Anti-D and B meson in nuclear medium at zero temperature Shigehiro YASUI (KEK) Recent progress in hadron physics -From hadrons to quark and University, Feb. 2013

Hadrons in nuclear medium are useful for study of … 1. Introduction (i) Interaction between hadron and nucleon (ii) Modification of properties of hadron (iii) Change of medium caused by embedded hadron Hyperon-nucleon interaction, hyperon-hyperon interaction π, ω, ρ, η ( ’ ) meson masses and decay widths in nuclear medium K bar -nucleon interaction Shrink of radii of hypernuclei (“glue” effect by hyperon) Possible high density state in K bar nuclei Fundamental questions in QCD: Color confinement, Spontaneous chiral symmetry breaking, …

1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry up down strange charm bottom mass Λ QCD ≈ Chiral Symmetry Heavy Quark Symmetry SU(3) L x SU(3) R SU(2N F ) [MeV] Change !!

1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry up down strange charm bottom mass Λ QCD ≈ Chiral Symmetry Heavy Quark Symmetry SU(3) L x SU(3) R SU(2N F ) [MeV] Change !! D(cq) or D(cq) D, D (B, B) mesic nuclei - D, D (B, B)-nucleon interaction? - Modification of D, D (B, B) mesons in nuclear matter (χSB)? - Change of nuclear matter? - How is QCD concerned?

1. Introduction Charm & Bottom → Change of Mass-scale and Symmetry up down strange charm bottom mass Λ QCD ≈ Chiral Symmetry Heavy Quark Symmetry SU(3) L x SU(3) R SU(2N F ) [MeV] Change !! D(cq) or D(cq) D, D (B, B) mesic nuclei - D, D (B, B)-nucleon interaction? - Modification of D, D (B, B) mesons in nuclear matter (χSB)? - Change of nuclear matter? - How is QCD concerned?

498 MeV 1870 MeV 5400 MeV Charge Conjugate Including u, d antiquark - Annihilation - Absorption Including u, d quark - NO annihilation - NO absorption “Particle” ≠ “Antiparticle” in nuclear matter “Particle” ≠ “Antiparticle” in nuclear matter “Particle” “Antiparticle”

D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel D and nucleon `Exotic channel‘ 1. Introduction π+Σc (2593 MeV) π+Σc* (2658 MeV) Λc(2595) 0(1/2 - ) Λc(2625) 0(3/2 - ) Σc(2800) 1(? ? ) D*+N (2947 MeV) D+N (2803 MeV) D and nucleon `Baryon channel‘ C<0C>0 differen t What is D/D-nucleon interaction ? cqqq q

D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel D and nucleon `Exotic channel‘ 1. Introduction C<0 What is D/D-nucleon interaction ? cqqq q C>0 π+Σc (2593 MeV) π+Σc* (2658 MeV) Λc(2595) 0(1/2 - ) Λc(2625) 0(3/2 - ) Σc(2800) 1(? ? ) D*+N (2947 MeV) D+N (2803 MeV) D and nucleon `Baryon channel‘ differen t cqqq q

Strangeness, Charm, Bottom,... DB K K* D* B* 400 MeV 140 MeV 45 MeV In cham/bottom, vector meson is also important! 500 MeV1870 MeV5280 MeV Only NG boson (K) is important in dynamics, and vector meson (K*) is almost irrelevant… pseudo- scalar vector 1. Introduction sqcqbqq=u,d

Strangeness, Charm, Bottom,... NK KN  Weinberg-Tomozawa interaction One-pion exchange potential (OPEP) ND(*)D(*) D(*)D(*) N NB(*)B(*) B(*)B(*) N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force)  SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) meson-nucleon interaction 1. Introduction

Strangeness, Charm, Bottom,... NK KN  One-pion exchange potential (OPEP) ND D*N NB B*N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force)  meson-nucleon interaction 1. Introduction SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) Weinberg-Tomozawa interaction

Strangeness, Charm, Bottom,... NK KN  One-pion exchange potential (OPEP) ND* DN NB* BN One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force)  meson-nucleon interaction 1. Introduction SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) Weinberg-Tomozawa interaction

Strangeness, Charm, Bottom,... NK KN  One-pion exchange potential (OPEP) ND* N NB* N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force)  meson-nucleon interaction 1. Introduction SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) Weinberg-Tomozawa interaction

