Kondo effect for charm hadrons in nuclear matter

Transcription

1 Kondo effect for charm hadrons in nuclear matter arxiv: [hep-ph] (accepted in PRC) Shigehiro YASUI Tokyo Institute of Technology in collaboration with K. Sudoh 1. Charm nucleus and Kodo effect 2. Kondo effect for D s - and D s * - meson 3. Kondo effect in atomic nucleus S.Y., Phys. Rev. C93, (2016) 4. Conclusion International Workshop on Strangeness Nuclear Physics 2017@ 大阪電通大 Mar. 2017

2 Kondo effect for charm hadrons in nuclear matter arxiv: [hep-ph] (accepted in PRC) Shigehiro YASUI Tokyo Institute of Technology in collaboration with K. Sudoh 1. Charm nucleus and Kodo effect 2. Kondo effect for D s - and D s * - meson 3. Kondo effect in atomic nucleus S.Y., Phys. Rev. C93, (2016) 4. Conclusion International Workshop on Strangeness Nuclear Physics 2017@ 大阪電通大 Mar. 2017

3 1. Charm nucleus and Kondo effect (Hyper)Nuclear chart extended to strangeness General nuclear force Neutron stars Heavy ion collisions Anti-K mesic nuclei Strangeness Further extension to charm/bottom?

4 D, D Meson Skyrmion 1. Charm nucleus and Kondo effect Chiral Symmetry Quark Condensate NJL-Model SU(4)/SU(8) Symmetry Color Dipole Q c Chiral EFT Lattice QCD X,Y, Z states c mass Quark Model Channel-Coupling Pion Condensate D <π> D* Chiral Partner J P J(-P) Mean-Field Trace Anomaly Gluon Condensate Q Jacobi coordinates c c Color Confinement Charmonium Few-Body Fermi Instability particle hole Kondo Effect D D D* D* D D Heavy Quark Symmetry SU(4) Symmetry N N N D-D* (D-D*) mixing Heavy Quark EFT P c pentaquark Charm Baryon Heavy Hadron EFT Brown-Muck" (Light Spin-Complex) Heavy Quark Spin j Velocity-Rearrangement v-frame w-frame mass Q Q c Λ c* (2625) Λ c* (2595) Σ c * Λ c Σ c 1 st 2 nd 3 rd" +2/3 u c t" -1/3 d s b

5 D, D Meson Skyrmion 1. Charm nucleus and Kondo effect c c D D D* D* D D 1. Hadron-nucleon J(-P) interaction Chiral Symmetry J Heavy Quark Symmetry P Flavor symmetry, chiral symmetry, heavy quark symmetry mass Channel-Coupling Pion Condensate D <π> D* Chiral Partner Fermi Instability particle Kondo Effect N N N D-D* (D-D*) mixing Heavy Quark EFT Quark Condensate NJL-Model 2. Hadron in medium Q Chiral EFT SU(4)/SU(8) Symmetry SU(4) Symmetry X,Y, Z states 3. Nuclear structure Color Dipole Quark Model P c pentaquark Charm Baryon Mean-Field Heavy Hadron EFT Λ c* (2625) Spin-isospin correlations, high density state (ρ>ρ 0 ) Trace Anomaly Brown-Muck" Λ c* (2595) Σ * c Gluon Condensate (Light Spin-Complex) Λ c Σ Q Q Heavy Quark Spin c Jacobi coordinates Lattice QCD Few-Body j Velocity-Rearrangement Q 1 st 2 nd 3 rd" c c Color Confinement Charmonium hole Chiral symmetry breaking, quark confinement v-frame w-frame mass c +2/3 u c t" -1/3 d s b

