Recent progress on anti-kaon--nucleon interactions and dibaryon - - PowerPoint PPT Presentation

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Recent progress on anti-kaon--nucleon interactions and dibaryon - - PowerPoint PPT Presentation

Apr 06, 2023 145 likes •435 views

Recent progress on anti-kaon--nucleon interactions and dibaryon resonances Yoichi IKEDA (RIKEN, Nishina Center) Recent progress in hadron physics --From hadrons to quark and gluon-- @Yonsei Univ., Korea, Feb.19, 2013. Outline of

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Recent progress on anti-kaon--nucleon interactions and dibaryon resonances

Yoichi IKEDA (RIKEN, Nishina Center)

“Recent progress in hadron physics” --From hadrons to quark and gluon-- @Yonsei Univ., Korea, Feb.19, 2013.

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Outline of lectures

  • Chiral symmetry in QCD
  • Chiral effective field theory (chiral perturbation theory)
  • Antikaon - nucleon interactions and nature of Λ(1405)

✦ Chiral symmetry and chiral dynamics ✦ Antikaon in nuclei

  • Antikaon-nucleon potentials model based on chiral dynamics
  • Faddeev equations to handle three-body dynamics (KbarNN - πYN coupled system)
  • Possible spectrum of KbarNN - πYN system

✦ Hadron interactions from lattice QCD

  • Introduction to lattice QCD
  • Hadron scattering on the lattice
  • Application to meson-baryon scattering
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(2) Antikaon in Nuclei

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Kbar-N and Kbar-nuclear physics

✓ KbarN (I=0) interaction is...

  • coupled with πΣ channel
  • strongly attractive

➡ quasi-bound state of Λ(1405)

  • Chiral unitary model --> two-pole structure, (KbarN: bound, πΣ: resonance)

✓ Quest for quasi-bound Kbar-NN systems

  • FINUDA, DISTO, J-PARC (E15, E27), ...

√s[MeV]

πΣ : 1330[MeV] ¯ KN : 1435[MeV]

Λ(1405)

Phenomenological construction of KbarN interaction leads to dense Kbar-nuclei Central density is much larger than normal nuclei <-- Λ(1405) doorway process to dense matter

Akaishi, Yamazaki, PRC65 (2002). Dote, Horiuchi, Akaishi, Yamazaki, PRC70 (2004).

✓ KbarN interaction is a fundamental building block for applications

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Kbar -- few-nucleon system

Phenomenological parametrization:

Gaussian form of KbarN potential (Akaishi-Yamazaki potential)

V AY

ij

(r) = CI

ijexp

⇥ −(r/a0)2⇤

Free parameters: coupling constant & range parameter 1) KbarN scattering lengths in I=0, 1 from partial wave analysis by Martin (’81) 2) Λ(1405) binding energy with KbarN bound state ansatz

Akaishi, Yamazaki, PRC65 (2002).

i, j = KbarN, πΣ, πΛ Kbar -- few-nucleon dynamics: G-matrix: G-matrix = T-matrix + Pauli blocking Many-body technique applied to Kbar-few-nucleon systems Kbar-nucleus optical potential is constructed...

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Kbar -- few-nucleon system (contd.)

“Kaonic nuclear states” in few-body systems Strange dibaryon as KbarNN bound state Binding energy : 48MeV (below KbarNN threshold) Width : 61MeV

Akaishi, Yamazaki, PRC65 (2002).

Phenomenological Kbar – nucleus optical potential These works motivate recent activities... testing ground: KbarNN simplest system Structures of “antikaonic” nuclei : Anti-symmetrized Molecular Dynamics (AMD) Phenomenological construction of KbarN interaction leads to dense Kbar-nuclei Central density is much larger than normal nuclei <- Λ(1405) doorway process to dense matter

Dote, Horiuchi, Akaishi, Yamazaki, PRC70 (2004).

4fm 4fm p

K-

n p

K-

p p

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Experimental studies

B.E.=115MeV Width=67MeV

Stopped K- reaction on 6Li, 7Li and 12C targets (FINUDA exp.)

Enhancement ~100MeV below KbarNN threshold

  • -> main component is KbarNN?

Enhancement as signal of KbarNN

fit region

pp->pΛK+ (DISTO exp.)

B.E.=105MeV Width=118MeV Enhancement as signal of KbarNN

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Kbar -- few-nucleon system

“Kaonic nuclear states” in few-body systems Strange dibaryon as KbarNN bound state Binding energy : 48MeV (below KbarNN threshold) Width : 61MeV

Akaishi, Yamazaki, PRC65 (2002).

