Chaejun Song(SNU & PNU)

with M. Harada, C. Sasaki (Nagoya), D.-P. Min (SNU), T.- S. Park (KIAS)

hep-ph/0410124

Nuclear Phase Diagram

T(MeV)

Density(n0)

~150

~10

Early Universe(RHIC)

Color SuperconductorNeutron Star

Hadron Gas

Quark-Gluon Plasma

Phase Transition

Atomic Nuclei

Hadrons in Medium

Pions in medium kaons in medium

Heavy Baryon Chiral Effective Theory

• Very powerful for a system of a few baryons

• Systematic expansion with Q/

• Applications to nuclear matter-> new scale appears!

• Purpose: study dense medium in a systematic way

Our scales

• Small scale Q: excitation scale from Fermi surface (or pion mass)

• Large scale : chiral symmetry breaking scale

• Intermediate scale : Fermi momentum

Fp

Expansion scales

• Q/

• /

Fp

Free Fermion Gas

Analogy from HDETSee D.K. Hong: PLB 473, 118 (00)

2nd transformation and projection

Pions in Medium

nucleon-pion interaction

self-interactions of nucleons

Power Counting Rule

Vector Correlator

0NE 2EE

1NL 0

Suppressed by

Axial Vector Correlator

.A

A

0NE

2EE

1NL

0

1-loop:

Pion Decay Constants in Medium

Decomposition into 4 parts:

20

0

( ( ) , ) Re[ ]

( ( ) , ) Re[ ]

t tA

s t sA

p v p p p f

p v p p p f f

v ( ) /p E p

Matching with HBChPT at some

Our result:

HBChPT from Meissner et al., Ann. Phys. 297, 27 (02)

Suzuki et al., PRL92, 072302(04)

Pion Velocity in Medium

Lee et al., NPA 741, 161(04)

Damping of Pions

• No Damping in our valid range

We will study…

How to determine our parametersHow to introduce and deal with

cutoffs around Fermi surface (go to Fermi liquid!)

How to make it more preciseHow to go to higher densities and to

check various scenarios