6 1. Charm nucleus and Kondo effect Review : Heavy Hadrons in Nuclear Matter (107 pages) arxiv: v1 [hep-ph] 28 Jun 2016 Heavy Hadrons in Nuclear Matter Atsushi Hosaka 1,2, Tetsuo Hyodo 3, Kazutaka Sudoh 4, Yasuhiro Yamaguchi 3,5,and Shigehiro Yasui 6 1 Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka, , Japan 2 J-PARC Branch, KEK Theory Center, Institute of Particle and Nuclear Studies, KEK, Tokai, Ibaraki, , Japan 3 Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, , Japan 4 Nishogakusha University, 6-16, Sanbancho, Chiyoda, Tokyo, , Japan 5 Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Genova, via Dodecaneso 33, Genova, Italy 6 Department of Physics, Tokyo Institute of Technology, Tokyo , Japan Abstract Current studies on heavy hadrons in nuclear medium are reviewed with a summary of the basic theoretical concepts of QCD, namely chiral symmetry, heavy quark spin symmetry, and the e ective Lagrangian approach. The nuclear matter is an interesting place to study the properties of heavy hadrons from many di erent points of view. We emphasize the importance of the following topics: (i) charm/bottom hadron-nucleon interaction, (ii) structure of charm/bottom nuclei, and (iii) QCD vacuum properties and hadron modifications in nuclear medium. We pick up three di erent groups of heavy hadrons, quarkonia (J/, ), heavy-light mesons (D/ D, B/B) and heavy baryons ( c, b ). The modifications of those hadrons in nuclear matter provide us with important information to investigate the essential properties of heavy hadrons. We also give the discussions about the heavy hadrons, not only in nuclear matter with infinite volume, but also in atomic nuclei with finite baryon numbers, to serve future experiments. Contents 1 Introduction 2 2 Theoretical basics Properties of QCD Symmetries Chiral symmetry Heavy quark symmetry Hadronic e ective theories Chiral e ective theory Heavy hadron e ective theory Theoretical approaches to finite density Few-body systems Treatment of nuclear matter in hadron e ective theories Chiral symmetry at finite density Quarkonia Quarkonium-nucleon interaction: gluon-exchange dominance Few-body systems Nuclear matter Heavy-light mesons Two-body interaction with nucleon Few-body systems Nuclear matter New aspects of heavy-light mesons in nuclear matter Heavy baryons Early studies on c N interaction and c nuclei Recent works on c N interaction Few-body systems Nuclear matter Summary and future prospects 83 1 Introduction It is an important problem to understand hadron properties based on the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Due to the non-trivial features of the QCD dynamics at low energies, the hadron physics shows us many interesting and even unexpected non-trivial phenomena. The fact that hadronic phenomena are so rich implies that various studies from many di erent views are useful and indispensable to reveal the nature of the hadron dynamics. Not only isolated hadrons but also hadronic matter under extreme conditions of high temperature, of high baryon density, and of many di erent flavors provide important hints to understand the hadron dynamics. One of familiar forms of hadronic matter is the atomic nucleus, the composite system of protons and neutrons. The nuclear physics has been developed so far, based on various phenomenological approaches (shell models, collective models, and so on). Recently, ab-initio calculations are being realized such that many-body nuclear problems are solved starting from the bare nucleon-nucleon interaction determined phenomenologically with high precision [1 3]. Yet a large step forward has been made; the lattice QCD has derived the nucleon-nucleon interaction [4, 5]. Thus the so far missing path from QCD to nucleus is now being exploited. Nevertheless, if we look at the problem, for instance, neutron stars, we confront with a di culty in explaining the so-called twice of the solar mass problem. Because of the high density environment in

7 1. Charm nucleus and Kondo effect What is new property of charm nuclei?

8 1. Charm nucleus and Kondo effect Heavy mass of charm hadron m c =1.3 GeV and m b =4.7 GeV Heavy Quark Symmetry (HQS) Hadron spin = light quark spin x heavy quark spin

9 1. Charm nucleus and Kondo effect Few-body study DNN HN1R J = 0 Minnesota Av18 J = 1 J = 0 J = 0 Unbound Bound Bound Bound B M B Ɣ πyc N E kin V (NN) V (DN) T nuc E NN P (odd) 75.0% 14.4% 7.4% 18.9% M. Bayer, C. W. Xiao, T. Hyodo, A. Dote, M. Oka, E. Oset, Phys. Rev. C86, (2012) D ( * ) NN B ( * ) NN Y. Yamaguchi, S.Y., A. Hosaka, Nucl. Phys. A927, 110 (2014) J/ψ-deuteron η c -deuteron -B [MeV] J/ψNN η c N N a [fm] A. Yokota, E. Hiyama, M. Oka, Pog. Ther. Exp. Phys. 2013, 113D01 Λ c N N S. Maeda, M. Oka, A. Yokota, E. Hiyama, Y-R. Liu, Pog. Ther. Exp. Phys. 2016, 023D02

