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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Neutral pion decay in dense skyrmion matter

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

Non-linear s Model

Pion dynamics

Higher order derivative terms

&

baryonic degrees of freedom


Skyrme s old idea

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 ?


Neutral pion decay in dense skyrmion matter

static

soliton

config.

fluctuating

pions

Unified approach

to

pion-baryon system


Skyrmion crystal

Skyrmion Crystal


Neutral pion decay in dense skyrmion matter

Pion in the dense

baryonic matter?

classical

ground state

config.

static

soliton

config.

fluctuating

pions


Basic idea

Basic Idea


E g effective mass

e.g. effective mass

H.-J. Lee, B.-Y. Park, D.-P. Min,

M. Rho, V. Vento,

Nucl. Phys. A (2003)


Skyrme model m p 0

Skyrme Model(mp=0)

\

Pion fluctuation

in rB=0 space

Vacuum : U=1


P dynamics r 0

pdynamics(r=0)

\

Skyrmion matter

Pion fluctuations

on top of the

skyrmion matter

+ p-skyrmion matter

interactions


P dynamics r 01

pdynamics(r=0)

\


P dynamics r 02

pdynamics(r=0)

\


P dynamics r 03

pdynamics(r=0)

\

In-Medium

pion decay

constant ?

In-Medium

pion mass ?


Pion effective 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

e.g.#2 pion velocity

H.-J. Lee, B.-Y. Park,

M. Rho, V. Vento,

Nucl. Phys. A (2004)


P dynamics r 04

pdynamics(r=0)

Pion-BG

interactions

0th-order

propagator

\


Neutral pion decay in dense skyrmion matter

S

=

….

+

+


Neutral pion decay in dense skyrmion matter

S

S

S

=

+

Pion propagator

in medium

+

+

Pion velocity

in medium


Pion velocity in medium

Pion velocity in medium

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


P 0 gg in dense skyrmion matter

p0 -> ggin Dense Skyrmion Matter

A. Kalloniatis, B.-Y. Park,

PRD71, 034010 (2005)


U 1 gauged skyrme model

U(1) gauged Skyrme Model

with

Gauging U(1) symmetry under

with


U 1 gauged skyrme model1

U(1) gauged Skyrme Model

Gauging U(1) symmetry under

with

Gauged Wess-Zumino-Witten term


Neutral pion decay in dense skyrmion matter

Pion fluctuation

in rB=0 space

Vacuum : U=1


Neutral pion decay in dense skyrmion matter

Pion fluctuation

in rB=0 space

Skyrmion matter : U0

\

s(x)

Gab(x)

C(U0)

D(U0)

F(U0)


Effective quantities

Effective quantities


P 0 gg in medium

p0 -> gg in medium


P 0 nn in dense skyrmion matter

p0 -> nnin Dense Skyrmion Matter

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

PRD71,114001 (2005)


Gauging skyrme model

Gauging Skyrme Model

Electroweak vector fields

with


Wzw term

& WZW term


Leptonic part

& Leptonic part


P 0 nn possible

p0 -> nn possible?

n

Z

n

Z

Z

p0

p0

_

_

n

n

Z

Impossible for massless neutrinos


In medium

In medium?

n

Z

p0

_

n

In-medium modified

“effective” vertex

Again impossible for massless neutrinos


In medium1

In medium?

n

Z

p0

_

n

possible if the background

potential provide momentum


In medium2

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 !


Neutral pion decay in dense skyrmion matter

10-4 ~ 10-3


Future work

Future Work

n

g

p0

_

g

n


Neutral pion decay in dense skyrmion matter

Pion in the dense

baryonic matter?

classical

ground state

config.

fluctuating

pions


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