nuclear symmetry energy from qcd sum rule the 5 th apfb problem in physics, august 25, 2011 kie sang...
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![Page 1: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/1.jpg)
Nuclear Symmetry Energy from QCD Sum Rule
The 5th APFB Problem in Physics, August 25, 2011
Kie Sang JEONG
Su Houng LEE (Theoretical Nuclear and Hadron Physics Group)
Yonsei UNIV.
![Page 2: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/2.jpg)
Motivation 1 – KoRIA plan
• Rare Isotope Accelerator Plan
(Quoted from Physics Today November 2008)
Nuclear symmetry energy plays key role in Rare Isotope and Neutron Star study
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Motivation 2 – RMFT vs QCD SR
• Dirac phenomenology of nucleon scattering on nuclear target suggest nucleon potential to consist of strong vector repulsion and scalar attraction
• This tendency also comes naturally in RMFT• For symmetric nuclear
matter, it is confirmed that this result can be justified with QCD, by Thomas Cohen et al. (1992)
• Motivated by these results, we applied QCD Sum Rule to asymmetric nuclear matter
Physical Review C 49, 464 (1993)
![Page 4: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/4.jpg)
Early attempt for finite nuclei
• Liquid drop model • Total shifted energy
Total shifted state number
Nuclear symmetry energy
We can generalize this concept to infinite matter case
![Page 5: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/5.jpg)
For infinite matter
• Energy per a nucleon
• Single nucleon energy
• Averaged single nucleon energy
Nuclear Symmetry Energy
![Page 6: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/6.jpg)
Mean field approximation
• Nucleon propagator in nuclear medium
How we can get nucleon self energies in the fundamental principle?QCD Sum Rule is well established method for investigating quasi-particle in medium
• Quasi-particle on the Fermi sea
(Up to linear density order)
![Page 7: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/7.jpg)
QCD Sum Rule
• Sum Rule Correlator
• At short distance, we can calculate Wilson coefficient in the OPE
• Phenomenological ansatz
• Borel transformationIoffe’s interpolating field for proton
To exclude the quasi-hole and continuum excitation
do not depend on external momentum
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• Iso-scalar and Iso-vector operator
• Scalar condensates
• Vector condensates
• Self energies with OPEs
QCD sum rule Formula
This relation comes from baryon octet mass relation
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QCD sum rule Formula• New symbols for self energies
• Expansion up to linear density order
• Expansion to contain higher density order terms
![Page 10: Nuclear Symmetry Energy from QCD Sum Rule The 5 th APFB Problem in Physics, August 25, 2011 Kie Sang JEONG Su Houng LEE (Theoretical Nuclear and Hadron](https://reader034.vdocuments.us/reader034/viewer/2022051316/5697bf721a28abf838c7ec53/html5/thumbnails/10.jpg)
Sum Rule Analysis• Borel window • Nuclear Symmetry
EnergyPole contribution be more than 50%Highest dim condensate be less than 50%
We will see Sum Rule result in
For both expansion, Nuclear Symmetry Energy is 30 MeV – 40 MeVThis has consistency with previous Nuclear symmetry energy study
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Sum Rule Analysis
• Main ingredient? • Density dependence
Do not strongly depend on q in q ≤ 0.6 GeV-> Our Sum Rule result consists of mainly “Potential like” part
f determines higher density behavior
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Comparison to RMFT• Meson exchange
channel• RMFT result
• In our result, both self energies give positive contribution
Vector meson exchange -> RepulsiveScalar meson exchange -> attractive
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Conclusion
• We have successfully reproduced numerical value of Nuclear Symmetry Energy of previous study
• Dim6 four quark condensates determine higher density behavior of Nuclear Symmetry Energy
• Nuclear Symmetry Energy can be understood via QCD
• Extremely high density behavior remains unclear, this also might be understood via QCD