10 1. Charm nucleus and Kondo effect Heavy-light meson D meson Qq

11 1. Charm nucleus and Kondo effect Heavy-light meson Kondo effect Heavy impurity nuclear physics Ds, Ds* (cs) c q Nucleus

12 1. Charm nucleus and Kondo effect What s Kondo effect?

13 1. Charm nucleus and Kondo effect

14 1. Charm nucleus and Kondo effect Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) Impurity atom with spin ½ with T a T a interaction T 2 (e - e - scattering) electron metal Log T/T K (quantum) T K : Kondo temperature T 1,..., T n^2-1 : generators of SU(n) (n=2 for spin ½) Kondo bound state binding energy ~ T K impurity spin electron spin

15 1. Charm nucleus and Kondo effect Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) Heavy impurity impurity fermion 1 Fermi surface (degenerate state) 2 3 Loop effect (particle-hole creation) Non-Abelian int. (SU(n) symmetry)

16 1. Charm nucleus and Kondo effect Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) Scattering amplitude: impurity fermion electron l k impurity atom j i (T a ) kl (T a ) ij interaction k, l, i, j=, in SU(n) (n=2 for spin ½) T 1,..., T n^2-1 : generators of SU(n)

17 1. Charm nucleus and Kondo effect Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) Scattering amplitude: impurity fermion electron l k impurity atom j i (T a ) kl (T a ) ij interaction k, l, i, j=, in SU(n) (n=2 for spin ½) T 1,..., T n^2-1 : generators of SU(n) l electron k l k + + j E: energy from Fermi surface i j hole i Log E divergence for infrared limit (E 0) for any small coupling Logarithmic divergence in resistance of electron

18 1. Charm nucleus and Kondo effect Application of Kondo effect to Hadron/nuclear physics impurity fermion Fermi gas electron gas nuclear matter (p,n) quark matter (u,d,s) Heavy impurity Fermi surface (degenerate state) spin-atoms D/B mesons c/b quarks Loop effect (particle-hole creation) Non-Abelian int. (SU(n) symmetry) electron-hole nucleon-hole quark-hole SU(2) spin SU(2) isospin SU(3) color 1. NJL-type: S.Y., K.Sudoh, Phys. Rev. C88, (2013) 2. QCD Kondo: K. Hattori, K. Itakura, S. Ozaki, S.Y., Phys. Rev. D92, (2015) 3. Magnetic catalysis QCD Kondo effect: S. Ozaki, K. Itakura, Y. Kuramoto, Phys. Rev. D94, (2016) 4. Kondo effect in atomic nucleus: S.Y., Phys. Rev. C93, (2016) 5. Kondo effect of Ds meson: S.Y., arxiv: [hep-ph] 6. QCD Kondo phase: S.Y., K. Suzuki, K. Itakura, arxiv: [hep-ph] 7. Single heavy-quark QCD Kondo cloud, S.Y., arxiv: [hep-ph] 8. Conformal theory, T. Kumura, S. Ozaki, arxiv: [cond-mat] 9. QCD Kondo effect and color superconductivity, T. Kanazawa, S. Uchino, Phys. Rev. D94, (2016) 10. Topology and stability of QCD Kondo phase, S.Y., K. Suzuki, K. Itakura, submitted to arxiv

19 D 0 (cu) D - (cd) D s- (cs)

20 2. Kondo effect for D s - and D s * - meson Ds/Ds * D/D * (cs) (cu,cd) Electric charge (Coulomb-assisted bound state) -1 0, -1 Long life-time of vector-meson < 1.9 MeV < 2.1 MeV, MeV Short-distance repulsion No Yes Non-Abelian interaction spin spin+isospin