Strangeness, Charm, Bottom,... NK KN  One-pion exchange potential (OPEP) ND(*)D(*) D(*)D(*) N NB(*)B(*) B(*)B(*) N One-pion exchange is absent. (short range force) One-pion exchange is present. (long range force)  meson-nucleon interaction 1. Introduction SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) Weinberg-Tomozawa interaction

D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel D and nucleon `Exotic channel‘ 1. Introduction C<0 What is D/D-nucleon interaction ? cqqq q D D N N ND* S-wave D-wave ・ Mass degeneracy for D and D* M D* -M D = 140 MeV ∝ 1/m c ・ π exchange (tensor force) S-D wave mixing (deuteron-like) π π → New mechanism of DN interaction SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) → Some bound/resonant states “D-D* mixing” via pion exchange

DN 2807 MeV DN state 2946 MeV D*N Λ(1405) KN πΣ 1433 MeV 1330 MeV ΞN ΛΛ 2255 MeV 2230MeV H dibaryon K nuclei Hypernuclei BN 6217 MeV BN state 6263 MeV B*N 1. Introduction From hadron-nucleon interaction to a variety of exotic nuclei From hadron-nucleon interaction to a variety of exotic nuclei K(sq), Ξ(ssq), … B nuclei ? D nuclei ?

DN 2807 MeV DN state 2946 MeV D*N Λ(1405) KN πΣ 1433 MeV 1330 MeV ΞN ΛΛ 2255 MeV 2230MeV H dibaryon K nuclei Hypernuclei BN 6217 MeV BN state 6263 MeV B*N B nuclei ? 1. Introduction D(cq), B(bq) ?? From hadron-nucleon interaction to a variety of exotic nuclei From hadron-nucleon interaction to a variety of exotic nuclei

From hadron-nucleon interaction to a variety of exotic nuclei From hadron-nucleon interaction to a variety of exotic nuclei How is D bar (B) meson bound in nuclear matter? D bar (B) meson – nucleon interaction must be very interesting !! B nuclei ? D nuclei ? 1. Introduction Cf. Yamaguchi’s talk on few-body D bar -nuclear systems in 19 Λ(1405) KN πΣ 1433 MeV 1330 MeV ΞN ΛΛ 2255 MeV 2230MeV H dibaryon K nuclei Hypernuclei BN 6217 MeV BN state DN 2807 MeV DN state 2946 MeV 6263 MeV D*N B*N Quark-meson coupling model (Quark model) ・ K. Tsushima, D. -H. Lu, A. W. Thomas, K. Saito and R. H. Landau, Phys. Rev. C 59, 2824 (1999). ・ A. Sibirtsev, K. Tsushima and A. W. Thomas, Eur. Phys. J. A 6, 351 (1999). ・ K. Tsushima and F. C. Khanna, Phys. Lett. B 552, 138 (2003). QCD sum rule ・ F. Klingl, S. -s. Kim, S. H. Lee, P. Morath and W. Weise, Phys. Rev. Lett. 82, 3396 (1999. ・ Y. -H. Song, S. H. Lee and K. Morita, Phys. Rev. C 79, (2009). ・ K. Morita and S. H. Lee, Phys. Rev. C 85, (2012). ・ A. Hayashigaki, Phys. Lett. B 487, 96 (2000). ・ B. Friman, S. H. Lee and T. Song, Phys. Lett. B 548, 153 (2002). ・ T. Hilger, R. Thomas and B. Kampfer, Phys. Rev. C 79, (2009). ・ T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, (2010). ・ Z. -G. Wang and T. Huang, Phys. Rev. C 84, (2011). Hadron dynamics I (W-T interaction from SU(4) symmetry with breaking term) ・ A. Mishra, E. L. Bratkovskaya, J. Schaner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, (2004). ・ M. F. M. Lutz and C. L. Korpa, Phys. Lett. B 633, 43 (2006). ・ L. Tolos, A. Ramos and T. Mizutani, Phys. Rev. C 77, (2008). ・ A. Mishra and A. Mazumdar, Phys. Rev. C 79, (2009). ・ A. Kumar and A. Mishra, Phys. Rev. C 81, (2010). ・ C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, (2011). ・ A. Kumar and A. Mishra, Eur. Phys. J. A 47, 164 (2011). ・ C. Garcia-Recio, J. Nieves, L. L. Salcedo and L. Tolos, Phys. Rev. C 85, (2012). Hadron dynamics II (π exchange interaction) ・ S. Yasui, K. Sudoh, Phys. Rev. C87, (2013). ← Heavy Quark Symmetry + π exchange

