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.20, 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

(3) Hadron interactions from LQCD

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) • Λ (1405) is the lowest state among negative parity baryons 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), ... ✓ Many theoretical studies have been motivated..., but...

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).

X X Importance of πΣ scattering Energy of strange dibaryon: ‣ Phenomenological potential / E-indep models --> deeply quasi-bound K bar NN state ‣ Chiral SU(3) potential models --> shallow quasi-bound K bar NN state Difference: πΣ pole position πΣ virtual pole πΣ resonance pole E-indep. model Chiral SU(3) model πΣ pole position is relevant to determine... • Nature of Λ (1405) : single resonance pole v.s. double resonance pole • Strange dibaryon energy, fate of “kaonic nuclei” How can we determine πΣ pole position? --> scattering parameter is key

Threshold behavior of πΣ scattering Scattering amplitude near threshold 1 f ( k ) = kcot δ ( k ) − ik kcot δ ( k ) = 1 a + 1 ⇣ 2 r e k 2 + · · · ⌘ Low-energy scattering parameters such as length, effective range... -> nature of πΣ pole position Y.I., Hyodo, Jido, Kamano, Sato, Yazaki, PTP125 (2011). Demonstration of classification input: KN scattering length --> πΣ scattering parameters

S-wave I=2 πΣ scattering on the lattice Threshold behavior of πΣ scattering Scattering amplitude near threshold 1 f ( k ) = kcot δ ( k ) − ik kcot δ ( k ) = 1 a + 1 ⇣ 2 r e k 2 + · · · ⌘ Low-energy scattering parameters such as length, effective range... -> nature of πΣ pole position Y.I., Hyodo, Jido, Kamano, Sato, Yazaki, PTP125 (2011). πΣ scattering length from Λ c decay Hyodo & Oka, PRC84 (2011). Two independent equations & three unknown valiables --> One of πΣ scattering lengths is important input ( Clear signal in I=2 πΣ scattering is expected from LQCD )

Monte Calro calculation Lattice QCD L QCD = − 1 2 trF µ ν F µ ν + ¯ ψ ( i γ µ D µ − m ) ψ Path integral formalism in Euclidean space-time X X L U n, ˆ µ space a ψ ( n ) Euclidean time • Quarks : ψ (n) h O ( τ ) i = 1 Z D Ue − S g ( U ) detD ( U, m ) O ( τ ) • Gluons : U n,µ Z : Quenched QCD detD ( U, m ) = 1 : Full QCD detD ( U, m ) 6 = 1 Well defined statistical field theory Gauge invariant formalism Non-perturbative method

Important limit in LQCD Quark mass ( m q --> m phys. ) Lattice QCD simulation with Lattice spacing (a --> 0) physical quark masses, finer lattice, Lattice volume ( 1/L, T --> 0 ) large volume is desirable • Physical quark (pion) mass (m phys. ) • Continuum limit (a --> 0) BMW Coll., Science (2008). PACS-CS Coll., PRD81 (2010). BMW Coll., Science (2008). • Thermodynamic limit (1/L, T --> 0): on-going 10fm 3 , phys. point, full QCD gauge configuration by PACS-CS Coll.

Scattering on the lattice • Scattering parameters: X low-energy expansion of phase shift kcot δ ( k ) = 1 a − 1 2 r e k 2 + · · · X L • Relevant to resonance property X x ~ X a X x, t ) � M ( ~ X, t = 0) † � B ( ~ Y , t = 0) † | 0 i ( ~ r, t ) = h 0 | � M ( ~ x + ~ r, t ) � B ( ~ τ x, ~ X, ~ ~ Y ψ (r > R): phase shift (Luscher’s formula) M. Lüscher, NPB354, 531 (1991). (asymptotic region) --> Ozaki’s talk(Tue.) [R : interaction range] (interacting region) CP-PACS Coll., PRD71, 094504(2005). ψ (r < R): potential --> observable Ishii, Aoki, Hatsuda, PRL99, 02201 (2007).

Potential method (recipe) Nambu-Bethe-Saltpeter wave function --> phase shift, T-matrix Potential defined on the lattice Baryon-Baryon, Baryon-Baryon-Baryon, Meson-Baryon, Meson-Meson, ... Many applications: nuclei, exotics, ... HAL QCD Collaboration astrophysics input... S. Aoki, B. Charron, T. Doi, T. Hatsuda, Y. Ikeda, T. Inoue, N. Ishii, K. Murano, H. Nemura, K. Sasaki

Nambu-Bethe-Salpeter wave function Full details, see, Aoki, Hatsuda, Ishii, PTP123, 89 (2010). Equal-time Nambu-Bethe-Salpeter(NBS) amplitudes (e.g., ππ scattering) x 2 , t ) ⌘ h 0 | ⇡ ( x 1 ) ⇡ ( x 2 ) | ⇡ ( ~ k ) ⇡ ( � ~ Ψ ( ~ x 1 , t ; ~ k ); in i q π + ~ r ; W ) e − iW t m 2 k 2 W = 2 = ππ ( ~ At large distance r, NBS amplitudes satisfy free Klein-Gordon equations: ( @ 2 t � r 2 i + m 2 π ) Ψ ( ~ x 1 , t ; ~ x 2 , t ) = 0 ( i = 1 , 2) r + ~ ( r 2 k 2 ) ππ ( ~ r ; W ) = 0 Spatial correlation ψ (r) is NBS wave function and satisfies Helmholtz equation Asymptotic form of NBS wave function: k ( r ) ∼ e i � l ( k ) ψ ( l ) � � --> faithful to scattering phase shift sin kr + δ l ( k ) − l π / 2 ~ kr NBS wave function in quantum field theory is the best analogue to wave function in quantum mechanics