Structures of the Λ(1405) in the Skyrme model...Method 3. KN Feshbach resonance 4. summary _ 8th...

8th International Conference on Quarks and Nuclear Physics (QNP2018) November 13‒17, 2018; Tsukuba, Ibaraki, Japan 1

Structures of the Λ(1405) in the Skyrme model

RCNP, Osaka University ASRC, Japan Atomic Energy Agency

Takashi Ezoe Atsushi Hosaka

Contents 1. Introduction 2. Method 3. KN Feshbach resonance 4. summary

_


1. Introduction


Introduction

・Experiment 　K. Moriya et al. [CLAS Collaboration], Phys. Rev. C 87, no. 3, 035206 (2013). ・Chiral theory 　T. Hyodo and D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012).　　K. Miyahara, T. Hyodo and W. Weise, Phys. Rev. C 98, no. 2, 025201 (2018).

1. Λ(1405): JP = 1/2-, I = 0・Difficult to explain Λ(1405) in a simple quark model ・KN bound state = Λ(1405)?

・KN and πΣ resonance = Λ(1405)_

N. Isgur and G. Karl, Phys. Rev. D 18, 4187 (1978).

2. Studies for Λ(1405)

Investigated the Λ(1405) in the Skyrme model, where the baryon is described as a soliton.

_R. H. Dalitz and S. F. Tuan, Phys. Rev. Lett. 2, 425 (1959). R. H. Dalitz and S. F. Tuan, Annals Phys. 8, 100 (1959).

T. Hyodo, and D. Jido, Prog. Part. Nucl. Phys. 67, 55 (2012).


2. Method


Method・Skyrme model J. K. Perring and T. H. R. Skyrme, Nucl. Phys. 31, 550 (1962).

T. H. R. Skyrme, Proc. Roy. Soc. Lond. A 260, 127 (1961).・Describe the interaction between mesons and baryons by mesons ・Baryon emerges as a soliton of meson fields


Method・Skyrme model

L =F 2⇡

16tr�@µU@µU †�+ 1

32e2tr⇥(@µU)U †, (@⌫U)U†⇤2 + LSB + LWZ

・Ansatz

(U⇡ ! A (t)U⇡A† (t)

UK = UK

U⇡ =

✓UH 00 1

◆

Hedgehog soliton (2×2 matrix)

A(t): Isospin rotation matrix

T. Ezoe and A. Hosaka Phys. Rev. D 94, 034022 (2016).[1] C. G. Callan and I. Klebanov, Nucl. Phys. B 262 (1985). C. G. Callan, K .Hornbostel and I. Klebanov, Phys. Lett. B 202 (1988).

[1]

34 第 4章束縛法

2. 質量による明示的なカイラル対称性の破れは以下のLagrangianにより表される [40,

41, 43]。

Lmass =1

48F 2π

!m2

π + 2m2K

"tr#U + U † − 2

$+

√3

24

!m2

π −m2K

"tr#λ8!U + U †"$

(4.3)

ここで、mπとmKはそれぞれπ中間子とK中間子の質量を表す。本論文ではCallan

とKlebanovの論文に従い、uクォークと dクォークの質量をゼロにとり、sクォークの質量を有限の大きさにとる [28, 29]。これにより、mπ = 0となる。

K中間子に質量を与えることで対称性が明示的に破れた場合の場の配位として、K中間子が励起し、なおかつ純粋なπ中間子のソリトンに近い配位を選ぶ。解としてはカイラル対称性の非線形表現 [37, 38]を用いて以下のものを考える [28, 29]。

U =√NUK

√N (4.4)

ここで、N は SU(3)に埋め込んだπ中間子のソリトン解であり以下のように定義する。

N =

%Uπ 0

0 1

&(4.5)

Uπ ≡ ξ2 = exp

'i2

Fπτ · π

((4.6)

UK = exp

'i2

FπλaKa

(, a = 3, 4, 5, 6 (4.7)

τ はアイソスピン行列であり、その値は pauliのスピン行列 (2.6)式と同じ値をとる。そして、λa(a = 4, 5, 6, 7)は (2.36)式のGell-Mann行列である。(2.36)式を用いて λaKaを以下のように書く。

λaKa =√2

%02×2 K

K† 0

&(4.8)

ただし、Kは 2成分アイソスピナー

K =

%K+

K0

&(4.9)

である。(4.1)式、(4.3)式に (4.4)式を代入し、Kの 2次まで展開すると

L = LSU(2) + LK (4.10)

K† =

✓K̄0

K�

◆K =

✓K+

K0

◆

UCK = (3 ⇥ 3 matrix) ! A (t)p

U⇡UK

pU⇡A

†(t)

UEH = A (t)pU⇡A

† (t)UKA (t)pU⇡A

† (t)

J. K. Perring and T. H. R. Skyrme, Nucl. Phys. 31, 550 (1962). T. H. R. Skyrme, Proc. Roy. Soc. Lond. A 260, 127 (1961).

Parameters: Fπ, e, Mπ = 0, MK ≠ 0

UK = exp

i2

F⇡�aKa

�, a = 4, 5, 6, 7

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・Describe the interaction between mesons and baryons by mesons ・Baryon emerges as a soliton of meson fields


Difference in CK and EH(1) Callan-Klebanov Ansatz UCK = A (t)

pU⇡UK

pU⇡A

† (t)

(2) Ezoe-Hosaka Ansatz UEH = A (t)pU⇡A

† (t)UKA (t)pU⇡A

† (t)

