RESONANCE STATES BETWEEN CHARMED BARYON AND NUCLEON Saori Maeda - - PowerPoint PPT Presentation

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RESONANCE STATES BETWEEN CHARMED BARYON AND NUCLEON Saori Maeda - - PowerPoint PPT Presentation

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THE INTERACTION AND 1 RESONANCE STATES BETWEEN CHARMED BARYON AND NUCLEON Saori Maeda Makoto Oka Tokyo Institute of technology MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 2 CONTENTS Introduction Interaction &

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THE INTERACTION AND RESONANCE STATES BETWEEN CHARMED BARYON AND NUCLEON

Saori Maeda

Makoto Oka

Tokyo Institute of technology

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 1

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CONTENTS

  • Introduction
  • 𝑍

𝑑𝑂 Interaction & Binding energy

  • Resonance states
  • Summary

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 2

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INTRODUCTION

  • Interesting properties of charm nuclei

・Heavy quark symmetry ・Channel coupling including higher state than strange sector.

  • We have obtained many experimental data related to

hypernuclei and hyperon-nucleon(YN) interactions.

the next stage

Approaching to charm nuclei structure with theoretical knowledge

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 3

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INTRODUCTION

  • Interesting properties of charm nuclei

・Heavy quark symmetry ・Channel coupling including higher state than strange sector.

  • We have obtained many experimental data related to

hypernuclei and hyperon-nucleon(YN) interactions.

the next stage

Approaching to charm nuclei structure with theoretical knowledge

12 12 6 2

Σ𝑑

βˆ— 2518 (c,u,u)(c,u,d) (c,d,d)

Σ𝑑 2454

(c,u,u)(c,u,d) (c,d,d)

Λ𝑑 2286

(c,u,d)

64[π‘π‘“π‘Š] 168 [π‘π‘“π‘Š]

12 12 6 2

Ξ£βˆ— 1385

(s,u,u)(s,u,d) (s,d,d)

Ξ£ 1189

(s,u,u)(s,u,d) (s,d,d)

Ξ› 1116

(s,u,d)

196 [π‘π‘“π‘Š] 73[π‘π‘“π‘Š]

Strange Charm

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 4

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𝑍

𝑑𝑂 INTERACTION

  • 𝑍

𝑑𝑂 potential (𝑍 𝑑 = Λ𝑑, Σ𝑑, Σ𝑑 βˆ—) In this study, we construct a hybrid potential using a hadron model and a quark model

・One Boson Exchange potential ・Quark Cluster Model π‘Š

(𝑍

𝑑𝑂) = π‘Š

𝑃𝐢𝐹𝑄 + π‘Š 𝑅𝐷𝑁

  • Channel coupling

[M.Oka, Nuclear Physics A 881 (2012) 6–13] [Y.R.Liu, M.Oka, Phys. Rev. D 85, 014015 (2012)]

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 5

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𝑍

𝑑𝑂 INTERACTION

  • One Boson Exchange potential

We assume that the pion and the sigma meson exchange between the charm baryon and the nucleon. At the vertices, we introduce the form factor 𝐺 π‘Ÿ as follows

𝐺 π‘Ÿ =

Ξ›2βˆ’π‘›2 Ξ›2βˆ’π‘Ÿ2

𝑍

𝑑( Τ¦

π‘ž) 𝑍

𝑑(π‘žβ€²)

𝐺 π‘Ÿ

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 6

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𝑍

𝑑𝑂 INTERACTION

  • One Boson Exchange potential

We assume that the pion and the sigma meson exchange between the charm baryon and the nucleon. At the vertices, we introduce the form factor 𝐺 π‘Ÿ as follows

𝐺 π‘Ÿ =

Ξ›2βˆ’π‘›2 Ξ›2βˆ’π‘Ÿ2

𝑍

𝑑( Τ¦

π‘ž) 𝑍

𝑑(π‘žβ€²)

𝐺 π‘Ÿ

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 7

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r b

𝑍

𝑑𝑂 INTERACTION

  • Quark Cluster Model (QCM)

The QCM considers two baryon clusters each made of three quarks. When two baryons overlap completely, r=0, all the six quarks occupy the lowest energy orbit with a single center. Potential equation

π‘Š

𝑅𝐷𝑁 = π‘Š 0π‘“βˆ’π‘ 2 𝑐2

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 8

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r b

𝑍

𝑑𝑂 INTERACTION

  • Quark Cluster Model (QCM)

The QCM considers two baryon clusters each made of three quarks. When two baryons overlap completely, r=0, all the six quarks occupy the lowest energy orbit with a single center. Potential equation

