Neutral pion decay in dense skyrmion matter
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KPS2005(LENS) October 20, 2005. Neutral pion decay in Dense Skyrmion Matter. B.-Y. Park (Chungnam Nat’l Univ.) A. Kalloniatis(Univ. of Adelaide). Non-linear s Model. Pion dynamics. Higher order derivative terms & baryonic degrees of freedom. Skyrme’s Old Idea.

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Neutral pion decay in Dense Skyrmion Matter

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KPS2005(LENS)

October 20, 2005

Neutral pion decayin Dense Skyrmion Matter

B.-Y. Park(Chungnam Nat’l Univ.)

A. Kalloniatis(Univ. of Adelaide)


Non-linear s Model

Pion dynamics

Higher order derivative terms

&

baryonic degrees of freedom


Skyrme’s Old Idea

U(x) : mapping fromR3-{ }=S3toSU(2)=S3

8

topological soliton

R ~ 1 f m

M ~ 1.5 GeV

1960, T. H. R. Skyrme

baryon ?


static

soliton

config.

fluctuating

pions

Unified approach

to

pion-baryon system


Skyrmion Crystal


Pion in the dense

baryonic matter?

classical

ground state

config.

static

soliton

config.

fluctuating

pions


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(mp=0)

\

Pion fluctuation

in rB=0 space

Vacuum : U=1


pdynamics(r=0)

\

Skyrmion matter

Pion fluctuations

on top of the

skyrmion matter

+ p-skyrmion matter

interactions


pdynamics(r=0)

\


pdynamics(r=0)

\


pdynamics(r=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)


pdynamics(r=0)

Pion-BG

interactions

0th-order

propagator

\


S

=

….

+

+


S

S

S

=

+

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)


p0 -> ggin Dense Skyrmion Matter

A. Kalloniatis, B.-Y. Park,

PRD71, 034010 (2005)


U(1) gauged Skyrme Model

with

Gauging U(1) symmetry under

with


U(1) gauged Skyrme Model

Gauging U(1) symmetry under

with

Gauged Wess-Zumino-Witten term


Pion fluctuation

in rB=0 space

Vacuum : U=1


Pion fluctuation

in rB=0 space

Skyrmion matter : U0

\

s(x)

Gab(x)

C(U0)

D(U0)

F(U0)


Effective quantities


p0 -> gg in medium


p0 -> nnin Dense Skyrmion Matter

A. Kalloniatis, C. Janathan, B.-Y. Park,

PRD71,114001 (2005)


Gauging Skyrme Model

Electroweak vector fields

with


& WZW term


& Leptonic part


p0 -> nn possible?

n

Z

n

Z

Z

p0

p0

_

_

n

n

Z

Impossible for massless neutrinos


In medium?

n

Z

p0

_

n

In-medium modified

“effective” vertex

Again impossible for massless neutrinos


In medium?

n

Z

p0

_

n

possible if the background

potential provide momentum


In medium?

_

n

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

n

Z

p0

In-medium modification

of the pion propagator

Lorentz symmetry

break down

possible !


10-4 ~ 10-3


Future Work

n

g

p0

_

g

n


Pion in the dense

baryonic matter?

classical

ground state

config.

fluctuating

pions


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