1. Introduction 2. D bar and B mesons bound in nuclear matter 3. “Strong coupling problem“ in heavy mass limit 4. Summary & perspectives

Heavy meson Lagrangian (heavy quark symmetry & chiral symmetry) G. Burdman and J.F. Donoghue (1992) M.B. Wise (1992) T.-M. Yan, H.-Y. Cheng, C.-Y. Cheung, G.-L. Lin, Y.C. Lin and H.-L. Yu (1997) vector + pseudoscalar P*=D* bar P=D bar Multiplet field Coupling const. from experimental value of deacy width of D*→Dπ Self-energy of D in nuclear matter at order of two pion exchange D D D D D*Λc N π π NNN in-medium nucleon propagator (Pauli exclusion principle) suppressed by 1/m D, 1/m D*, 1/m N Cf. Nuclear matter Kaiser, Fritsch, Weise, NPB697, 255 (2002); ibid. A750, 259 (2005) Fiorilla, Kaiser, Weise, Prog. Part. Nucl. Phys. 67, 317 (2012) Hypernuclear matter Kaiser, Weise, PRC71, (2005) Kaiser, PRC71, (2005) SY and Sudoh, PRC87, (2013) 2. D bar and B mesons in nuclear matter ・ Mass degeneracy of D bar and D* bar in heavy quark limit ・ Vertex strength: g πDD* =g πD*D* (spin symmetry) D D N N ND* π π D D N π π DN scattering in vacuumD self-energy in matter

2. D bar and B mesons in nuclear matter Self-energy of D in nuclear matter D D* D π π N D D SY and Sudoh, PRC87, (2013) FreePauli exclusion in Fermi surface In-medium fermion propagator (k F : Fermi momentum) “particle”“hole”“particle”“hole”

2. D bar and B mesons in nuclear matter Self-energy of D* in nuclear matter D* D D π π N SY and Sudoh, PRC87, (2013) “hole” “particle”

Numerical results self-energy of D, B mesons in nuclear matter momentum cutoff : 1.27 × 0.7 GeV for D bar 1.22 × 0.7 GeV for B -35 MeV -107 MeV Negative self-energies Bound in nuclear matter D B 2. D bar and B mesons in nuclear matter Normal nuclear matter density radius ratio × hyperon cutoff

Numerical results self-energy of D*, B* mesons in nuclear matter 2. D bar and B mesons in nuclear matter momentum cutoff : 1.27 × 0.7 GeV for D bar 1.22 × 0.7 GeV for B Negative self-energies (real), but large imaginary parts Bound but unstable in nuclear matter -150 – i160 MeV -200 – i120 MeV D* B* radius ratio × hyperon cutoff Normal nuclear matter density

・ Atomic nuclei with D meson 2. D bar and B mesons in nuclear matter Fine splittings (≈ten MeV) Applications SY and Sudoh, PRC87, (2013) V 0 =-35 MeV δ : density difference between p and n Cf. “Isovector deformation” in K bar nuclei Dote, Akaishi, Horiuchi, Yamazaki, PLB590, 51 (2004) ・ Isospin polarization embedded in symmetric nuclear matter “Stable” distribution of isospin density → “Unstable” distribution of isospin density

2. D bar and B mesons in nuclear matter D bar (0 - ) : Q bar + q + q bar qq + gq + … D* bar (1 - ) : Q bar + q + q bar qq + gq + … ↑ ↓ ↑ ↑ Discussion on spin in heavy quark limit in QCD D bar and D* bar should be degenerate in vacuum. (Bottom is much better.) in vacuum “brown muck” - everything that is not the heavy quark (Isgur) degenerate

D bar (0 - ) : Q bar + q + q bar qq + gq + … + matter D* bar (1 - ) : Q bar + q + q bar qq + gq + … + matter ↑ ↓ ↑ ↑ in medium Discussion on spin in heavy quark limit in QCD 2. D bar and B mesons in nuclear matter D bar and D* bar should be degenerate in vacuum. (Bottom is much better.) “in-medium brown muck” degenerate