21 L 2. Kondo effect for D s - and D s * - meson S.Y., arxiv: [hep-ph] 1 Interaction of Ds (Ds*) meson and nucleon L int = c s ϕ ϕ ( δ ij Psv i Psv j + P svp ) sv + ic t ϕ σ k ϕ ( ϵ ijk P i k sv P j spin-exchange term sv ( Psv k ϕ : nucleon field spin-nonexchange term P sv P svp k sv )) heavy quark limit (m Q ) P s * P s vector pseudoscalar heavy quark spin light quark spin heavy quark spin light quark spin

22 2. Kondo effect for D s - and D s * - meson S.Y., K. Sudoh, arxiv: [hep-ph] 2 Renormalization group equation nucleon Λ~Λ+dΛ Ds, Ds* + Ds, Ds* Λ~Λ+dΛ nucleon (hole) N N N bare Ds, Ds* Ds, Ds* dressed by nucleon/hole

23 2. Kondo effect for D s - and D s * - meson S.Y., K. Sudoh, arxiv: [hep-ph] 2 Renormalization group equation nucleon Λ~Λ+dΛ Ds, Ds* + Ds, Ds* Λ~Λ+dΛ nucleon (hole) l = ln Λ/k F (Λ: loop momentum) spin-nonexchange term spin-exchange term d dl c s(l) =0 d dl c t(l) = mk F 2π c t(l) 2 2

24 2. Kondo effect for D s - and D s * - meson 2 Renormalization group equation nucleon S.Y., K. Sudoh, arxiv: [hep-ph] Λ~Λ+dΛ Ds, Ds* + Ds, Ds* Λ~Λ+dΛ nucleon (hole) l = ln Λ/k F (Λ: loop momentum) spin-nonexchange term spin-exchange term c s (l) =c s c t (l) = c t >0 c t 1 mk F 2π c tl 2 Kondo scale (infrared singularity) ) Λ K = k F exp ( 2π2 mk F c t

25 2. Kondo effect for D s - and D s * - meson 2 Renormalization group equation S.Y., K. Sudoh, arxiv: [hep-ph] spin-flipping int. c t Strong coupling breakdown of perturbation c t >0 c t <0 0 high energy (l=0) ) Λ K = k F exp ( 2π2 mk F c t low energy (l ) Fermi surface l = ln Λ/k F Weak coupling no transition between D s - and D s * -

26 2. Kondo effect for D s - and D s * - meson 3 Mean-field approach (c t >0) S.Y., K. Sudoh, arxiv: [hep-ph] Kondo scale non-perturbative treatment D ( ) s i 2 C t ψi σ k,σ ψ i σ ϕ kσ s quark field (σ: light-spin, i:heavy-quark spin) gap: mixing of s quark and nucleon Spectral function ρ(ω) (iii) v >> i δ δ 0 δ/2 δ/2 δ δ Kondo resonance ) Λ K = k F exp ( 2π2 mk F c t 2v Ds 0 Ds* energy Research spectral function of D s bar meson in nucleus! ω

27 D 0 (cu) D - (cd) D s- (cs)

28 3. Kondo effect in atomic nuclei simple model for atomic nucleus -shell model-like picture- S.Y., Phys. Rev. C93, (2016) nucleon sector (N states) / for proton/neutron interaction H K D sector ε k D meson D 0 (cu) D - (cd) isospin 1/2 H 0 = ϵ k c kσ c kσ k = N H = H 0 + H K Purpose: the ground state energy? kinetic term H K =g ( ck c k T + +c k c k T +(c k c k c k c k ) T 3 ) Kondo (isospin-flipping) interaction cf. We consider one shell space. But this method can be extended to multi-shells. à la Lipkin model c kσ : annihilation operator for nucleon in level k and isospin σ T +, T -, T 3 : isospin operator for D meson Cf. π-exchange interaction: S.Y. and K.Sudoh, Phys. Rev. D80, (2009)

