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

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 lectures ✦ Chiral symmetry and chiral dynamics ‣ Chiral symmetry in QCD ‣ Chiral effective field theory (chiral perturbation theory) ‣ Antikaon - nucleon interactions and nature of Λ (1405) ✦ Antikaon in nuclei ‣ Antikaon-nucleon potentials model based on chiral dynamics ‣ Faddeev equations to handle three-body dynamics (K bar NN - π YN coupled system) ‣ Possible spectrum of K bar NN - π YN system ✦ Hadron interactions from lattice QCD ‣ Introduction to lattice QCD ‣ Hadron scattering on the lattice ‣ Application to meson-baryon scattering

(2) Antikaon in Nuclei

K bar -N and K bar -nuclear physics ✓ K bar N (I=0) interaction is... ¯ π Σ : 1330[MeV] KN : 1435[MeV] • coupled with πΣ channel • strongly attractive √ s [MeV] Λ (1405) ➡ quasi-bound state of Λ (1405) • Chiral unitary model --> two-pole structure, (K bar N: bound, πΣ : resonance) Phenomenological construction of K bar N interaction leads to dense K bar -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). ✓ Quest for quasi-bound K bar -NN systems • FINUDA, DISTO, J-PARC (E15, E27), ... ✓ K bar N interaction is a fundamental building block for applications

K bar -- few-nucleon system Phenomenological parametrization: Akaishi, Yamazaki, PRC65 (2002). Gaussian form of K bar N potential (Akaishi-Yamazaki potential) V AY ( r ) = C I − ( r/a 0 ) 2 ⇤ ⇥ ij exp i, j = K bar N, πΣ , πΛ ij Free parameters: coupling constant & range parameter 1) K bar N scattering lengths in I=0, 1 from partial wave analysis by Martin (’81) 2) Λ (1405) binding energy with K bar N bound state ansatz K bar -- few-nucleon dynamics: G-matrix: G-matrix = T-matrix + Pauli blocking K bar -nucleus optical potential is constructed... Many-body technique applied to K bar -few-nucleon systems

K bar -- few-nucleon system (contd.) Phenomenological K bar – nucleus optical potential Akaishi, Yamazaki, PRC65 (2002). “Kaonic nuclear states” in few-body systems Strange dibaryon as K bar NN bound state Binding energy : 48MeV (below K bar NN threshold) Width : 61MeV K - K - n p p p p Structures of “antikaonic” nuclei : Anti-symmetrized Molecular Dynamics (AMD) Phenomenological construction of K bar N interaction leads to dense K bar -nuclei 4fm 4fm Central density is much larger than normal nuclei <- Λ (1405) doorway process to dense matter Dote, Horiuchi, Akaishi, Yamazaki, PRC70 (2004). These works motivate recent activities... testing ground: K bar NN simplest system

Experimental studies Stopped K - reaction on 6 Li, 7 Li and 12 C targets (FINUDA exp.) Enhancement as signal of K bar NN B.E.=115MeV fit region Width=67MeV pp->p Λ K + (DISTO exp.) Enhancement as signal of K bar NN B.E.=105MeV Width=118MeV Enhancement ~100MeV below K bar NN threshold --> main component is K bar NN?

K bar -- few-nucleon system Phenomenological K bar – nucleus optical potential Akaishi, Yamazaki, PRC65 (2002). “Kaonic nuclear states” in few-body systems Strange dibaryon as K bar NN bound state Binding energy : 48MeV (below K bar NN threshold) Width : 61MeV Key issue of this investigation is K bar N- πΣ resonance, Λ (1405) l It will be very important to take into account full dynamics of K bar N- πΣ system in order to investigate energy of strange dibaryon system More realistic calculations: coupled-channel 1) Effective K bar N potential from bare K bar N- πΣ potential 2) Faddeev equations in coupled-channel formalism

Overview • Binding energy and width of quasi-bound [K bar [NN] I=1 ] Variational approach [1] Akaishi, Yamazaki, B [MeV] Γ two-body input: K bar N interaction PLB535, 70 (2002); PRC76, 045201 (2007). 48 61 Phenomenological optical potential [1] [2] Dote, Hyodo, Weise, NPA804, 197 (2008); 17-23 40-70 Effective chiral SU(3) potential [2] PRC79, 014003 (2009). [3] Wycech, Green, 40-80 40-85 Phenomenological potential [3] PRC79, 014001 (2009). [4] Barnea, Gal, Liverts, 16 42 Effective chiral SU(3) potential [4] PLB712, 132 (2012). [5] Shevchenko, Gal, Coupled-channel Faddeev approach Mares, (+Revay,) PRL98, 082301 (2007); B [MeV] Γ two-body input: K bar N interaction PRC76, 044004 (2007). 50-70 90-110 Phenomenological potential [5] [6] Ikeda, Sato, PRC76, 035203 (2007); 45-80 45-75 Chiral SU(3) potential (E-indep.) [6] PRC79, 035201 (2009). [6] Ikeda, Kamano, Sato, 9-16 34-46 Chiral SU(3) potential (E-dep.) [7] PTP124, 533 (2010).

