1. Charm quark in nuclear systems Strangeness and charm hadron physics@KEK Tokai, 3-7 Aug. 2015 S. Yasui Tokyo Tech.

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

4. 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 MeV

5. Λ(uds) → Λ c (udc) 1. Multi-flavor nucleus StrangenessCharm H.Bando, “Flavor Nuclei”, PTP Suppl. 81, 197 (1985) Charm baryon Λ c (udc)

6. Λ(uds) → Λ c (udc) 1. Multi-flavor nucleus K(qs) → D(qc) StrangenessCharm Repulsive (Chiral symmetry) Attractive (Heavy-quark spin symmetry) No quark-antiquark annihilation in nuclear medium

7. [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, 025202 (2009). [16] T. Hilger, R. Schulze and B. Kampfer, J. Phys. G G 37, 094054 (2010). [17] Z. -G. Wang and T. Huang, Phys. Rev. C 84, 048201 (2011). [18] A. Mishra, E. L. Bratkovskaya, J. Schaffner-Bielich, S. Schramm and H. Stoecker, Phys. Rev. C 69, 015202 (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, 015207 (2008). [21] A. Mishra and A. Mazumdar, Phys. Rev. C 79, 024908 (2009). [22] A. Kumar and A. Mishra, Phys. Rev. C 81, 065204 (2010). [23] C. E. Jimenez-Tejero, A. Ramos, L. Tolos and I. Vidana, Phys. Rev. C 84, 015208 (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, 025203 (2012). [26] S. Yasui, K. Sudoh, Phys. Rev. C87, 015202 (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 systems Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction),... Binding energy in nuclear matter [MeV]

8. Nucleus D, D* q c Quark-meson coupling model, QCD sum rules, hadronic interactions (mean-field approach, channel coupling, pion interaction),... 1. Multi-flavor nucleus D (B) meson in nuclear systems Binding energy Dispersion relation Spectral function Reaction etc. Heavy quark spin

9. Contents 1. Multi-flavor nucleus 2. Heavy quark symmetry 3. Application 1: Leading order in 1/m Q expansion 4. Application 2: Next-to-Leading order in 1/m Q expansion 5. Conclusion

10. 2. Heavy quark symmetry Heavy quark spin in m Q →∞ is conserved. LO Manohar, Wise, Luke, Grinstein,... Heavy quark symmetry (HQS) 1/m Q expansion (positive energy state Q v with velocity v)

11. 2. Heavy quark symmetry Heavy quark symmetry (HQS) Normal hadrons, exotic hadrons, hadronic molecules, exotic nuclei,... Naive picture in quark model HQS Heavy quark spin × Light quark and gluon total spin S Q =1/2 j Brown muck (Spin-complex) Total spin = j ± 1/2

12. 2. Heavy quark symmetry HQS singlet (j=0) J + = 1/2 J + = j + 1/2 J - = j - 1/2 Hadron mass 1/m Q HQS doublet (j≠0) Heavy quark symmetry (HQS) Normal hadrons, exotic hadrons, hadronic molecules, exotic nuclei,... OR

13. π ρ K K* D D* B B* → HQS doublet 770 MeV 140 MeV 500 MeV 890 MeV 1870 MeV 2010 MeV 5280 MeV 5325 MeV 630 MeV390 MeV140 MeV 45 MeV Spin 1 Spin 0 2. Heavy quark symmetry

14. N Δ Σ Σ* ΣcΣc Σc*Σc* ΣbΣb Σb*Σb* 940 MeV 1230 MeV 1190 MeV 1385 MeV 2520 MeV 2455 MeV 5810 MeV 5830 MeV 290 MeV195 MeV65 MeV 20 MeV → HQS doublet Spin 1/2 Spin 3/2 2. Heavy quark symmetry Λ 1115 MeV ΛcΛc 2286 MeV ΛbΛb 5619 MeV → HQS singlet

15. Charm (bottom) exotic hadrons and nuclei HQS doublet!! Hadronic molecule (A=1) Nucleus (A: large) Nucleon D meson HQS doublet or singlet? Question c c

16. 3. Application 1: Leading order in 1/m Q expansion Heavy hadron effective theory LO 1/m Q expansion in quark ⇄ 1/M expansion in hadron