29 3. Kondo effect in atomic nuclei Exact solution Simple case: ε k =ε Case hof unknown nucleon coeffici #=1 ( ψ (1) 0,0 = ( ) Γ k ck imp c ) H ψ (1) 0,0 = E ψ(1) 0,0 k imp ε {Γ k } = {Γ 1,...,Γ N }. S.Y., Phys. Rev. C93, (2016) k = N singlet w.f. ϵ Γ k 3 2 g Γ n = E Γ k linear algebraic equation E = ϵ 3 Ng (n.d.f. =1), ϵ (n.d.f. = N 1) 2 solution!! ε ε-3ng/2 : Kondo bound state (superposed state of nucleons and D meson) k = N

30 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Step 1. Introduce auxiliary fermion fields f σ (SU(2)) T + = f f, T = f f, T 3 = 1 2 (f f f f ). Step 2. Introduce Lagrange multiplier λ H = ϵ k c kσ c kσ +g Step 4. Variation by λ and Δ S.Y., Phys. Rev. C93, (2016) ( ) fermion # 1 ( ) fσ f σ =1. ( fσ f σ c k σ c kσ 1 2 ck σ c kσ )+λ ( fσ f σ 1 ) Step 3. Apply mean-field (Δ) approx. fermion # 0, 2 = g f σ c kσ physical space auxiliary fermion # constraint H MF = ϵ k c kσ c kσ + ( ) f σ c kσ + c kσ f σ + λ fσ f σ λ + 2 λ g λ H MF =0, H MF =0 gap singlet

31 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Step 1. Introduce auxiliary fermion fields f σ (SU(2)) T + = f f, T = f f, T 3 = 1 2 (f f f f ). Step 2. Introduce Lagrange multiplier λ H = ϵ k c kσ c kσ +g Step 4. Variation by λ and Δ ( ) fermion # 1 ( ) fσ f σ =1. S.Y., Phys. Rev. C93, (2016) fermion # 0, 2 auxiliary fermion # constraint ( fσ f σ c k σ c kσ 1 2 ck σ c kσ )+λ ( fσ f σ 1 ) Step 3. Apply mean-field (Δ) approx. = g f σ c kσ physical space H MF = ϵ k c kσ c kσ + ( ) f σ c kσ + c kσ f σ + λ fσ f σ λ + 2 λ g λ H MF =0, H MF =0 gap singlet

32 Step 3 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Matrix Attraction by N-D mixing (Δ) New ground state H H cf = N N D N N D Simple case: ε k =ε H MF = ψ H cf ψ + 2 g λ, N N D N N D ϵ ϵ λ ϵ ϵ λ ε S.Y., Phys. Rev. C93, (2016) k = N Basis ψ = c 1. c N f c 1. c N f Diagonalization (next page)

33 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε H MF = φ H diag cf φ + 2 g = E k d kσ d kσ + 2 λ, Diagonalized matrix g D = (ϵ λ) = diag (ϵ,...,ϵ, 2 +4N 12 (ϵ + λ D), 12 (ϵ + λ + D), ϵ,...,ϵ, 12 (ϵ + λ D), 12 ) 2 (ϵ + λ + D) H diag cf Step 3 λ ε S.Y., Phys. Rev. C93, (2016) ( k = N New basis φ = d 1. d N d N+1 d 1. d N d N+1 lowest energy ( ) d 1σ = 1 (c 1σ c 2σ ) 2 d 2σ = 1 2 (c 1σ c 3σ ). d N 1σ = 1 2 (c 1σ c Nσ ) d Nσ = d N+1σ = lowest energy ( ) Linear combination of (coherent) nucleon and D meson ψ 0 = d N d N ϵ λ 2N D (c 1σ c Nσ ) ϵ λ 2N D (c 1σ c Nσ ) ϵ λ D f σ 1 ϵ λ D f σ

34 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε H MF = φ H diag cf φ + 2 g = E k d kσ d kσ + 2 λ, Diagonalized matrix g D = (ϵ λ) = diag (ϵ,...,ϵ, 2 +4N 12 (ϵ + λ D), 12 (ϵ + λ + D), ϵ,...,ϵ, 12 (ϵ + λ D), 12 ) 2 (ϵ + λ + D) H diag cf Step 3 λ ε S.Y., Phys. Rev. C93, (2016) ( k = N lowest energy ( ) lowest energy ( ) Step 4 E MF (λ, ) = ψ 0 H MF ψ 0 λ = ϵ, =2E N + 2 g = Ng. λ Variation by ψ 0 = d N d N 0 λ E MF =0, E MF =0, E MF (ϵ, Ng)=ϵ Ng Kondo bound state Binding energy (MF): Ng different form exact solution 3Ng/2?