K Hedgehog soliton

the kaon around the hedgehog soliton

the kaon around the “rotating” hedgehog soliton

K Hedgehog soliton

8th International Conference on Quarks and Nuclear Physics (QNP2018) November 13‒17, 2018; Tsukuba, Ibaraki, Japan

KN (JP = 1/2-, I = 0) Bound stateWave func

tion [1/fm

3/2 ]

Wave function Potential

⌦r2N

↵=

Z 1

0dr r2⇢B (r) , ⇢B (r) = � 2

⇡sin2 FF 0 G. S. Adkins, C. R. Nappi and E. Witten,

Nucl. Phys. B 228 (1983)⌦r2K

↵=

ZdV r2

⇥Y00 (r̂) k

00 (r)

⇤2=

Z 1

0dr r4k2 (r) Y00 =

1p4⇡

・Parameter sets and bound state properties

Repulsive core

Attractive pocket

mK = 495 MeV mK = 495 MeV

_T. E. and A. Hosaka Phys. Rev. D 94, 034022 (2016).

F⇡ [MeV] e B.E. [MeV]p

hr2N i [fm]p

hr2Ki [fm]Parameter set A 205 4.67 19.9 0.43 1.30Parameter set B 186 4.82 32.2 0.46 1.15

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Kaon-Nucleon scattering states (JP = 1/2-)Parameter set A: mK = 495 MeV, Fπ = 205 MeV, e = 4.67

Binding energy = 19.9 MeV__


3. KN Feshbach resonance_


Λ(1405) as a Feshbach resonance

Λ(1405)N Σ

πK＿

NΣ

K_ π

s-quarkdi-quark

KN bound state_



・s-creation ・Strong coupling limit 　(the CK approach)

・K-annihilation ・Weak coupling limit 　(the EH approach)

_

NΣ

πK＿

di-quark

s-quarkAxial current: J5,aµ

Lint =1

F⇡@µ⇡aJ5,a

µ<latexit sha1_base64="TG83jjRWHW06Qgy8jCWJotmGVv8=">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</latexit><latexit sha1_base64="TG83jjRWHW06Qgy8jCWJotmGVv8=">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</latexit><latexit sha1_base64="TG83jjRWHW06Qgy8jCWJotmGVv8=">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</latexit><latexit sha1_base64="TG83jjRWHW06Qgy8jCWJotmGVv8=">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</latexit>




_

NΣ

πK＿

di-quark


Lint =1

F⇡@µ⇡aJ5,a



(a = -1, 0, 1)Lint =

1

F⇡@µ⇡aJ5,a

µ<latexit sha1_base64="/4ePD8NyMM7ZRZuUxH8/mbJs1fg=">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</latexit><latexit sha1_base64="/4ePD8NyMM7ZRZuUxH8/mbJs1fg=">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</latexit><latexit sha1_base64="/4ePD8NyMM7ZRZuUxH8/mbJs1fg=">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</latexit><latexit sha1_base64="/4ePD8NyMM7ZRZuUxH8/mbJs1fg=">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</latexit>

h⇡⌃| Lint |K̄Ni = 1

F⇡h⇡| @µ⇡a |0i h⌃| J5,a

µ |K̄Ni = g⇤⇤⇡⌃<latexit sha1_base64="xlRz7sKrdRS4z7lfDAxD8u2Z1Jc=">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</latexit><latexit sha1_base64="xlRz7sKrdRS4z7lfDAxD8u2Z1Jc=">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</latexit><latexit sha1_base64="xlRz7sKrdRS4z7lfDAxD8u2Z1Jc=">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</latexit><latexit sha1_base64="xlRz7sKrdRS4z7lfDAxD8u2Z1Jc=">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</latexit>


Axial current and matrix elementL =

F 2⇡

16tr�@µU@µU †�+ 1

32e2tr⇥(@µU)U †, (@⌫U)U†⇤2 + LSB + LWZ

1. Axial current

Axial transformation:U ! exp

✓i✓ · T

2

◆U exp

✓i✓ · T

2

◆

J5,aµ = J (0),5,a

µ + J (2),5,aµ

h⌃0| J (2),5,a=3µ=0 |K̄Ni

for Λ(1405) → π0Σ0 in the non-relativistic limit

Rµ = U@µU†, Lµ = U†@µU

The axial current has O(Nc0) and O(1/Nc) components

J5,aµ = J5,a(kin)

µ + J5,a(Skyrme)µ + J5,a(WZ)

µ

= iF 2⇡

16tr [T a (Rµ + Lµ)] +

i

16e2tr [T a {[R⌫ , [R⌫ , R

µ]]� [L⌫ , [L⌫ , Lµ]]}]

� Nc

96⇡2✏µ⌫↵�tr [T a (R⌫R↵R� + L⌫L↵L�)]

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4. Summary


SummaryWe have constructed a new method to investigate the Λ(1405) resonance in the Skyrme model

Future work ・Full-calculation for the KN and πΣ coupled channel

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Results ・One bound state exists in KN(JP = 1/2-, I = 0) channel ・Phase shift indicates that KN interaction is attractive and 　KN one is weakly repulsive ・We have obtained the coupling constant for the KN-πΣ 　vertex ・Λ(1405) can be formed as the KN Feshbach resonance ・Decay width of the KN Feshbach resonance seems small

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Thank you for you attention!!

Structures of the Λ(1405) in the Skyrme model...Method 3. KN Feshbach resonance 4. summary _ 8th...

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Transcript of Structures of the Λ(1405) in the Skyrme model...Method 3. KN Feshbach resonance 4. summary _ 8th...