Recent theoretical studies Akinobu Dot (KEK Theory Center, IPNS / - - PowerPoint PPT Presentation

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Recent theoretical studies Akinobu Dot (KEK Theory Center, IPNS / - - PowerPoint PPT Presentation

Jan 07, 2023 137 likes •459 views

The simplest kaonic nucleus K - pp Recent theoretical studies Akinobu Dot (KEK Theory Center, IPNS / J-PARC branch) Takashi Inoue (Nihon university) Takayuki Myo (Osaka Institute of Technology) 1. Introduction K - pp

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SLIDE 1

The simplest kaonic nucleus “K-pp” － Recent theoretical studies －

1. Introduction 2. “K-pp” investigated with Fully coupled-channel Complex Scaling Method

  • Formalism
  • Chiral SU(3)-based potential
  • Self-consistency for energy-dependent potential in coupled-channel case

3. Result 4. Discussion 5. Summary and future prospects

Akinobu Doté (KEK Theory Center, IPNS / J-PARC branch) Takashi Inoue (Nihon university) Takayuki Myo (Osaka Institute of Technology) 『2017年度 KEK 理論センターJ-PARC 分室活動 総括研究会』,
  • 02. Feb. ’18 @ IQBRC, Tokai, Ibaraki, Japan
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SLIDE 2
  • 1. Introduction
  • Kaonic nuclei = Nuclear system with Kbar mesons
  • Strongly attractive KbarN potential

Excited hyperon Λ(1405) = KbarN quasi-bound state

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

Kaonic nuclei = Exotic system!?

Doorway to dense matter?

  • A. Dote, H. Horiuchi, Y. Akaishi, T. Yamazaki, PRC70, 044313 (2004)
  • Y. Akaishi, T. Yamazaki, PRC65, 044005 (2002)
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SLIDE 3

We are investigating ...

A prototype of kaonic nuclei

... a bridge from Λ(1405) to general kaonic nuclei

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SLIDE 4

Experimental search for K-pp

  • Deeply bound region (near πΣN threshold = 103 MeV below KbarNN threshold)
FINUDA (2005), DISTO (2010), J-PARC E27 (2013)
  • Shallowly bound region (near KbarNN threshold)
J-PARC E15 1st run (2013)
  • No signal in bound region
LEPS/SPring8 (2015) and more ...

Clear evidence of K-pp bound state

J-PARC E15 (2nd run): Exclusive exp. 3He(K-, Λp)nmissing

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SLIDE 5

Theoretical studies of “K-pp”

J-PARC E15 J-PARC E27 DISTO FINUDA Faddeev-AGS
  • Pheno. pot. (E-indep.)
Variational (Gauss)
  • Pheno. pot. (E-indep.)
Variational (Gauss)
  • Chial. pot. (E-dep.)
Faddeev-AGS Chiral pot. (E-dep.) K-pp binding energy [MeV]
  • K-pp should be bound. BK-pp < 100 MeV

Resonance between πΣN and KbarNN thresholds.

  • Binding energy depends
  • n potential type.
KbarNN threshold πΣN threshold
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SLIDE 6
  • 2. “K-pp” investigated with

Fully coupled-channel Complex Scaling Method

  • Formalism
  • Chiral SU(3)-based potential
  • Self-consistency for energy-dependent potential

in coupled-channel case

Discussed with Harada-san, Shinmura-san, and Akaishi-san in J-PARC branch activities
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SLIDE 7

According to early studies ...

