Kondo effect in charm/bottom nuclei International workshop on J-PARC hadron physics in Tokai, 2-4 Mar Shigehiro Yasui Tokyo Institute of Technology arXiv: [hep-ph]

1. Hadron-nucleon interaction 1. Multi-flavor nucleus Nucleus + Strangeness 2. Hadron in medium 3. Nuclear structure Impurity physics

1. Hadron-nucleon interaction 1. Multi-flavor nucleus Nucleus + Charm 2. Hadron in medium 3. Nuclear structure Mass hierarchy (m c >>Λ QCD ) ~1.2 GeV ~0.2 GeV Impurity physics ??? S. H. Lee’s talk D. Suenaga’s talk

Nucleus D, D* q c 1. Multi-flavor nucleus - Binding energy - Dispersion relation - Spectral function - Reaction - Restoration of χSB - Nuclear structure - etc. Kondo effect : quantum impurity physics Charm nucleus mass spectroscopy

Contents 1. Multi-flavor nucleus 2. Kondo effect 2.1 What’s Kondo effect? 2.2 Kondo effect in atomic nuclei (mean-field + RPA) 3. Conclusion F. Takano, T. Ogawa, Prog. Theor. Phys. 35, 343 (1966) A. Yoshimori, A. Sakurai, Suppl. Prog. Theor. Phys. 46, 162 (1970) M. Eto, Y. V. Narazov, Phys. Rev. B 64, (2001) bulk systemsfinite systems This work Mean-field approach to Kondo effect

2. Kondo effect J UN K ONDO (1930-)

2.1 What’s Kondo effect? Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) Log T/T K (quantum) T 2 (classical) T K : Kondo temperature Impurity atom with spin ½ with T a ・ T a interaction electron metal T 1,..., T n^2-1 : generators of SU(n) (n=2 for spin ½) impurity spin electron spin “Kondo bound state”

3 2 1Fermi surface (particle-hole creation) Loop effect Non-Abelian int. (SU(n) symmetry) Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) 2.1 What’s Kondo effect? Heavy impurity impurity fermion

2.1 What’s Kondo effect? Original Work: J. Kondo (Prog. Theor. Phys. 32, 37 (1964)) Scattering amplitude at tree and one-loop levels k, l, i, j=↑, ↓ in SU(n) (n=2 for spin ½) T 1,..., T n^2-1 : generators of SU(n) Log E divergence for infrared limit (E→0) for any small coupling E: energy from Fermi surface impurity atom electron → Logarithmic divergence in resistance of electron ++ electron hole k l i j l j l j k i k i (T a ) kl (T a ) ij interaction

2.1 What’s Kondo effect? nucleon D, B meson “Isospin Kondo effect” u,d,s quark c, b quark “Color (QCD) Kondo effect” ① nuclear matter ② nucleon-hole loop ③ isospin SU(2) symmetry ① quark matter ② quark-hole loop ③ color SU(3) symmetry Application to nuclear/quark matter NJL-type: S.Y., K.Sudoh, Phys. Rev. C88, (2013) QCD: K. Hattori, K. Itakura, S. Ozaki, S. Y., Phys. Rev. D92, (2015) (τ a ) kl (τ a ) ij interaction(λ a ) kl (λ a ) ij interaction Cf. “Magnetic catalysis QCD Kondo effect” S. Ozaki, K. Itakura, Y. Kuramoto, arXiv:1509:06966 [hep-ph]

2.1 What’s Kondo effect? Application to nuclear/quark matter nucleon D, B meson “Isospin Kondo effect” u,d,s quark c, b quark “Color (QCD) Kondo effect” NJL-type: S.Y., K.Sudoh, Phys. Rev. C88, (2013) QCD: K. Hattori, K. Itakura, S. Ozaki, S. Y., Phys. Rev. D92, (2015) What’s about in atomic nuclei? (finite size nuclear systems) ① nuclear matter ② nucleon-hole loop ③ isospin SU(2) symmetry ① quark matter ② quark-hole loop ③ color SU(3) symmetry (τ a ) kl (τ a ) ij interaction(λ a ) kl (λ a ) ij interaction Cf. “Magnetic catalysis QCD Kondo effect” S. Ozaki, K. Itakura, Y. Kuramoto, arXiv:1509:06966 [hep-ph]

2.2 Kondo effect in atomic nuclei D meson Simple model for atomic nucleus Purpose: the ground state energy? k = 123N nucleon sector (N states) ↑/↓ for proton/neutron D sector εkεk kinetic term Kondo (isospin-flipping) interaction c kσ : annihilation operator for nucleon in level k and isospin σ T +, T -, T 3 : isospin operator for D meson HKHK à la Lipkin model Cf. π-exchange interaction: S.Y., K.Sudoh, Phys. Rev. D80, (2009)

2.2 Kondo effect in atomic nuclei Exact solution Case of nucleon #=1 singlet w.f. linear algebraic equation solution !! ε ε-3Ng/2 : “Kondo bound state” (superposed state of nucleons and D meson) k’ = 123N Simple case: ε k =ε ε k = 123N

2.2 Kondo effect in atomic nuclei What’s about more general cases? Mean-field (+RPA) approach Step 2. Introduce Lagrange multiplier λ Step 4. Variation by λ and Δ Step 3. Apply mean-field (Δ) approx. “gap” color singlet Step 1. Introduce auxiliary fermion fields f σ (SU(2)) auxiliary fermion # constraint fermion # 0, 2 fermion # 1 physical space How does it work?