Overview • Binding energy and width of quasi-bound [K bar [NN] I=1 ] Energy independent Variational approach [1] Akaishi, Yamazaki, B [MeV] Γ two-body input: K bar N interaction PLB535, 70 (2002); PRC76, 045201 (2007). 48 61 Phenomenological optical potential [1] [2] Dote, Hyodo, Weise, NPA804, 197 (2008); 17-23 40-70 Effective chiral SU(3) potential [2] PRC79, 014003 (2009). [3] Wycech, Green, 40-80 40-85 Phenomenological potential [3] PRC79, 014001 (2009). [4] Barnea, Gal, Liverts, 16 42 Effective chiral SU(3) potential [4] PLB712, 132 (2012). [5] Shevchenko, Gal, Coupled-channel Faddeev approach Mares, (+Revay,) PRL98, 082301 (2007); B [MeV] Γ two-body input: K bar N interaction PRC76, 044004 (2007). 50-70 90-110 Phenomenological potential [5] [6] Ikeda, Sato, PRC76, 035203 (2007); 45-80 45-75 Chiral SU(3) potential (E-indep.) [6] PRC79, 035201 (2009). [6] Ikeda, Kamano, Sato, 9-16 34-46 Chiral SU(3) potential (E-dep.) [7] PTP124, 533 (2010).

Overview • Binding energy and width of quasi-bound [K bar [NN] I=1 ] Energy dependent Variational approach [1] Akaishi, Yamazaki, B [MeV] Γ two-body input: K bar N interaction PLB535, 70 (2002); PRC76, 045201 (2007). 48 61 Phenomenological optical potential [1] [2] Dote, Hyodo, Weise, NPA804, 197 (2008); 17-23 40-70 Effective chiral SU(3) potential [2] PRC79, 014003 (2009). [3] Wycech, Green, 40-80 40-85 Phenomenological potential [3] PRC79, 014001 (2009). [4] Barnea, Gal, Liverts, 16 42 Effective chiral SU(3) potential [4] PLB712, 132 (2012). [5] Shevchenko, Gal, Coupled-channel Faddeev approach Mares, (+Revay,) PRL98, 082301 (2007); B [MeV] Γ two-body input: K bar N interaction PRC76, 044004 (2007). 50-70 90-110 Phenomenological potential [5] [6] Ikeda, Sato, PRC76, 035203 (2007); 45-80 45-75 Chiral SU(3) potential (E-indep.) [6] PRC79, 035201 (2009). [6] Ikeda, Kamano, Sato, 9-16 34-46 Chiral SU(3) potential (E-dep.) [7] PTP124, 533 (2010).

Overview • Binding energy and width of quasi-bound [K bar [NN] I=1 ] Topics covered... Variational approach [1] Akaishi, Yamazaki, B [MeV] Γ two-body input: K bar N interaction PLB535, 70 (2002); PRC76, 045201 (2007). 48 61 Phenomenological optical potential [1] [2] Dote, Hyodo, Weise, NPA804, 197 (2008); 17-23 40-70 Effective chiral SU(3) potential [2] PRC79, 014003 (2009). [3] Wycech, Green, 40-80 40-85 Phenomenological potential [3] PRC79, 014001 (2009). [4] Barnea, Gal, Liverts, 16 42 Effective chiral SU(3) potential [4] PLB712, 132 (2012). [5] Shevchenko, Gal, Coupled-channel Faddeev approach Mares, (+Revay,) PRL98, 082301 (2007); B [MeV] Γ two-body input: K bar N interaction PRC76, 044004 (2007). 50-70 90-110 Phenomenological potential [5] [6] Ikeda, Sato, PRC76, 035203 (2007); 45-80 45-75 Chiral SU(3) potential (E-indep.) [6] PRC79, 035201 (2009). [6] Ikeda, Kamano, Sato, 9-16 34-46 Chiral SU(3) potential (E-dep.) [7] PTP124, 533 (2010).

Effective K bar N potential Hyodo, Weise, PRC77 (2008). • K bar N- π Y coupled-channel system: Feshbach projection --> equivalent K bar N single-channel effective potential K K K K K K K + = t KN-KN t KN-KN v eff v eff N N N N N N N π π π K K = + + + …… v eff Y Y Y N N Equivalent K bar N single-channel effective potential is... • Highly energy dependent due to presence of Λ (1405) • Complex (imaginary parts: decay to π Y channels)

Effective K bar N potential (contd.) • In chiral SU(3) dynamics, tow-pole structure of Λ (1405) is predicted... ➡ different spectral maxima in K bar N and πΣ channels Hyodo, Weise, PRC77 (2008). • Chiral K bar N subthreshold amplitude • Chiral πΣ amplitude Chiral effective K bar N potential must be constructed to reproduce.. • spectral maximum at 1420MeV (NOT 1405MeV)

Effective K bar N potential (contd.) Hyodo, Weise, PRC77 (2008). AY potential Chiral effective potential πΣ K bar N • Above K bar N threshold : good agreement in both models • K bar N subthreshold : large deviation ➡ Chiral SU(3) dynamics predicts significantly weaker subthreshold attraction than AY potential ➡ Solve Schrodinger equation for 3-body K bar NN system ➡ Weak binding system of K bar NN (+c.c.) system; B.E.~20MeV Question: 1) Where is 3-body πΣ N pole in chiral SU(3) dynamics? 2) If it exists, can the pole affect 3-body spectrum like Λ (1405)? --> explicit dynamics of πΣ N system is important --> Coupled-channel Faddeev approach