⇒ “Fully coupled-channel Complex Scaling Method”

Resonant state of KbarNN-πΣN-πΛN coupled channel three-body system

Prototype system of kaonic nuclei “K-pp”

  • Akaishi, Yamazaki, PRC76, 045201 (2007)
  • Ikeda, Sato, PRC76, 035203 (2007)
  • Shevchenko, Gal, Mares, PRC76, 044004 (2007)
  • Doté, Hyodo, Weise, PRC79, 014003 (2009)
  • Ikeda, Kamano, Sato, PTP124, 533 (2010)
  • Barnea, Gal, Liverts, PLB712, 132 (2012)

Resonance & Channel coupling

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SLIDE 8

Complex Scaling Method

… Powerful tool for resonance study of many-body system

  • S. Aoyama, T. Myo, K. Kato, K. Ikeda, PTP116, 1 (2006)
  • T. Myo, Y. Kikuchi, H. Masui, K. Kato, PPNP79, 1 (2014)
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SLIDE 9

Full ccCSM with a pheno. potential

NN: Av18 pot. KbarN-πY: Akaishi-Yamazaki pot. (Pheno., E-indep.) Scaling angle θ=30° Dimension = 6400 Λ*N cont. Λ* pole BKN = 28 MeV, ΓπΣ /2 = 20 MeV

The “K-pp” pole for AY-potential case: BKNN = 51 MeV, ΓπYN /2 = 16 MeV

KbarNN cont. πΛN cont. πΣN cont.
  • A. Dote, T. Inoue, T. Myo, PRC 95, 062201(R) (2017)
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SLIDE 10

Comparison of typical calculations of K-pp

Variational method (Dote-Hyodo-Weise, Akaishi-Yamazaki, Barnea-Gal-Liverts) Faddeev-AGS (Ikeda-Kamano-Sato, Shevchenko-Gal-Mares) coupled-channel CSM (Dote-Inoue-Myo) Resonance Coupled-channel Wave function Potential type

×

Bound state approximation

○

Pole on complex energy plane

○ △

Single channel calc. incorporating πY channels into the effective KbarN potential

○

Explicit treatment
  • f all channels

○ ○ ×

（△？）

○ ○ ×

Separable type

○

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SLIDE 11

Hamiltonian

        

1,2 3, MB MB MB MB i V V i          ... symmetric for baryon’s site (i=1,2) Glöckle, Miyagawa, Few-body Systems 30, 241 (2001)

1 2 3

Baryon Baryon Meson
  • A. Dote, T. Inoue, T. Myo, NPA 912, 66 (2013)
  • R. B. Wiringa, V. G. J. Stoks, and R. Schiavilla, PRC 51, 38 (1995)

 NN potential = Av18 potential  KbarN-πY potential = Chiral SU(3)-based potential

Theoretical energy-dependent potential

 Ignore YN and πN potentials

( ) ( ) , bar NN MB MB K N

H M T V V

          

   

 

 

 

( 0,1) ( 0,1) 2 1 8 I ij I ij i i j j i j C V r g r f m m            3 2 /2 3 ex 1 p ij ij ij g r d r d          : Gaussian form
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SLIDE 12

Wave function

 Baryon-Baryon are antisymmetrized on space, spin and isospin as well as label (flavor). Glöckle, Miyagawa, Few-body Systems 30, 241 (2001)  Spatial part = Correlated Gaussian function  including 3 types of Jacobi coordinates  projected onto a parity eigenstate of B1B2,

M3 B2 B1

x1 (3) x2 (3)
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SLIDE 13

Just diagonalize the complex-scaled Hamiltonian matrix!

No channel elimination!!

KbarNN

  • KbarNN

θ

KbarNN

  • πΣN

KbarNN

  • πΛN

πΣN

  • πΣN

πΣN

  • πΛN

πΛN

  • πΛN

＊ ＊ ＊

Hij

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SLIDE 14
  • 2. “K-pp” investigated with

Fully coupled-channel Complex Scaling Method

  • Formalism
  • Chiral SU(3)-based potential
  • Self-consistency for energy-dependent potential

in coupled-channel case

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SLIDE 15

Chiral SU(3)-based KbarN potential

  • Coupled-channel chiral dynamics
(Chiral Unitary model)
  • N. Kaiser, P.B. Siegel, W. Weise, NPA 594 (1995) 325
  • E. Oset, A. Ramos, NPA 635 (1998) 99
  • Weinberg-Tomozawa term
  • f effective chiral Lagrangian
  • Based on Chiral SU(3) theory

