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.

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

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)

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

For infinite matter

• Energy per a nucleon

• Single nucleon energy

• Averaged single nucleon energy

Nuclear Symmetry Energy

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)

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

• 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

QCD sum rule Formula• New symbols for self energies

• Expansion up to linear density order

• Expansion to contain higher density order terms

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

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

Comparison to RMFT• Meson exchange

channel• RMFT result

• In our result, both self energies give positive contribution

Vector meson exchange -> RepulsiveScalar meson exchange -> attractive

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