Structure and formation spectraof Dbar meson-nucleus systems
Junko Yamagata-Sekihara(Nara Women’s Univ.)
Collaborator :L. Tolos (Barcelona Univ.)
J. Nieves (IFIC, Valencia Univ.)
C. Garcia-Recio (Granada Univ.)

Contents• Introduction• D-(cd)-Nucleus systems• D--Nucleus interaction• D- -11B bound systems• Formation spectrum by 12C(p,D) reaction• D0(cu)-Nucleus systems• D0-Nucleus interaction• D0-11B bound systems• Formation spectrum by 12C(p,D) reaction• Summary- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

Introduction• Meson-Nucleus systems are very importantand useful objects to extract the meson
properties at finite density.
Pionic atoms, Kaonic atoms/Kaonic nuclei,
Eta mesic nuclei, Eta’ mesic nuclei,
Phi mesic nuclei …
Recently, heavy meson-nucleus systems arestudied by many theorists. One of the mostinteresting meson ismeson, which has acharm quark.

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

Introduction• Theoretical Works- Tsushima, Lu, Thomas, Saito, Landau, PRC59(99)2824
Quark-meson coupling model, Dbar in 208Pb.
- Yasui, Sudoh, PRD80(09)034008- Yamaguchi, Yasui, Hosaka, NPA927(14)110
Heavy Quark Symmetry. One pion exchange interaction.
DbarN bound state, DbarNN bound state- Garcia-Recio, Nieves, Tolos, PLB690(10)369
D0 in 12C up to 208Pb, D+ in 12C- Garcia-Recio, Nieves, Salcedo, Tolos, PRC85(12)025203
D- in 12C up to 208Pb- Ikeno, Nagahiro, Hirenzaki, JPS Meeting 2010
Formation spectrum of D0 in 12C by Effective number approach- Nagahiro at KEK workshop, Formation spectrum of D- in 12Cetc …

• Experiments- New Facility FAIR @ GSIHigh intensity pbar beam up to 15 GeV/c.
- J-PARC

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

Introduction• Our motivation- We’d like to know the possibility of theobservation forbound states by 12C(pbar,reaction at the incident p beam = 8GeV/c.

)- We’d like to focus on the structure of theformation spectrum.
“ The peak structure corresponding to bound states
appear or not”

- This is the first calculation for the formation
spectra formesic nuclear states with energy
dependent optical potential with the Green’s function
method .

- Intro.

mesic Nucleus- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary•(cq)meson-nucleus Interaction

Garcia-Recio, Nieves, Salcedo, Tolos, PRC85(12)05203.

- Unitarized coupled-channel theory
I=0

J=1/2

I=1

J=1/2

- Medium effect• Optical potential with 11B at E=0

- Intro.

- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

mesic Nucleus• Klein-Gordon equation

- Intro.

mesic Nucleus- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary• Klein-Gordon equation• Bound state for 11B
Atomic State

Nuclear Sate : BE (Width) [ MeV ]1s : 21.662 (0.458)
2p: 14.451(2.359)

Only Coulomb

Deeply bound Dbar mesic nuclear states
exist with narrow width !!

How can we observe these states ?

- Intro.

- Dbar Nucleus-Interaction-Bound Systems-Formation
Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

mesic Nucleus• Formation reaction
Target Nucleus : 12C• Momentum transfer
We consider the incident pbar beam as 8 GeV/c.
This energy will be achieved in PANDA
experiments at the future FAIR facility.

- Intro.

- Dbar Nucleus-Interaction-Bound Systems-Formation
Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

mesic Nucleus• Formulation : Green’s function method

In this calculation, we doesn’t include the elementary crosssection.
So, the calculated formation spectra has arbitrary unit.
This is very simple calculation of the formation spectra.
We’d like to know if the signals of bound states could appear inthat spectra or not.

- Intro.

- Dbar Nucleus-Interaction-Bound Systems-Formation
Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

mesic Nucleus• Formulation : Green’s function method

In this calculation, we doesn’t include the elementary crosssection.
So, the calculated formation spectra has arbitrary unit.
This is very simple calculation of the formation spectra.
We’d like to know if the signals of bound states could appear inthat spectra or not.

- Intro.

- Dbar Nucleus

mesic Nucleus-Interaction-Bound Systems-Formation
Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary• Results : formation spectra

2p state
Nuclear Sate :1s : 21.662 (0.458)
2p: 14.451(2.359)

Preliminary

The peak corresponding to the 2p state might appear, and very small.
One of the reason of that is the momentum transfer is very large.
In this calculation, we consider Dbar state up to L=15.
 Different formation reaction is needed to get clearer peak structure.

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

mesic Nucleus•

meson-nucleus Interaction

Tolos, Garcia-Recio, Nieves, PRC80(09)065202.
Garcia-Recio, Nieves, Tolos, PLB690(10)369.