→ Energy dependence

  • Anti-kaon, Pion = Nambu-Goldstone boson

... governed by chiral dynamics

Constrained by KbarN scattering length

  • Old data: aKN(I=0) = -1.70 + i0.67 fm, aKN(I=1) = 0.37 + i0.60 fm
  • A. D. Martin, NPB179, 33(1979)
  • SIDDHARTA K-p data with a coupled-channel chiral dynamics:
aK-p = -0.65 + i0.81 fm, aK-n = 0.57 + i0.72 fm
  • M. Bazzi et al., NPA 881, 88 (2012)
  • Y. Ikeda, T. Hyodo, W. Weise, NPA 881, 98 (2012)

 

 

 

( 0,1) ( 0,1) 2 1 8 I ij I ij i i j j i j C V r g r f m m            3 2 /2 3 ex 1 p ij ij ij g r d r d         

Non-relativistic potential : Gaussian form

ωi: meson energy

  • A. Dote, T. Inoue, T. Myo, NPA 912, 66 (2013)
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SLIDE 16
  • 2. “K-pp” investigated with

Fully coupled-channel Complex Scaling Method

  • Formalism
  • Chiral SU(3)-based potential
  • Self-consistency for energy-dependent potential

in coupled-channel case

  • A. Dote, T. Inoue, T. Myo, arXiv: 1710.07589
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SLIDE 17

How to deal with E-dep. potential?

 

 

 

( 0,1) ( 0,1) 2

1 8

I ij I ij i i j j i j

C V r g r f m m

 

 

  

Chiral SU(3)-based potential = Energy-dependent potential

  • How to treat energy-dependent potentials

in many-body system?

  • Moreover, coupled-channels case???

“Self-consistency for Meson-Baryon energy”

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SLIDE 18

Outline: Self-consistent calc. for E-dep. potential

E(MB)In= E(MB)Cal

 Find a pole of the KbarNN-πYN three-body system with ccCSM

 

" " " " " " K p M p K pp K pp B

H E E

     

  

 Self-consistency for complex Meson-Baryon energy
  • E(MB)In : assumed in the MB potential
  • E(MB)Cal : calculated with
the obtained “K-pp”  Estimation of Meson-Baryon pair energy in “K-pp”
  • Use averaged meson binding energy B(M)
  • A. D., T. Inoue, T. Myo, arXiv: 1710.07589
  • Examine extreme two ansatz
  • A. D., T. Hyodo, W. Weise, PRC79, 014003 (2009)
An interacting MB pair carries 100% of B(M) = “Field picture” 50% of B(M) = “Particle picture”
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SLIDE 19
  • 3. Result
  • A. Dote, T. Inoue, T. Myo, arXiv: 1710.07589
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SLIDE 20

Realization of self-consistency

Indicator Δ [MeV]
  • Re E(MB)In [MeV]
Chiral SU(3) pot. (fπ=110 MeV, Martin) Field picture

Indicator of self-consistency Δ=|E(MB)Cal – E(MB)In|

Self-consistent solution : BK-pp = 23.5 MeV, ΓπYN /2 = 9.1 MeV

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SLIDE 21

Result

Martin constraint SIDDHARTA constraint Field: (B, Γ/2) = (19－36, 8－14) Particle: (B, Γ/2) = (30－47, 12－14) Field: (B, Γ/2) = (14－28, 8－15) Particle: (B, Γ/2) = (22－38, 13－18)

(-BKNN, -Γ/2) [MeV] 120 100 90 (-BKNN, -Γ/2) [MeV] fπ=120 MeV 90 100 120 fπ=120 MeV
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SLIDE 22

Results of “K-pp”

J-PARC E15-1st J-PARC E27 DISTO FINUDA Faddeev-AGS
  • Pheno. pot. (E-indep.)
Variational (Gauss)
  • Pheno. pot. (E-indep.)
Variational (Gauss)
  • Chial. pot. (E-dep.)
Faddeev-AGS Chiral pot. (E-dep.) K-pp binding energy [MeV] KbarNN threshold πΣN threshold Full ccCSM (Gauss)
  • Pheno. pot. (E-indep.)
Full ccCSM (Gauss) Chiral pot. (E-dep.)
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SLIDE 23

P P

K-

  • 4. Discussion
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SLIDE 24
  • 1. Dense matter or not?