17. 3. Application 1: Leading order in 1/m Q expansion Qq H.Georgi, Phys. Lett. B240, 447 (1990) A.F.Falk, H.Georgi, B.Grinstein, Nucl. Phys. B343, 1 (1990) 1-1- 0-0- P*PP(*)P(*) or = D*DB*BQ=cQ=b same mass

18. 3. Application 1: Leading order in 1/m Q expansion Qq H.Georgi, Phys. Lett. B240, 447 (1990) A.F.Falk, H.Georgi, B.Grinstein, Nucl. Phys. B343, 1 (1990) 0-0- 1-1-

19. 3. Application 1: Leading order in 1/m Q expansion Qq H.Georgi, Phys. Lett. B240, 447 (1990) A.F.Falk, H.Georgi, B.Grinstein, Nucl. Phys. B343, 1 (1990) P(0 - ) P*(1 - ) π P(0 - ) π P*(1 - ) π kinetic terminteraction with pion HQS

20. 3. Application 1: Leading order in 1/m Q expansion Qq Nucleon q Q q q q D ( * ) meson ← No quark-antiquark annihilation (very simple system!) Hadronic molecule HQS doublet or singlet? =P ( * ) π π

21. 3. Application 1: Leading order in 1/m Q expansion Qq S-wave D-wave S-wave Tensor force and... (mixing of S-wave and D-wave, like in deuteron) π π S-wave π P(0 - )-P*(1 - ) mixing is important ! Hadronic molecule P P* P =P ( * ) N N N N  J P =1/2 - case Nucleon q Q q q q D ( * ) meson HQS doublet or singlet? Time π π

22. 3. Application 1: Leading order in 1/m Q expansion P(*)NP(*)N Mass CharmBottomm Q →∞ B*N BN D*N DN 0 MeV 142 MeV 0 MeV 46 MeV 0 MeV PN, P*N π exchange N P(*)P(*) Isospin 0

23. 3. Application 1: Leading order in 1/m Q expansion P(*)NP(*)N Mass CharmBottomm Q →∞ 3/2 - 1/2 - Predictions π exchange N P(*)P(*) Isospin 0 142 MeV 0 MeV 46 MeV 0 MeV

24. 46 MeV 0 MeV 3. Application 1: Leading order in 1/m Q expansion Mass 1/2 - 3/2 - 1/2 - 3/2 - 1/2 - CharmBottomm Q →∞ P(*)NP(*)N Predictions HQS doublet D(*)ND(*)N B(*)NB(*)N π exchange N P(*)P(*) Isospin 0 J P =3/2 - : {PN( 2 D 3/2 ), P*N( 4 S 3/2 ), P*N( 4 D 3/2 ), P*N( 2 D 3/2 )} Feshbach resonance (Γ=18 MeV) 142 MeV 0 MeV

25. 3. Application 1: Leading order in 1/m Q expansion P ( * ) NN Mass 0-0- 1-1- 0-0- 1-1- CharmBottomm Q →∞ 1-0-1-0- Predictions HQS doublet D ( * ) NN B ( * ) NN Argonne v 8 ’ pot. (with tensor force) AV8’ π π N N P(*)P(*) Isospin 1/2 142 MeV 0 MeV 46 MeV 0 MeV

26. 3. Application 1: Leading order in 1/m Q expansion P ( * ) in nuclear matter P ( * ) meson P(*)P(*) P(*)P(*) P(*)P(*) NN -1 π π in-medium mass of P ( * ) in nuclear matter HQS doublet Cf. HQS singlet in “pion condensate” (Suenaga, He, Ma, Harada, PRC89, 068201 (2014)) Mass(P)=Mass(P*)

27. 1/m Q expansion LONLO+ 4. Appl.2: Next-to-Leading order in 1/m Q expansion

28. Heavy hadron mass “parametrization” 1/m Q expansion at NLO Color electric gluon Color magnetic gluon 4. Appl.2: Next-to-Leading order in 1/m Q expansion NLO in 1/m Q expansion M.Neubert, Phys. Lett. B322, 419 (1994) 1/m Q Q gluon (magnetic) spin-flip ρ: nuclear matter density Coupling to magnetic gluon at 1/m Q “Non-perturbative” gluon

29. Can we calculate hadron state in nuclear medium from QCD? 4. Appl.2: Next-to-Leading order in 1/m Q expansion Very difficult, but…

30. Heavy hadron effective theory LO + NLO 4. Appl.2: Next-to-Leading order in 1/m Q expansion 1/m Q expansion in quark ⇄ 1/M expansion in hadron Question: what is NLO?