D bar (0 - ) : Q bar + q + q bar qq + gq + … + matter D* bar (1 - ) : Q bar + q + q bar qq + gq + … + matter ↑ ↓ ↑ ↑ D bar and D* bar should be degenerate also in matter. (Bottom is much better.) in medium D D* D π π N D π π N Q. Is there mass degeneracy in our formalism based on π exchange interaction? degenerate “in-medium brown muck” QCD-based result Discussion on spin in heavy quark limit in QCD 2. D bar and B mesons in nuclear matter A. Yes. D bar and D* bar in matter are degenerate in heavy mass limit (Δ ∝ m D* -m D →0).

1. Introduction 2. D bar and B mesons bound in nuclear matter 3. “Strong coupling problem“ in heavy mass limit 4. Summary & perspectives

3. “Strong coupling problem” in heavy mass limit We critically discuss heavy mass limit in matter at zero temperature. Heavy quark limit exists in matter as well as in vacuum. BUT always so? Fermi gas by fermion ψ Heavy “flavorerd” particle Φ (mass: M B →∞) Assumptions SY and Sudoh, arXiv ・ Fundamental representation of SU(n) symmetry (isospin doublet for n=2) ・ Current-current interaction with λ f ・ λ B factor (λ f/B : generator of SU(n) group) ・ Small coupling constant G B (so that perturbation can be applied.) “D bar, B meson” “Nuclear matter”

3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion ψ and heavy boson Φ SY and Sudoh, arXiv Heavy boson Φ with mass M B Fermion ψ (matter) + + = + … 1 st order (tree) 2 nd order (one-loop) Heavy boson Φ in matter Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson particle hole

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy boson Φ in matter Logarithmic enhancement in loop diagram in heavy mass limit (M B →∞) Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle ≈ G B M B λ f ・ λ B ≈ G B 2 M B Log(M B ) λ f ・ λ B

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle Fermi surface M B : heavy boson mass, m: fermion mass

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle Fermi surface Singularity on Fermi surface denominator = 0 for M B = ∞ case M B : heavy boson mass, m: fermion mass

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle Fermi surface No singularity on Fermi surface denominator = 0 for M B = finite case M B : heavy boson mass, m: fermion mass

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle Fermi surface M B = ∞M B = finite SingularityNo singularity Log M B Logarithmic M B : heavy boson mass, m: fermion mass

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Scattering amplitude for fermion ψ and heavy boson Φ Fermion ψ (matter) Heavy boson Φ with mass M B particle hole ↑ ↑ ↑ ↑↑↑ ↑↑↑↑↑ ↑ 1. Spin non-flip in intermediate state → Logarithmic singularity at Fermi surface is canceled.

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Scattering amplitude for fermion ψ and heavy boson Φ Fermion ψ (matter) Heavy boson Φ with mass M B particle hole ↑ ↑ ↓ ↑↑↑ ↓↑↑↓↑ ↓ 2. Spin flip in intermediate state

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … Heavy boson Φ in matter Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Scattering amplitude for fermion ψ and heavy boson Φ Fermion ψ (matter) Heavy boson Φ with mass M B particle hole ↑ ↑ ↓ ↑↑↑ ↓↑↑↓↑ ↓ 2. Spin flip in intermediate state → Logarithmic singularity at Fermi surface is NOT canceled. Cf. “Kondo problem” by J. Kondo (1964); log|q-k F | for q→k F, M B =∞.

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy boson Φ in matter Logarithmic enhancement in loop diagram in heavy mass limit (M B →∞) Scattering amplitude for fermion ψ and heavy boson Φ Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Heavy boson Φ with mass M B Fermion ψ (matter) hole particle ≈ G B M B λ f ・ λ B ≈ G B 2 M B Log(M B ) λ f ・ λ B

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy boson Φ in matter “Strong coupling problem” in λ f ・ λ B -dependent interaction in M B →∞ (isospin) Nuclear matter with isospin SU(2) ψ: nucleon Φ: D bar (B) meson Scattering amplitude for fermion ψ and heavy boson Φ Fermion ψ (matter) Heavy boson Φ with mass M B particle hole ≈ G B M B λ f ・ λ B ≈ G B 2 M B Log(M B ) λ f ・ λ B