2.2 Kondo effect in atomic nuclei What’s about more general cases? Mean-field (+RPA) approach Step 2. Introduce Lagrange multiplier λ Step 4. Variation by λ and Δ Step 3. Apply mean-field (Δ) approx. “gap” color singlet Step 1. Introduce auxiliary fermion fields f σ (SU(2)) auxiliary fermion # constraint fermion # 0, 2 fermion # 1 physical space

2.2 Kondo effect in atomic nuclei What’s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε N↑N↑ N↑N↑ D↑D↑ N↓N↓ N↓N↓ D↓D↓ N↑N↑ N↑N↑ D↑D↑ N↓N↓ N↓N↓ D↓D↓ Diagonalization (next page) MatrixBasis ε k = 123N Step 3 Attraction by N-D mixing (Δ) ↓ New ground state

2.2 Kondo effect in atomic nuclei What’s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε Diagonalized matrix New basis lowest energy (↑) lowest energy (↓) ε k = 123N Step 3 Linear combination of (coherent) nucleon and D meson

2.2 Kondo effect in atomic nuclei What’s about more general cases? Mean-field (+RPA) approach Simple case: ε k =ε Diagonalized matrix Variation by lowest energy (↓) lowest energy (↑) ε k = 123N Step 3 Step 4 “ Kondo bound state ” Binding energy (MF): Ng different form exact solution 3Ng/2?

2.2 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. ε k = 123N ② Fluctuation effect (random-phase approximation; RPA) Binding energy (MF+RPA): 1.378Ng close to exact solution 3Ng/2=1.5Ng!! zero-point energy in H.O. potential

2.2 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) ε+δε ε k = 123N ε ↑ =ε+δε, ε ↓ =ε Δ=0 at δε=4Ng E MF =ε at δε=4Ng Δ δε 4Ng0

3. Conclusion 2. We apply the mean-field + RPA approach to the ground state in a simple model in success. 1. We study the ground state of charm nucleus (D meson) with isospin Kondo effect. Future works: 1. Application to realistic D meson-nucleon interaction. 2. Effect by nuclear shell effects/collective modes. 3. Observables for experiments. 4. etc. 3. This method can be applied to realistic nuclear structure with charm/bottom hadron. Isospin-dependent interaction x Nuclear system with D meson = “Kondo bound state”

References S.Y., K.Sudoh, Phys. Rev. D80, (2009) Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D84, (2011) Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D85, (2013) Y.Yamaguchi, S.Y., A.Hosaka, Nucl. Phys. A927, 110 (2014) Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D87, (2013) S.Y., K.Sudoh, Y.Yamaguchi, S.Ohkoda, A.Hosaka, T.Hyodo, Phys. Lett. B727, 185 (2013) Y.Yamaguchi, S.Ohkoda, T.Hyodo, A.Hosaka, S.Y., Phys. Rev. D91, (2015) HQS doublet/singlet in exotic hadrons and nuclei D ( * ) N, D ( * ) NN hadronic molecules D ( * ) N hadronic molecules S.Y., K.Sudoh, Phys. Rev. C89, (2014) NLO in 1/m Q expansion for D ( * ) in nuclear matter D ( * ) in nuclear matter and Kondo effects S.Y., K.Sudoh, Phys. Rev. C87, (2013) S.Y., K.Sudoh, Phys. Rev. C88, (2013)

[6] K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999). [7] A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999). [15] T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, (2009). [16] T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, (2010). [17] Z. -G. Wang and T. Huang, Phys. Rev. C 84, (2011). [18] A. Mishra, E. L. Bratkovskaya, J. Schaffner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, (2004). [19] M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006). [20] L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, (2008). [21] A. Mishra and A. Mazumdar, Phys. Rev. C 79, (2009). [22] A. Kumar and A. Mishra, Phys. Rev. C 81, (2010). [23] C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, (2011). [24] A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011). [25] C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, (2012). [26] S. Yasui, K. Sudoh, Phys. Rev. C87, (2013). [27] A. Hayashigaki, Phys. Lett. B487, 96 (2000) [28] K. Suzuki, P. Gubler, M. Oka, Pos Hadron2013, 179 (2014). [29] K. Azzi, N. Er, H. Sundu, Eur. Phys. J. C74, 3021 (2014). Quark-meson coupling modelQCD rum rule Mean field WT-type coupling Hadron dynamics π exchange -50 MeV [27] [26] -66 MeV [29] +30 MeV [28] 1. Multi-flavor nucleus D (B) meson in nuclear matter Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction),... Binding energy [MeV] ~ a few ten MeV (Repulsive? Attractive?)