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Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with

Effective field theory approach for Fluctuations near Fermi Surface. Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with M. Harada, D.-P. Min, C. Sasaki, C. Song. HIM, Feb. 23-24 (2006), Yong-Pyung. Problems of ChPT at finite .

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Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with

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  1. Effective field theory approach for Fluctuations near Fermi Surface Tae-Sun Park Korea Institute for Advanced Study (KIAS) in collaboration with M. Harada, D.-P. Min, C. Sasaki, C. Song HIM, Feb. 23-24 (2006), Yong-Pyung

  2. Problems of ChPT at finite  • ChPT is an expansion scheme wrt Q/ • Q: typical momentum scale, m, kF • when kF is large, no small scale expansion parameter • too large medium-modifications even at '0 (c1, c2, c3, , are unnaturally large) ft=f (1-0.23 /0), fs=f (1 - 1.26 /0), which means, at =0, DF-1 (, q) = (2 – q2 – m2) ! (0.77 2 + 0.26 q2 –m*2)

  3. Strategy for a new finite-density EFT • Let’s build an EFT on the Fermi surface • integrate out | p – kF | À, ¿ kF • chiral symmetry is still (spontaneously) broken • dof.s: pions and nucleons • LECs: -dependent • assumption: Q ¿ kF (okay), kF¿ (to be improved) • matching to PT at some matching-density, M < 0 • cf) D.-K. Hong’s High Density ET • chiral symmetry is unbroken • d.o.f.s: (massless) quarks and gluons. • assumption: Q ¿ kF, g ¿ 1. • matching to pQCD at some high density, MÀ0

  4. Formulation • A free Lagranian with chemical potential: • i i' pF, remove large momentum by defining 1 as • i r= p – pF» Q, even when pF is large.

  5. remove off-diagonal components by introducing 2 as

  6. Decompose 2 into two parts, 2= + + -

  7. Integrate out “anti-particle” part (-) : • leading order propagator :

  8. Power counting • Very similar to the PT, but nucleonic loop integrals ~ 4 2 kF2 Q2 (in PT, loops ~ 2Q4)

  9. Building blocks • =exp( i /Ft), = a=13a Ta !’ = h  gRy = gL hy, h= h(,gL,gR) • covariant derivatives of pion • ! h(,gL,gR)  • covariant derivatives of nucleon

  10. Leading order Lagrangian • pion sector: • nucleon’s kinetic term • NN term cf) axial-charge term has been promoted to LO from NLO cf)

  11. Leading order Lagrangian • 4-nucleon contact terms :

  12. VV correlator • (a): =0, LN=1, (b,c): =2, LN=0 .

  13. AA correlator • Matching to ChPT 1-loop results:

  14. Results (ft/f & fs/f) M=0.4 0 M=0.2 0 M=0.3 0

  15. Results (v) M=0.2 0 M=0.3 0 M=0.4 0

  16. Discussions/Problems/Future works • Resummation scheme for all orders in (pF/) is needed. • Requires input from ChPT, progresses in ChPT at finite-density are needed. • How to treat density-dependences of LECs ? • Search for applications.

  17. Results (ft,s/f (0=10 MeV), v2=fs/ ft) dotted: NLO (1-loop) sold : NNLO (2-loop) unfortunately, 2-loop contributions are neglegible ... ...

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