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 Physics Group) Yonsei UNIV.

2. 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

3. 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)

4. Early attempt for finite nuclei Liquid drop modelTotal shifted energy Total shifted state number Nuclear symmetry energy We can generalize this concept to infinite matter case

5. For infinite matter Energy per a nucleon Single nucleon energy Averaged single nucleon energy Nuclear Symmetry Energy

6. 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)

7. QCD Sum Rule Sum Rule Correlator At short distance, we can calculate Wilson coefficient in the OPE Phenomenological ansatz Borel transformation Ioffe’s interpolating field for proton To exclude the quasi-hole and continuum excitation do not depend on external momentum

8. 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

9. QCD sum rule Formula New symbols for self energies Expansion up to linear density order Expansion to contain higher density order terms

10. Sum Rule Analysis Borel windowNuclear Symmetry Energy Pole contribution be more than 50% Highest dim condensat e be less than 50% We will see Sum Rule result in For both expansion, Nuclear Symmetry Energy is 30 MeV – 40 MeV This has consistency with previous Nuclear symmetry energy study

11. 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

12. Comparison to RMFT Meson exchange channelRMFT result In our result, both self energies give positive contribution Vector meson exchange -> Repulsive Scalar meson exchange -> attractive

13. 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