Phenomenological Kbar – nucleus optical potential Key issue of this investigation is KbarN-πΣ resonance, Λ(1405) l It will be very important to take into account full dynamics of KbarN-πΣ system in order to investigate energy of strange dibaryon system More realistic calculations: coupled-channel 1) Effective KbarN potential from bare KbarN-πΣ potential 2) Faddeev equations in coupled-channel formalism

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Coupled-channel Faddeev approach

B [MeV] Γ two-body input: KbarN interaction

Overview

Variational approach

B [MeV] Γ two-body input: KbarN interaction 48 17-23 40-80 16 61 40-70 40-85 42 Phenomenological optical potential [1] Effective chiral SU(3) potential [2] Phenomenological potential [3] Effective chiral SU(3) potential [4] 50-70 45-80 9-16 90-110 45-75 34-46 Phenomenological potential [5] Chiral SU(3) potential (E-indep.) [6] Chiral SU(3) potential (E-dep.) [7]

[1] Akaishi, Yamazaki, PLB535, 70 (2002); PRC76, 045201 (2007). [2] Dote, Hyodo, Weise, NPA804, 197 (2008); PRC79, 014003 (2009). [3] Wycech, Green, PRC79, 014001 (2009). [4] Barnea, Gal, Liverts, PLB712, 132 (2012).

  • Binding energy and width of quasi-bound [Kbar[NN]I=1]

[5] Shevchenko, Gal, Mares, (+Revay,) PRL98, 082301 (2007); PRC76, 044004 (2007). [6] Ikeda, Sato, PRC76, 035203 (2007); PRC79, 035201 (2009). [6] Ikeda, Kamano, Sato, PTP124, 533 (2010).

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Coupled-channel Faddeev approach

B [MeV] Γ two-body input: KbarN interaction

Overview

Variational approach

B [MeV] Γ two-body input: KbarN interaction

[2] Dote, Hyodo, Weise, NPA804, 197 (2008); PRC79, 014003 (2009). [3] Wycech, Green, PRC79, 014001 (2009). [4] Barnea, Gal, Liverts, PLB712, 132 (2012).

  • Binding energy and width of quasi-bound [Kbar[NN]I=1]

[5] Shevchenko, Gal, Mares, (+Revay,) PRL98, 082301 (2007); PRC76, 044004 (2007). [6] Ikeda, Sato, PRC76, 035203 (2007); PRC79, 035201 (2009). [6] Ikeda, Kamano, Sato, PTP124, 533 (2010).

Energy independent

[1] Akaishi, Yamazaki, PLB535, 70 (2002); PRC76, 045201 (2007).

48 17-23 40-80 16 61 40-70 40-85 42 Phenomenological optical potential [1] Effective chiral SU(3) potential [2] Phenomenological potential [3] Effective chiral SU(3) potential [4] 50-70 45-80 9-16 90-110 45-75 34-46 Phenomenological potential [5] Chiral SU(3) potential (E-indep.) [6] Chiral SU(3) potential (E-dep.) [7]

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[6] Ikeda, Sato, PRC76, 035203 (2007); PRC79, 035201 (2009). [5] Shevchenko, Gal, Mares, (+Revay,) PRL98, 082301 (2007); PRC76, 044004 (2007). [3] Wycech, Green, PRC79, 014001 (2009).

Coupled-channel Faddeev approach

B [MeV] Γ two-body input: KbarN interaction

Overview

Variational approach

B [MeV] Γ two-body input: KbarN interaction

[2] Dote, Hyodo, Weise, NPA804, 197 (2008); PRC79, 014003 (2009). [4] Barnea, Gal, Liverts, PLB712, 132 (2012).

  • Binding energy and width of quasi-bound [Kbar[NN]I=1]

[6] Ikeda, Kamano, Sato, PTP124, 533 (2010).

Energy dependent

[1] Akaishi, Yamazaki, PLB535, 70 (2002); PRC76, 045201 (2007).

48 17-23 40-80 16 61 40-70 40-85 42 Phenomenological optical potential [1] Effective chiral SU(3) potential [2] Phenomenological potential [3] Effective chiral SU(3) potential [4] 50-70 45-80 9-16 90-110 45-75 34-46 Phenomenological potential [5] Chiral SU(3) potential (E-indep.) [6] Chiral SU(3) potential (E-dep.) [7]

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SLIDE 12

[4] Barnea, Gal, Liverts, PLB712, 132 (2012). [6] Ikeda, Kamano, Sato, PTP124, 533 (2010). [2] Dote, Hyodo, Weise, NPA804, 197 (2008); PRC79, 014003 (2009). [6] Ikeda, Sato, PRC76, 035203 (2007); PRC79, 035201 (2009). [5] Shevchenko, Gal, Mares, (+Revay,) PRL98, 082301 (2007); PRC76, 044004 (2007). [3] Wycech, Green, PRC79, 014001 (2009).

Coupled-channel Faddeev approach

B [MeV] Γ two-body input: KbarN interaction

Overview

Variational approach

B [MeV] Γ two-body input: KbarN interaction

  • Binding energy and width of quasi-bound [Kbar[NN]I=1]

Topics covered...