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv Heavy fermion Ψ in matter Scattering amplitude for fermion ψ and heavy fermion Ψ Fermion ψ (matter) Heavy fermion Ψ with mass M F

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy fermion Ψ in matter “Strong coupling problem” in λ f ・ λ F -dependent interaction in M F →∞ Scattering amplitude for fermion ψ and heavy fermion Ψ Fermion ψ (matter) Heavy fermion Ψ with mass M F particle hole ≈ G F λ f ・ λ F ≈ G F 2 Log(M F ) λ f ・ λ F

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy fermion Ψ in matter ≈ G F λ f ・ λ F ≈ G F 2 Log(M F ) λ f ・ λ F “Strong coupling problem” in λ f ・ λ F -dependent interaction in M F →∞ Nuclear matter with isospin SU(2) ψ: nucleon Ψ: Λ c baryon ??? Not applicable, because Λ c is NOT doublet in SU(2) !! Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ with mass M F Fermion ψ (matter) particle hole

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy fermion Ψ in matter “Strong coupling problem” in λ f ・ λ F -dependent interaction in M F →∞ Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3 c representation of color SU(3) (color) Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ with mass M F Fermion ψ (matter) particle hole ≈ G F λ f ・ λ F ≈ G F 2 Log(M F ) λ f ・ λ F

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy fermion Ψ in matter “Strong coupling problem” in λ f ・ λ F -dependent interaction in M F →∞ Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3 c representation of color SU(3) (color) Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ with mass M F Fermion ψ (matter) particle hole ≈ G F λ f ・ λ F ≈ G F 2 Log(M F ) λ f ・ λ F R R RR RR R R R R R R “color non-flip”

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy fermion Ψ in matter “Strong coupling problem” in λ f ・ λ F -dependent interaction in M F →∞ Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3 c representation of color SU(3) (color) Scattering amplitude for fermion ψ and heavy fermion Ψ Heavy fermion Ψ with mass M F Fermion ψ (matter) particle hole ≈ G F λ f ・ λ F ≈ G F 2 Log(M F ) λ f ・ λ F R R RR RR R R B B B B “color flip”

3. “Strong coupling problem” in heavy mass limit SY and Sudoh, arXiv = + … 1 st order (tree) 2 nd order (one-loop) Heavy fermion Ψ in matter Quark matter with color SU(3) ψ: light quark Ψ: charm (bottom) quark → 3 c representation of color SU(3) Scattering amplitude for fermion ψ and heavy fermion Ψ Quark matter with charm (bottom) quark at zero temperature may not be perturbative system, but be strongly coupled one!! particle Heavy fermion Ψ with mass M F Fermion ψ (matter) hole ≈ G F λ f ・ λ F ≈ G F 2 Log(M F ) λ f ・ λ F R RRR RR R R B B B B

4. Summary & perspectives ・ Heavy quark symmetry & chiral symmetry is important to understand open charm and bottom mesons in nuclear medium. ・ Pseudoscalar (D bar, B) mesons are bound in nuclear matter. Vector (D bar *, B*) mesons are bound, but with large widths. ・ For embedded particle, λ f ・ λ B/F -dependent interaction will become strong by logarithmic enhancement in heavy mass limit. ・ How to deal with “strong coupling problem”? Application to nuclear matter and quark matter? ・ Charmed nuclei are interesting for experiments at J-PARC. → D bar, D, J/Ψ, Λ c, Σ c ( * ) embedded in atomic nuclei To study “new” physics in charmed (bottom) nuclear systems will be important for J-PARC (and others).

[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. Schaner-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). 2. D bar and B mesons in nuclear matter Comparison with other works Quark-meson coupling modelQCD rum rule Mean field Channel-coupling (w/o π exchange) Hadron dynamics π exchange Binding energy [MeV]

3. “Strong coupling problem” in heavy mass limit Scattering amplitude for fermion and heavy flavor boson 1 st order (tree level) ≈ G B M B Fermion ψ (matter) Heavy flavor boson Φ with mass M B GBMBGBMB SY and Sudoh, arXiv a ( ’ ), b ( ’ ) =1, …, n

3. “Strong coupling problem” in heavy mass limit 2 nd order (one-loop level) GBMBGBMB GBMBGBMB GBMBGBMB GBMBGBMB SY and Sudoh, arXiv Scattering amplitude for fermion and heavy flavor boson Fermion ψ (matter) Heavy flavor boson Φ with mass M B

