Neutral pion decayin

Dense Skyrmion Matter

KPS2005(LENS) October 20, 2005

B.-Y. Park(Chungnam Nat’l Univ.)A. Kalloniatis(Univ. of Adelaide)

Non-linear Model

Pion dynamics

Higher order derivative terms&

baryonic degrees of freedom

Skyrme’s Old Idea 1960, T. H. R. Skyrme

R ~ 1 f m M ~ 1.5 GeV

baryon ?

U(x) : mapping from R3-{ }=S3 to SU(2)=S38

topological soliton

Unified approach to

pion-baryon system

static soliton config.

fluctuating pions

Skyrmion Crystal

static soliton config.

fluctuating pions

Pion in the dense baryonic matter?

classicalground state

config.

Basic Idea

e.g. effective mass

H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento,

Nucl. Phys. A (2003)

Skyrme Model(m=0)\

Pion fluctuation in B=0 spaceVacuum : U=1

dynamics(=0)\

+ -skyrmion matterinteractions

Skyrmion matter

Pion fluctuations on top of the

skyrmion matter

dynamics(=0)\

dynamics(=0)\

dynamics(=0)\

In-Medium pion decay constant ?

In-Medium pion mass ?

pion effective mass

H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A (2003)

e.g.#2 pion velocity

H.-J. Lee, B.-Y. Park, M. Rho, V. Vento,

Nucl. Phys. A (2004)

dynamics(=0)\

0th-orderpropagator

Pion-BGinteractions

=

+ + ….

= +

+

Pion propagator in medium

+

Pion velocity in medium

Pion velocity in medium

H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A (2004)

0 -> in

Dense Skyrmion Matter

A. Kalloniatis, B.-Y. Park, PRD71, 034010 (2005)

U(1) gauged Skyrme Model

Gauging U(1) symmetry under

with

with

U(1) gauged Skyrme Model

Gauging U(1) symmetry under

with

Gauged Wess-Zumino-Witten term

Pion fluctuation in B=0 spaceVacuum : U=1

Pion fluctuation in B=0 space

Skyrmion matter : U0

\

Gab(x) (x)

C(U0)

D(U0)

F(U0)

Effective quantities

0 -> in medium

0 -> in

Dense Skyrmion Matter

A. Kalloniatis, C. Janathan, B.-Y. Park, PRD71,114001 (2005)

Gauging Skyrme Model

Electroweak vector fields

with

& WZW term

& Leptonic part

0 -> possible?

Impossible for massless neutrinos

0 Z

_

0 Z

_

Z

Z

0 Z

_

In medium?

Again impossible for massless neutrinos

In-medium modified “effective” vertex

In medium?

possible if the background potential provide momentum

0 Z

_

In medium?

possible !

0 Z

_

In-medium modificationof the pion propagator

Lorentz symmetry break down

A. Kalloniatis, C. Janathan, B.-Y. Park, PRD71, 114001 (2005)

10-4 ~ 10-3

Future Work

_

fluctuating pions

Pion in the dense baryonic matter?

classicalground state

config.