[1] Akaishi, Yamazaki, PLB535, 70 (2002); PRC76, 045201 (2007).

48 17-23 40-80 16 61 40-70 40-85 42 Phenomenological optical potential [1] Effective chiral SU(3) potential [2] Phenomenological potential [3] Effective chiral SU(3) potential [4] 50-70 45-80 9-16 90-110 45-75 34-46 Phenomenological potential [5] Chiral SU(3) potential (E-indep.) [6] Chiral SU(3) potential (E-dep.) [7]

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Effective KbarN potential

  • KbarN-πY coupled-channel system:

Feshbach projection --> equivalent KbarN single-channel effective potential

tKN-KN

veff veff

+ =

tKN-KN N K N N N N N N K K K K K K

veff

π Y N N K K

= + + + ……

π π Y Y

Equivalent KbarN single-channel effective potential is...

  • Highly energy dependent due to presence of Λ(1405)
  • Complex (imaginary parts: decay to πY channels)

Hyodo, Weise, PRC77 (2008).

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Effective KbarN potential (contd.)

  • In chiral SU(3) dynamics, tow-pole structure of Λ(1405) is predicted...

➡ different spectral maxima in KbarN and πΣ channels

Chiral effective KbarN potential must be constructed to reproduce..

  • spectral maximum at 1420MeV (NOT 1405MeV)

Hyodo, Weise, PRC77 (2008).

  • Chiral KbarN subthreshold amplitude
  • Chiral πΣ amplitude
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KbarN πΣ Chiral effective potential AY potential

Effective KbarN potential (contd.)

  • Above KbarN threshold : good agreement in both models
  • KbarN subthreshold : large deviation

➡ Chiral SU(3) dynamics predicts significantly weaker subthreshold attraction

than AY potential

➡ Solve Schrodinger equation for 3-body KbarNN system ➡ Weak binding system of KbarNN (+c.c.) system; B.E.~20MeV

Hyodo, Weise, PRC77 (2008).

Question: 1) Where is 3-body πΣN pole in chiral SU(3) dynamics? 2) If it exists, can the pole affect 3-body spectrum like Λ(1405)?

  • -> explicit dynamics of πΣN system is important
  • -> Coupled-channel Faddeev approach
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Potential model of KbarN interaction

  • Starting with Tomozawa-Weinberg term

Weinberg, PRL 17, 616 (1966). Tomozawa, Nuov. Cim. 46A, 707 (1966).

Φ : PS meson fields , B : baryon fields

LTW = i 8f 2 tr[ ¯ Bγµ[vµ, B]]

vµ = Φ(∂µΦ) − (∂µΦ)Φ + · · ·

derive the potentials from tree level amplitudes

Vij(E) = Cij 2f 2

π

(2E − Mi − Mj)

Energy-dependent potential (E-dep.)

Cij = λSU(3)

ij

/(16π2√ωiωj)

Non-perturbative dynamics through Lippmann-Schwinger eq. Phenomenological dipole form factor to regularize loop integrals

Tij(pi, pj; E) = Vij(pi.pj) + X

n

Z dqnq2

nVin(pi, qn)

1 E − En(qn) − ⇥n(qn) + iTnj(qn, pj; E)

Vij → gi(pi)Vijgj(pj)

gi(pi) = ( Λ2

i

p2

i + Λ2 i

)2

Vij = Cij 2f 2

π

(mi + mj)

Energy-independent potential (E-indep.)

...energy dependence is fixed at threshold

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dN dm ∝ |tπΣ−πΣ|2pc.m.

Cross section & mass spectrum

Cutoff of dipole form factor is determined to reproduce K-p cross section data

dN dm ∝ |tπΣ−πΣ|2pc.m.

E-dep. potential E-indep. potential

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Λ(1405) pole position

two resonance poles

Jido et al., NPA723, 205 (2003). Hyodo, Weise, PRC77, 035204 (2008).

|t| πΣ KbarN

One resonance pole

|t| πΣ KbarN

Vij = Cij 2f 2

π

(mi + mj)

Vij(E) = Cij 2f 2

π

(2E − Mi − Mj)

Pole positions of the Λ(1405) [(ΛKN, ΛπΣ)=(1000, 700)MeV]

Different subthreshold KbarN amplitudes would contribute to the energy of strange dibaryon

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Three-body equations

Faddeev Equations

! W : 3-body scattering energy ! i(j) = 1, 2, 3 (Spectator particles) ! T(W)=T1(W)+T2(W)+T3(W) (T : 3-body amplitude) ! ti(W, E(pi)) : 2-body t-matrix with spectator particle i ! G0(W) : 3-body Green’s function

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Three-body equations (contd.)