- Unitarized coupled-channel theory- Medium effect• Optical potential with 11B at E=0

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction

mesic Nucleus• Klein-Gordon equation-Bound systems-Formation Spectrum- Summary• Bound state for 11B
Nuclear Sate : BE (Width) [ MeV ]1s : 6.525(10.78)
Deeply bound D0 mesic nuclear states exist !!
This result is consistent with Ikeno’s calculation.

Does this state appear in the spectrumby (pbar,Dbar) reaction ?
From Ikeno’s slide @ JPS Meeting 2010

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems

mesic Nucleus• Formation reaction-Formation
Spectrum- Summary• Momentum transfer

Target Nucleus : 12C
The difference of D0 and Dbar
production is just the emitted
particle.
In this case, the emitted
particle is Dbar meson.

As same as Dbar mesic nucleus, we consider
the incident pbar beam as 8 GeV/c.
This energy will be achieved in PANDA
experiments at the future FAIR facility.
Momentum transfer is almost same as Dbar
production.

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems

mesic Nucleus• Formulation : Green’s function method-Formation
Spectrum- Summary

Elementary Cross section (Theory)• aAssumption :a flat angular distribution in CM.

0.05 mb

Kaidalov, Volkovitsky,
ZPC63(94)517

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems

mesic Nucleus• Formulation : Green’s function method-Formation
Spectrum- Summary- Distortion factor F(r)Theory :J. Haidenbauer et al., EPJA37(08)55

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus

mesic Nucleus• Results : formation spectra-Interaction-Bound systems-Formation
Spectrum- Summary

2p state
Nuclear Sate :1s : 6.525(10.78)

The peak corresponding to the 1s state doesn’t appear.
The momentum transfer is very large.

Preliminary

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus

mesic Nucleus• Results : formation spectra-Interaction-Bound systems-Formation
Spectrum- Summary

Nuclear Sate :1s : 6.525(10.78)
Preliminary
There are two peaks in the spectrum.
However, we don’t have an eigen state around this energy.

What are these peaks ?

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus

mesic Nucleus• Results : formation spectra-Interaction-Bound systems-Formation
Spectrum- Summary

Nuclear Sate :1s : 6.525(10.78)
PreliminaryThere are two peaks in the spectrum.
However, we don’t have an eigen state around this energy.

What are these peaks ?

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus

mesic Nucleus• Results : Formation spectra-Interaction-Bound systems-Formation
Spectrum- Summary

Shell model
L=0 L=1 L=200

Preliminary
Two peaks appear in each angular momentum of D0 meson at similar energy.
According to the shell model structure, it is strange that L=0 and L=1 havebound states at similar energy.

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum

Optical potential (rho, E)- D0 Nucleus-Interaction-Bound systems-Formation
Spectrum- Summary

These structures may
appear from the energy
dependence of thestrength of the opticalpotential.

This origin is from theandstates as meson-baryon
bound state..
Tolos, Garcia-Recio, Nieves,PRC80(09)065202.

Preliminary???

???

- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

Summary• We calculated the formation spectra of
mesic
nuclear states via pbar beam.
•mesic nuclear states exist as same as othertheoretical works.
• We consider the (pbar,) reaction at = 8GeV/c.
• The momentum transfer is large.
• For meson, 2p bound state may appear as smallpeak.
• For meson, the bound state doesn’t appear in
the spectrum, but large peaks appear at deepenergy region in this work.
• We should consider different production reaction
with small momentum transfer.

Ikeno’s slide @ JPS Meeting 2010

• We calculated the formation spectra of
mesic
nuclear states via pbar beam.
•mesic nuclear states exist as same as otherwork.
• It is difficult to observe the bound states by(pbar,) reaction at = 8 GeV/c.
• The momentum transfer is large.
• We should consider different production reaction
with small momentum transfer.
Future Work• We do more realistic calculation.
(Elementary cross section, Distortion factor
Different reaction … )- Intro.
- Dbar Nucleus-Interaction-Bound Systems-Formation Spectrum- D0 Nucleus-Interaction-Bound systems-Formation Spectrum- Summary

Summary
Future Work• We do more realistic calculation for both meson.
(Elementary cross section, Distortion factor
Different reaction … )Dbar meson nucleus potential
Garcia-Recio, Nieves, Salcedo, Tolos, PRC85(12)05203.
I=0

J=1/2

I=1

J=1/2

- SU(8) spin-flavor symmetry- The optical potential is obtained by Tρ approximation.
Amplitude T has a pole X(2805) state : I=0, J=1/2- Decay mode :For atomic states, a bound Dbar meson may falls to lower level.
For nuclear states, the decay width comes from the existence ofX(2805) state, which appears around threshold energy.

D meson nucleus potential
Tolos, Garcia-Recio, Nieves, PRC80(09)065202.
Garcia-Recio, Nieves, Tolos, PLB690(10)369- SU(8) spin-flavor symmetry- Optical potential is obtained by T ρ approximation.
- Amplitude T has a pole of Σc(2556) state (I=1, J=1/2) and Λc(2595) state (I=0,J=1/2).