3. “Strong coupling problem” in heavy mass limit 2 nd order (one-loop level) GBMBGBMB GBMBGBMB GBMBGBMB GBMBGBMB (Log M B )/M B M B : heavy boson mass, m: fermion mass ≈ G B 2 M B Log(M B ) Logarithmic enhancement in heavy mass limit (M B →∞) !! Log M B from loop contribution with particles and holes SY and Sudoh, arXiv Scattering amplitude for fermion and heavy flavor boson Fermion ψ (matter) Heavy flavor boson Φ with mass M B

3. “Strong coupling problem” in heavy mass limit GBMBGBMB GBMBGBMB GBMBGBMB GBMBGBMB (Log M B )/M B λ f ・ λ B -independent term → Log M B λ f ・ λ B -dependent term → Log M B SY and Sudoh, arXiv Scattering amplitude for fermion and heavy flavor boson Fermion ψ (matter) Heavy flavor boson Φ with mass M B 2 nd order (one-loop level) ≈ G B 2 M B Log(M B ) Logarithmic enhancement in heavy mass limit (M B →∞) !! M B : heavy boson mass, m: fermion mass

3. “Strong coupling problem” in heavy mass limit λf・λBλf・λB λf・λBλf・λB λf・λBλf・λB λf・λBλf・λB Opposite signs in λ f ・ λ B are important for presence of Log(M B ). < 0> 0 SY and Sudoh, arXiv Scattering amplitude for fermion and heavy flavor boson Fermion ψ (matter) Heavy flavor boson Φ with mass M B 2 nd order (one-loop level) ≈ G B 2 M B Log(M B ) Logarithmic enhancement in heavy mass limit (M B →∞) !!

3. “Strong coupling problem” in heavy mass limit Brief summary Heavy boson in matter ≈ G B 2 M B Log(M B ) ≈ G B M B Logarithmic enhancement in loop diagram in heavy mass limit (M B →∞) Heavy flavor boson Φ with mass M B Fermion ψ (matter) Nuclear matter with isospin SU(n=2) ψ: nucleon Φ: D bar (B) meson + + SY and Sudoh, arXiv “Strong coupling problem” in λ f ・ λ B -dependent interaction (isospin) λf・λBλf・λB λf・λBλf・λB λf・λBλf・λB λf・λBλf・λB λf・λBλf・λB

3. “Strong coupling problem” in heavy mass limit Heavy fermion in matter ≈ G F Brief summary Heavy flavor fermion Ψ with mass M F Fermion ψ (matter) Logarithmic enhancement in loop diagram in heavy mass limit (M F →∞) + + SY and Sudoh, arXiv Nuclear matter with isospin SU(n=2) ψ: nucleon Ψ: Λ c and Σ c ( * ) baryon ??? Not applicable, because Λ c and Σ c ( * ) are NOT doublet in SU(2) !! + + λf・λFλf・λF λf・λFλf・λF λf・λFλf・λF λf・λFλf・λF λf・λFλf・λF “Strong coupling problem” in λ f ・ λ F -dependent interaction (isospin) ≈ G F 2 Log(M F )

3. “Strong coupling problem” in heavy mass limit Heavy fermion in matter ≈ G F 2 Log(M F ) ≈ G F Brief summary Heavy flavor fermion Ψ with mass M F Fermion ψ (matter) Logarithmic enhancement in loop diagram in heavy mass limit (M F →∞) + + SY and Sudoh, arXiv Quark matter with color SU(n=3) ψ: light quark Ψ: charm (bottom) quark → 3 c representation of color SU(3) λf・λFλf・λF λf・λFλf・λF λf・λFλf・λF λf・λFλf・λF λf・λFλf・λF “Strong coupling problem” in λ f ・ λ F -dependent interaction (color) Quark matter with charm (bottom) quark at zero temperature may not be perturbative system, but be strongly coupled one!!

What is D/D-nucleon interaction ? 1. Introduction D*+N (2947 MeV) D+N (2803 MeV) D and nucleon D*+N D+N bound state resonant states SY and Sudoh, PRD80, (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, (2012) `Exotic channel‘ Only DN and D*N channel Heavy quark symmetry + π exchange (tensor force) C<0 cqqq q