Alt-Grassberger-Sandhas (AGS) equations Xi,j(~ pi, ~ pj; W ) = (1 − i,j)Zi,j(~ pi, ~ pj; W )

+ X

i6=n

Z d~ pnZi,n(~ pi, ~ pn; W )⌧n(~ pn; W )Xi,j(~ pn, ~ pj; W )

Xij Xij τn = +

Faddeev equations

(Separable two-body interactions)

Ti(W ) = ti(W, E(pi)) + X

j6=i

ti(W, E(pi))G0(W )Tj(W )

ti(W, E(pi)) = vi + viG0(W )ti(W, E(pi))

vi = |giii(W, ~ pi)hgi|

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Coupled-channel AGS equations

! Z(pi,pj;W) : Particle exchange potentials ! τ(pn;W) : Isobar propagators KbarNN-πYN coupled-channel formalism

π Σ, , Λ$ Λ$ K N N N N N N N K Σ, , Λ$ Λ$ Σ, , Λ$ Λ$ π π

Alt-Grassberger-Sandhas (AGS) equations --> KbarNN - πΣN - πΛN Xi,j(~ pi, ~ pj; W ) = (1 − i,j)Zi,j(~ pi, ~ pj; W )

+ X

i6=n

Z d~ pnZi,n(~ pi, ~ pn; W )⌧n(~ pn; W )Xi,j(~ pn, ~ pj; W )

Xij Xij τn = +

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Model space

Three-body couple-channel analysis is performed by taking into account all s-wave 2-body scatterings in KbarNN-πYN system with JP=0- Meson-Baryon KbarN-πΣ (I=0) KbarN-πΣ-πΛ (I=1) πN (I=1/2, 3/2) Baryon-Baryon NN (I=1) ΛN-ΣN (I=1/2) ΣN (I=3/2) Only the mesonic-decay modes are taken into account t

S11 phase shift S31 phase shift Exp. Exp. Our scattering length Our scattering length

Model of pN interactions

Ikeda, Kamano, Sato, PTP124, 533 (2010). Ikeda, Sato,PRC76, 035203 (2007);PRC79, 035201 (2009).

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Results on resonance energies

KbarNN : 2370 πΣN : 2267 E (MeV) 100 200 300 Γ (MeV) ~15MeV(shallow) ~55MeV(deep) ~35MeV Blue : E-dep. Red : E-indep.

Vij = Cij 2f 2

π

(mi + mj)

Vij(E) = Cij 2f 2

π

(2E − Mi − Mj)

(E, Γ) = (2312-2326, 34-40) MeV (Energy independent potential) (E, Γ) = (2354-2361, 34-46) & (2281-2303, 244-320) MeV (Energy dependent potential)

  • Resonance energies are determined by the pole of 3-body amplitudes
  • Two poles in E-dep model are found,

but πΣN pole has huge width (250-320MeV)

Ikeda, Kamano, Sato, PTP124, 533 (2010). Ikeda, Sato,PRC76, 035203 (2007);PRC79, 035201 (2009).

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Signature of strange dibaryon

Ohnishi, Ikeda, Kamano, Sato, arXiv:1302.2301 [nucl-th] (2013).

  • Examine possible signatures of strange dibaryon in kaon- and photo-productions

( e.g.) E15@J-PARC, LEPS@SPring-8)

  • Calculation of “breakup probability” of (KbarN)I=0N-->πΣN reaction

=

X τ g X τ g X τ g X τ g

+ + +

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Signature of strange dibaryon (contd.)

  • Break-up probability of (KbarN)I=0N --> πΣN reaction

E-indep potential: peak around 2310MeV E-dep potential: bump around 2350MeV

Ohnishi, Ikeda, Kamano, Sato, arXiv:1302.2301 [nucl-th] (2013).

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W (MeV) 100 200 300 Γ (MeV) ~15MeV(shallow) ~55MeV(deep) ~35MeV Blue : E-dep. Red : E-indep.

Signature of strange dibaryon (contd.)

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Summary -- antikaon in nuclei --

Energy of strange dibaryon:

  • Phenomenological potential / E-indep models --> deep quasi-bound KbarNN state
  • Chiral SU(3) potential models --> shallow quasi-bound KbarNN state

Effective KbarN potential:

  • Start with coupled-channel
  • Feshbach projection onto KbarN channel --> effective KbarN potential

√s[MeV]

πΣ : 1330[MeV] ¯ KN : 1435[MeV]

Λ(1405)

Signatures in amplitudes

  • Enhancement observed
  • Effect of πΣN pole seems quite small due to huge width
  • Comparison with experiment:

initial, (non-mesonic) final state interactions (e.g.) K-+3He --> “KbarNN”+n --> ΛN+n πΣ virtual pole

X

πΣ resonance pole E-dep. model

X

E-indep. model