear in a peak around D*+ mass

0SK ,KK,K ,K ,Kπ πππ ππ ππ

SK ,K ,KKπ ππ π

(*) (*)ISR ISR

(*) 2 2rec ISR CMS D D

M (D ) (E E ) p+ ++

γ γγ = − −

Belle measurements

65

* *(e e D D )+ − + −σ →

*(e e D D )+ − ±σ → ∓

Similar technique can be use to obtain σ(DD) and maybe the σ(D*0D0) , butdifficult to σ(D*0D*0)directly.

66

Measurementof resonanceparameters of highercharmoniumstates

Interference effects must be taken intoaccount carefully

In addition, the non-resonance DDbar production should be included

X(3872)The 1– family, Y(4260) etc

The 3940 familyCharged states

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Exotic charmonium states

X(3872) ππ J/ψ

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The X(3872) puzzle

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Not matching any predicted state?

Above DD threshold (allowed):should have large width but it is narrow

Charmonium is suppressed due todecay into J/ψ ρ (isospin violation)

Open options•DD* molecule

•Right at the threshold•favours DD* decay over J/ψππ over J/ψγ(as observed)

•Tetraquark•Explains small width•Predicts a set of 4 states (2 charged and2 neutral).

•Finding the charged states is critical•Charmonium

•Not ruled out, but which state is it?

X(3872) D0D*0

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Belle [PRL 97, 162002 (2006)] observed X(3872) D0D0π0

Confirmation and integration from BaBar in B DD*K

The 1– family: Several bumps observed in e+e- Y γISR

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A new state: Y(4260)PRL 95, 142001 (2005)

Yet another state Y(4350)PRL 98, 212001 (2007)

The youngest of the 1-- family

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The 3940 family

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Y J/ψωX D*D

The first charged state: Z(4430)

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summary

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Charmonium below DDb threshold completed

Above open charm threshold, lots of blanks need to be filled

Exotic charmonium states discovered recently need understanding

BESIII will have great opportunities to make contribtions to charmonium physics

祝同学们学习愉快！谢谢！！