π‘Š

𝑅𝐷𝑁 = π‘Š 0π‘“βˆ’π‘ 2 𝑐2

π‘Š 𝑠 = 0 β‰ˆ< 6π‘Ÿ 𝐼 6π‘Ÿ > βˆ’2 < 3π‘Ÿ 𝐼 3π‘Ÿ >

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 9

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𝑍

𝑑𝑂 INTERACTION

  • Parameter fix

we determine the parameters of the potential so as to reproduce the NN interaction data using the same model. ・Fixed parameter Pi-baryon coupling constants, Range parameter of QCM ・Determined parameter Cutoff parameter (Ξ›πœŒ, Ξ›πœ), sigma-baryon coupling constants

YcN-CTNN

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 10

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𝑍

𝑑𝑂 INTERACTION

  • Parameter fix

we determine the parameters of the potential so as to reproduce the NN interaction data using the same model. ・Fixed parameter Pi-baryon coupling constants, Range parameter of QCM ・Determined parameter Cutoff parameter (Ξ›πœŒ, Ξ›πœ), sigma-baryon coupling constants

YcN-CTNN

𝒁𝒅𝑢-Corresponding To NN

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 11

[Prog. Theor. Exp. Phys. (2016) 023D02]

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𝑍

𝑑𝑂 INTERACTION

  • Result of binding energy and scattering length

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 12

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

In the previous calculation, we consider only the state under the Λ𝑑𝑂 threshold. So, we calculate with the Complex scaling method

[J. Aguilar, J.M. Combes, Commun. Math. Phys. 22 (1971) 269.]

to search the state above the

Λ𝑑𝑂 threshold with 𝑍

𝑑𝑂-CTNN

d-potential.

12 12 6 2

Σ𝑑

βˆ—π‘‚ 3457 (c,u,u)(c,u,d) (c,d,d)

Σ𝑑𝑂 3393

(c,u,u)(c,u,d) (c,d,d)

Λ𝑑𝑂 3225

(c,u,d)

64[π‘π‘“π‘Š] 168 [π‘π‘“π‘Š]

Charm

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 13

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・𝐾𝑄 = 2+

Λ𝑑𝑂 and Σ𝑑𝑂 channel have no S-wave because of

the rule of total angular momentum. The S-wave and G-wave are the characteristic behavior of Σ𝑑

βˆ— having the spin =

3 2

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 14

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・Result

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 15

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・Result

𝐾𝑄 = 0+ 𝐾𝑄 = 2+ 𝐾𝑄 = 1+

Σ𝑑

βˆ—π‘‚

Λ𝑑𝑂 Σ𝑑𝑂

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 16

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・Result with partial channel coupling

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 17

Σ𝑑𝑂 threshold: 167.10 MeV Σ𝑑

βˆ—π‘‚threshold: 231.51 MeV

potential 𝑲𝑸 = 𝟏+(πš»π’…π‘Ά) 𝑲𝑸 = 𝟐+(πš»π’…π‘Ά) 𝑲𝑸 = 𝟐+(πš»π’…

βˆ—π‘Ά)

𝑲𝑸 = πŸ‘+(πš»π’…

βˆ—π‘Ά)

CTNN-d 2.22[MeV] 14.28[MeV] 7.67[MeV] 17.68[MeV]

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・Heavy quark limit We assume Σ𝑑𝑂 and Σ𝑑

βˆ—π‘‚ are doublet, so we set the

𝑍

𝑑𝑂 threshold in substitute for Σ𝑑𝑂 and Σ𝑑

βˆ—π‘‚ threshold. Σ𝑑

βˆ—π‘‚ 3457 (c,u,u)(c,u,d) (c,d,d)

Σ𝑑𝑂 3393

(c,u,u)(c,u,d) (c,d,d)

Λ𝑑𝑂 3225

(c,u,d)

𝑍

𝑑𝑂 3414 (c,u,u)(c,u,d) (c,d,d)

Λ𝑑𝑂 3225

(c,u,d)

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 18

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・Result

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 19

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𝑍

𝑑𝑂 INTERACTION

  • Resonance

・Result

𝐾𝑄 = 0+ 𝐾𝑄 = 2+ 𝐾𝑄 = 1+

𝑍

𝑑𝑂

Λ𝑑𝑂

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 20

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SUMMARY

  • We propose the 𝑍

𝑑𝑂 potential model based on the

hadron model and the quark model, and find four parameter set to reproduce experimental data of NN system.

  • Calculating the 𝑍

𝑑𝑂 2-body system, we get not only

the shallow bound state but also resonance states for several potential models.

MIN16 - Meson in Nucleus 2016, YITP, 31th July 2016 21