35 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε 1 Mean-value of auxiliary fermion number is one. ψ 0 f σ f σ ψ 0 =1, ε k = N ( )( ) ( 2 Fluctuation [ effect [ (random-phase ]] approximation; RPA) ( A B )( B A X Y ) = Ω ν ( X Y ) S.Y., Phys. Rev. C93, (2016) A µνρσ = ψ 0 [ a 0ν a 1µ, [ H, a 1ρ a 0σ ]] ψ0 B µνρσ = ψ 0 [ a 0ν a 1µ, [ H, a 0σ a 1ρ ]] ψ0 {Ω ν } = {Ω ±1, Ω ±2, Ω ±3, Ω 0 } { = ± 2Ng,± 2Ng,± } 2Ng,0 E RPA = 1 2 Ω ν 1 2 TrA ν>0 = 1 2 (3 2 5)Ng 0.378Ng, zero-point energy in H.O. potential Binding energy (MF+RPA): 1.378Ng close to exact solution 3Ng/2=1.5Ng!! E MF+shift+RPA = E MF+shift + E RPA = ϵ 1 2 (7 3 2)Ng ϵ 1.378Ng.

36 3. Kondo effect in atomic nuclei What s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε 3 Violation of isospin symmetry (application) H 0 H 0 = ϵ kσ c kσ c kσ, ε+δε ε S.Y., Phys. Rev. C93, (2016) k = N λ = ϵ δϵ, = Ng Ẽ MF (ϵ δϵ, Ng ε =ε, ε =ε+δε 1 (δϵ)2 16N 2 g 2. 1 (δϵ)2 16N 2 g 2 ) Δ Δ=0 at δε =4Ng δε 0 4Ng isospin breaking = ϵ Ng + 1 (δϵ)2 δϵ 2 16Ng. E MF =ε at δε=4ng

37 4. Conclusion 1 We study the Kondo effect of Ds/Ds * meson in nuclear matter. 2 We apply the renormalization group equation and find fixed point at the Kondo scale. 3 The Kondo scale is relevant to the width of the Kondo resonance as mixing of Ds/Ds* meson and nucleon in the ground state. Future works: 1. Application to realistic Ds/Ds* meson-nucleon interaction. 2. Application to other heavy hadrons. 3. Observables and reactions for experiments. 4. etc.

38 Conclusion 1 We study the Kondo effect of Ds/Ds * meson in nuclear matter. Heavy meson in nuclear matter 2 We apply the renormalization group equation and find fixed point at the Kondo scale. x HQS interaction (non-abelian) = Kondo resonance/bound state 3 The Kondo scale is relevant to the width of the Kondo resonance as mixing of Ds/Ds* meson and nucleon in the ground state. Future works: 1. Application to realistic Ds/Ds* meson-nucleon interaction. 2. Application to other heavy hadrons. 3. Observables and reactions for experiments. 4. etc.

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40 2. Kondo effect for D - s and D s * - meson S.Y., K. Sudoh, arxiv: [hep-ph] Quantum Dots (QDs) QD triplet S=1 electron + quantum mechanical superposition Impurity spin S 1 No Kondo effect in n( 2) loops ( underscreening ) P. Nizières and A. Blandin, J. Phys. (Paris) 41, 193 (1980) Mixing of triplet and singlet QDs makes the Kondo effect. M. Pustilnik and L. I. Glazman, Phys. Rev. Lett. 85, 2993 (2000) M. Eto and Y. V. Nazarov, Phys. Rev. Lett. 85, 1306 (2000) M. Eto and Y. V. Nazarov, Phys. Rev. B 64, (2001) W. Izumida, O. Sakai and S. Tarucha, Phys. Rev. Lett. 87, (2001) Similar to Ds-Ds* Kondo effect! Mixing by heavy quark symmetry singlet S=0 Impurity spin S=0 No Kondo effect