31. 4. Appl.2: Next-to-Leading order in 1/m Q expansion Question: what is NLO? 1. Heavy quark symmetry is conserved at O(1). 2. Inv. under velocity rearrangement at O(1)+O(1/M). v → w = v + q/M ( q/M << 1 ) = How to construct effective Lagrangian? Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) v w = v - q/M H v (x) v-frame w-frame H w (x) “Velocity rearrangement” : Lorentz boost between v-frame and w-frame up to O(1/M) Heavy quark Light quark

32. 4. Appl.2: Next-to-Leading order in 1/m Q expansion 2. Inv. under velocity rearrangement at O(1)+O(1/M). 3. Heavy quark symmetry breaking terms at O(1/M). v → w = v + q/M ( q/M << 1 ) = ≠ 1. Heavy quark symmetry is conserved at O(1). Heavy quark Light quark How to construct effective Lagrangian?

33. Kitazawa, Kurimoto, PLB323, 65 (1994) 4. Appl.2: Next-to-Leading order in 1/m Q expansion Heavy meson effective theory with 1/M corrections spin-flip (1/M) LO: g NLO: g/M, g 1 /M, g 2 /M, λ/M Some terms are constrained by invariance under velocity rearrangement. “Covariant” field for velocity-rearrangement

34. P ( * ) in nuclear matterBreaking of HQS 4. Appl.2: Next-to-Leading order in 1/m Q expansion P(*)P(*) P(*)P(*) P(*)P(*) g P*P*π = g + (g 1 + g 2 )/M ≠ g P*Pπ = g + (g 1 - g 2 )/M M P* = M-2 λ /M ≠ M P = M+6 λ /M particle-hole NN -1 π π

35. “Color electric gluon enhanced” “Color magnetic gluon suppressed” 4. Appl.2: Next-to-Leading order in 1/m Q expansion vacuum normal nuclear matter λ 1 (ρ) λ 2 (ρ,m c ) λ 2 (ρ,m b )

36. 4. Appl.2: Next-to-Leading order in 1/m Q expansion Nucleus D, D* q c Heavy quark spin Probe gluon fields

37. 5. Conclusion 1. We discuss heavy quark symmetry (HQS) at LO in 1/m Q expansion. 2. HQS gives doublet/singlet in mass spectrum in exotic heavy hadrons and nuclei. 4. Toward experiments at J-PARC, GSI-FAIR !! 3. Mass modifications and splitting of D and D* mesons are concerned with gluon in medium.

38. 5. Conclusion Many open problems... - Relation to other fundamental aspects of QCD ？ (Dynamical breaking of chiral symmetry, Quark Confinement,...) - Hadron-nucleon interaction ？ Many-body physics ？ (Pion exchange, Mean field approximation, Symmetry restoration,...) - What about atomic nucleus with charm ？ - Lattice QCD: what QCD says about charm nucleus ？ - Production cross sections of charm nucleus ？ - etc.

40. Unitary transformation HQS doublet 4. Application to heavy-quark nuclear systems π exchange N P(*)P(*) 1/2 - is degenerate with 3/2 -. J P =1/2 -, 3/2 - {P ( * ) N( 2S+1 L J )} J P =1/2 - : {PN( 2 S 1/2 ), P*N( 2 S 1/2 ), P*N( 4 D 1/2 )} J P =3/2 - : {PN( 2 D 3/2 ), P*N( 4 S 3/2 ), P*N( 4 D 3/2 ), P*N( 2 D 3/2 )} K L : kinetic term (a.m. L) C: central potential T: tensor potential

41. Charm (bottom) exotic hadrons and nuclei Question Qqq HHHN 2n+1 HN 2n doublet singlet doublet singlet doublet singlet doublet Qq D, D* Σ c, Σ c * ΛcΛc ？

42. P* P P P 123 + = P ( * ) in nuclear matter π π particle- hole NN -1 * There is no PPπ vertex. A i ~ε ijk V j V k 4. Application to heavy-quark nuclear systems HQS doublet Cf. HQS singlet in “pion condensate” (Suenaga, He, Ma, Harada, Phys. Rev. C89, 068201 (2014)) M(P*)=M(P) P* meson P meson