P

K-

P P

K- Chiral SU(3) potential (E-dep.)

  • A. Dote, T. Inoue and T. Myo,
NPA 912, 66 (2013)
  • B. E. (Λ*) ~ 15 MeV

⇒ Λ* = Λ(1420)

  • B. E. (“K-pp”) = 14-38 MeV

NN distance = 2.2 fm

⇒ ~ ρ0 (=0.17 fm-3)

  • Pheno. potential

(E-indep.)

  • Y. Akaishi and T. Yamazaki,
PRC 65, 044005 (2002)
  • B. E. (Λ*) = 28 MeV

⇒ Λ* = Λ(1405)

  • B. E. (“K-pp”) = 51 MeV

NN distance = 1.9 fm

⇒ ~ 1.6 ρ0

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SLIDE 25
  • 2. Comparison of Theory and Experiment
0 [MeV] KbarNN thr.
  • 50 [MeV]
J-PARC E15 (1st run) B ~ 16 MeV Γ ~ 110 MeV
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SLIDE 26
  • 2. Comparison of Theory and Experiment
0 [MeV] KbarNN thr.
  • 50 [MeV]
J-PARC E15 (1st run) B ~ 16 MeV Γ ~ 110 MeV J-PARC E15 (2nd run)

Full ccCSM calculation

  • Phenomenological pot. : BK-pp = 51 MeV
(Martin)
  • Chiral SU(3)-based pot. : BK-pp = 14－28 MeV
(SIDDHARTA, Field) Chiral SU(3) pot.
  • Pheno. pot.
Yamaga’s talk (JPS symposium 2017)
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SLIDE 27
  • 5. Summary

and Future prospects

slide-28
SLIDE 28 “K-pp” studied with Fully coupled-channel Complex Scaling Method
  • Chiral SU(3)-based KbarN potential constrained with the latest KbarN data (SIDDAHRTA)
K-pp (Jπ=0-, T=1/2) … (BK-pp, ΓπYN /2) = (14--28, 8--15) MeV (Field picture) (22--38, 13--18) MeV (Particle picture)
  • Phenomenological KbarN potential (Akaishi-Yamazaki potential; Energy-independent)
K-pp (Jπ=0-, T=1/2) …. (BK-pp, ΓπYN /2) = (51, 16) MeV Self-consistency for meson-baryon energy is considered.
  • At the moment, J-PARC E15 (2nd run) seems consistent with the result of
K-pp (Jπ=0-, T=1/2) calculated with a phenomenological potential ???
  • NN mean distance of “K-pp” system = 2.2 fm (Chiral pot.), 1.9 fm (AY pot.)
 If KbarN potential is so attractive as Akaishi-Yamazaki potential, kaonic nuclei could be a gateway to dense matter. Among kaonic nuclei, “K-pp” is the most essential system: All theoretical studies predict B(K-pp) < 100 MeV. “K-pp” = Resonance state of KbarNN-πYN coupled system Kaonic nuclei are expected to have exotic nature, such as formation of “Dense and cold” state, due to the strongly attractive KbarN interaction.
  • 5. Summary
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SLIDE 29
  • Semi-relativistic treatment

... Pion mass is small. Influence to decay width?

  • Lower pole of K-pp?

… E-dep. Chiral SU(3) pot. may have the double pole structure.

  • Reaction spectrum

... Direct comparison with experimental data. It can be calculated using the Green function obtained with ccCSM. (“Morimatsu-Yazaki Green function method”)

  • ...
  • 5. Future prospects
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SLIDE 30

References:

  • A. Dote, T. Inoue, T. Myo, PRC 95, 062201(R) (2017)
  • A. Dote, T. Inoue, T. Myo, arXiv: 1710.07589

Thank you very much!