Charmonium Dynamicsat

Thresholds

H. Lenske

Institut für Theoretische Physik, JLU Giessen

and

GSI Darmstadt

2

Agenda:

• Charmonium Spectroscopy

• Charmonium Production

• Physics Content of Line Shapes

3

Charmonium at the DD-Threshold

• Closed quarkonic channels: confined cc states• Closed hadronic channels : sub-threshold DD-states• Open hadronic channels : DD-channels

4

Charmonium Spectroscopy in the Quark Model

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Quarkonium: Confined Systems of Heavy (cc,bb) Quarks

cc

e- e+

6

Charmomium Spectrum in the Quark Model

0

4( ) ( , )

3Breit s

hyperfineV r V r V rr

J. Lopez, H.L., 2014

• Unified description of D-mesons and Charmonium• Spectra, wave functions, form factors…

7

Charmonium Production and Spectroscopy at the Threshold

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The „BIC“-view of Continuum Spectra

• Closed channel E* is embedded into a continuum of open channels• E* decays only via interaction V(r) with open channels

BIC - Bound State Embedded into the Continuum Scale-independent, universal phenomenon

BIC{

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• Quark model description of charmonium and D-mesons• „3P0“ Lagrangian for pair creation in ccD(cq)D(qc) coupling

gm h.c. 30

q q qPL

Charmonium Wave Function at the DD Threshold

3 1c b b k DD

b DD

3 3 31 1 1

0 0 *0 0

~ z (cc) d k z k

e.g. b= '(3686)2 S , ''(3770)1 D , '''(4040)3 S ...

DD=D D ,D D ,D D ...

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Channel Coupling and the 13D1 cc Component of y(3770)

2 1( ) Im ( )

JS G

1

( ) 1 ( )P

Spectral Distribution Spectral Factor

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DD elastic scattering: total p-wave cross sectionIsoscalar 2p and vector meson exchange plus channel coupling

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Charmonium Production Scenario:Coherent cc and DD production

Quarkonic HadronicProduction Form Factor

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Spectral Properties of cc-States(Cornell-Breit Potential)

Quark Model predictions for e+e- width and 3D1 suppression:

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3 1c b b k DD ~ z (cc) d k z k

Wave Function at the Charmonium Threshold

Single confined channel b=y(13D1) and single open channnel s=DD:

} }

Quarkonic„hard“ component

Hadronic„soft“ component

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Production Cross Sections at the Charmonium Threshold

2

rDD 2

r

q cote e DD ~

1 cot

c sr1

cDD

| T | e e x ( ) q= ; cot

x ( )k | T | e e

Single confined channel c=y(13D1) and single open channnel s=DD:

2

( )1

c s

qM T

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2

rDD 2

r

2 3 21F DD

DD DD5/2

20R

r R R RR R

q cote e DD ~

1 cot

8 kk T e e

3s

m scot ; m m m (s)

m (s)

Charmonium Production@BES III and PANDA:BIC and Fano-Resonances

The line shape parameter:

b

1DD

(cc) | T | e e q=

k | T | e e

• Controlling the line shape asymmetry • Indicator of the reaction scenario: quarkonic vs.

hadronic

Xu Cao, H. L., arXiv:1408.5600 [nucl-th]

DD-Dynamics at Threshold Channel Coupling and the Line Shape of y‘‘(3770)

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0 0D D threshold

3729.7 MeV

D D threshold

3739.2 MeV

3.65

(2s / 3686)

X(3900) ??

q=-2.1±0.3

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Line Shape of Reaction Form Factor and Physics Content

cc

DD

| T | Quarkonic q= ~ e e , pp ,...

k | T | Hadronic

q=-0.2 q=-1 q=-10

Dominance of hadronic

production

balanced quarkonic and

hadronic production

Dominance of quarkonic production

• Line shape controlled by quarkonic content • Line shape depends on production reaction• Spectral distribution of the SAME final state depend on initial state

cc

cc

cc

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Production of y‘‘(3770) and the DD Spectral Distributions

(Data: BES Collaboration)

Derived Parameters:

Xu Cao, H.L., 2015

20Science 340,716 (2013)

Laser-Modelling of Fano-Line Shapes

Defining features of Fano-Resonances:

Asymmetric line shapes and GR<<mR

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Summary and Outlook

• Charmonium Spectroscopy

• Dynamics of charmonium production in (e+,e-), (p,p)…

• Resonances, closed and open channels

• Charmonium cross sections and spectral distributions

• Physics content of charmonium line shapes

• Charmonium production and spectroscopy at PANDA

• Production of charmed baryons at PANDA

Credits to Xu Cao, Juan Lopez, and Radhey Shyam