1. Charm hadrons in nuclear medium S. Yasui (KEK) K. Sudoh (Nishogakusha Univ.) “Hadron in nucleus” workshop@YITP, 31 Nov. – 2 Dec. 2013 arXiv:1308:0098 [hep-ph]

2. Contents 1. Introduction to charm (bottom) nuclei 2. Mass formula with 1/m Q expansion 3. Anti-D (B) meson in nuclear medium - Heavy meson effective theory with 1/M corretions 4. Summary & perspectives

3. 1. Introduction to charm (bottom) nuclei 1. D (B) meson and nucleon interaction 2. Modifications of D (B) meson chiral condensate, gluon condensate,... 3. Modifications of nuclear structure glue-like role? D ( * ) (B ( * ) ) meson in nuclear matter Cf. Kondo effect K.Sudoh, S.Y., PRC88, 015201 (2013) → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki

4. 1. Introduction to charm (bottom) nuclei D ( * ) (B ( * ) ) meson in nuclear matter Quark-meson coupling model QCD sum rulesMean field models Coupled-channel models with contact interactions Perturbation by pion exchanges SY and Sudoh, PRC87, 105202 (2013) Binding energy of D ( * ) (B ( * ) ) meson in nuclear matter (MeV) → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki

5. 1. Introduction to charm (bottom) nuclei 1. D (B) meson and nucleon interaction 2. Modifications of D (B) meson chiral condensate, gluon condensate,... 3. Modifications of nuclear structure glue-like role? D ( * ) (B ( * ) ) meson in nuclear matter Cf. Kondo effect K.Sudoh, S.Y., PRC88, 015201 (2013) → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki

6. 1. Introduction to charm (bottom) nuclei D ( * ) (B ( * ) ) meson in nuclear matter 1. D (B) meson and nucleon interaction 2. Modifications of D (B) meson chiral condensate, gluon condensate,... 3. Modifications of nuclear structure glue-like role? 4. Probe for “gluon dynamics” New from heavy quark! Cf. Kondo effect K.Sudoh, S.Y., PRC88, 015201 (2013) → L. Tolos A. Yokota Y. Yamaguchi K. Suzuki

7. 2. Mass formula with 1/m Q expansion Heavy Quark Effective Theory (HQET)

8. 2. Mass formula with 1/m Q expansion Heavy quark effective theory (HQET) QvQv HQET 1/m Q expansion Light quarks & gluons

9. 2. Mass formula with 1/m Q expansion Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in vacuum) rest frame QvQv HQET 1/m Q expansion Light quarks & gluons

10. 2. Mass formula with 1/m Q expansion Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in vacuum) LO NLO O(1/m Q ) rest frame Bigi, Shifman, Uraltsev, Vainshtein, PRD52, 196 (1995) Neubert, PLB322, 419 (1994) “Virial theorem” QvQv HQET 1/m Q expansion Matrix elements scale anomaly chromoelectric gluon chromomagnetic gluon Light quarks & gluons

11. Heavy Quark Effective Theory (HQET) 3. Anti-D (B) meson in nuclear medium In-medium

12. 3. Anti-D (B) meson in nuclear medium Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) LO NLO O(1/m Q ) rest frame QvQv HQET 1/m Q expansion Matrix elements scale anomaly chromoelectric gluon chromomagnetic gluon Light quarks & gluons

13. 3. Anti-D (B) meson in nuclear medium Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) LO NLO O(1/m Q ) rest frame QvQv HQET 1/m Q expansion Matrix elements scale anomaly chromoelectric gluon chromomagnetic gluon Light quarks & gluons

14. 3. Anti-D (B) meson in nuclear medium Heavy quark effective theory (HQET) Mass of heavy meson H containing a heavy quark Q (in medium at T and ρ) LO NLO O(1/m Q ) rest frame QvQv HQET 1/m Q expansion Matrix elements scale anomaly chromoelectric gluon chromomagnetic gluon 1/m Q Light quarks & gluons

15. 3. Anti-D (B) meson in nuclear medium Λ, λ 1 and λ 2 change in medium. Gluon fields change in medium. Q gluon E a, B a

16. Heavy meson effective theory (HMET) 3. Anti-D (B) meson in nuclear medium Non-perturbative dynamics by light quarks and gluons?? LO + NLO

17. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Heavy-meson effective field and separation of momentum four-velocity + residual momentum v w H v (x) H w (x) Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) vector meson pseudoscalar mesonSpin degeneracy at LO 1/M correction (NLO) : uncertainty of four-velocity or residual momentum (change of frame with v to frame with w) P ( * ) =(Qq) spin 0 (1)

18. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Heavy-meson effective field and separation of momentum 1/M correction (NLO) : uncertainty of four-velocity or residual momentum (change of frame with v to frame with w) four-velocity + residual momentum v w H v (x) H w (x) p/M Luke, Manohar, PLB286, 348 (1992), Kitazawa, Kurimoto, PLB323, 65 (1994) vector meson pseudoscalar mesonSpin degeneracy at LO P ( * ) =(Qq) spin 0 (1)

19. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by H v :

20. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : HQSS conserved (Γ=1, iγ 5, γ μ ) HQSS=Heavy quark spin symmetry O(1/M 0 ) or O(1/M 1 )

21. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : HQSS broken (Γ=γ μ γ 5, σ μν ) smaller than or equal to O(1/M 1 ) HQSS=Heavy quark spin symmetry

22. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : HQSS broken (Γ=γ μ γ 5, σ μν ) smaller than or equal to O(1/M 1 ) HQSS=Heavy quark spin symmetry

23. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Axial-currents composed by H v : O(1/M 0 ) or O(1/M 1 ) HQSS conserved O(1/M 1 ) HQSS broken HQSS=Heavy quark spin symmetry

24. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET Kitazawa, Kurimoto, PLB323, 65 (1994) P-P* mass splitting Axial-vector current by pions H H pion axial-current coupling g 1, g 1 /M, g 2 /M

25. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET --- How to fix couplings g, g 1 and g 2 ? --- LONLO Lattice QCD simulations by Detmold, Lin, Meinel, PRD.85, 114508 (2012) g g=0.4-0.5 Kitazawa, Kurimoto, PLB323, 65 (1994)

26. 3. Anti-D (B) meson in nuclear medium Heavy meson effective theory with 1/M corrections Effective Lagrangian for HMET --- How to fix couplings g, g 1 and g 2 ? --- LONLO Decay width of D* → Dπ (PDG2012) ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) for g=0.5 (Set 1) (0.4, 0, -0.17) for g=0.4 (Set 2) Constraint on g 1 and g 2 We assume g 1 =0. (Conclusion is not qualitatively changed.) Kitazawa, Kurimoto, PLB323, 65 (1994)

27. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter NNNN -1 Cf. Λ-Σ mixing in nuclear matter anti-D mesonanti-D* meson

28. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter NNNN -1 anti-D mesonanti-D* meson Cf. Λ-Σ mixing in nuclear matter Kitazawa, Kurimoto, PLB323, 65 (1994)

29. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter NNNN -1 anti-D mesonanti-D* meson 1/M corrections from HMET Cf. Λ-Σ mixing in nuclear matter g →g + (g 1 +g 2 )/M Kitazawa, Kurimoto, PLB323, 65 (1994) g →g + (g 1 +g 2 )/M g →g + (g 1 -g 2 )/M

30. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter ρ=0.17 fm -3

31. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon @ mediu m @ vacuum ρ=0.17 fm -3 about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)

32. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon @ mediu m @ vacuum ρ=0.17 fm -3 about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)

33. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon @ mediu m @ vacuum ρ=0.17 fm -3 about 0.9 suppression in gluon condensate (T. Cohen et al. 1992)

34. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD → suppressed Energy contribution from gluons becomes small. (Suppression of quantum effects.) ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) (0.4, 0, -0.17) normal density @ mediu m @ vacuum Λ

35. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromoelectric gluon → suppressed → enhanced Energy contribution from gluons becomes small. (Suppression of quantum effects.) Kinetic energy becomes large, due to the binding energy. normal density ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) (0.4, 0, -0.17) normal density @ mediu m @ vacuum Λ λ1λ1

36. 3. Anti-D (B) meson in nuclear medium In-medium masses of anti-D ( * ) (B ( * ) ) meson in nuclear matter scale anomaly in QCD chromomagnetic gluon chromoelectric gluon → suppressed → enhanced → suppressed Energy contribution from gluons becomes small. (Suppression of quantum effects.) Kinetic energy becomes large, due to the binding energy. D-D* (B-B*) splitting become small. normal density ( g, g 1 /M D, g 2 /M D ) = (0.5, 0, -0.07) (0.4, 0, -0.17) normal density @ mediu m @ vacuum Λ λ1λ1 λ2λ2

37. 3. Anti-D (B) meson in nuclear medium Gluon dynamics in “single particle state” in atomic nuclei with anti-D ( * ) (Λc) anti-D 12 C ( Λc 12 C) B.E. thr. g.s. e.s. j-1/2 j+1/2

38. 3. Anti-D (B) meson in nuclear medium Gluon dynamics in “single particle state” in atomic nuclei with anti-D ( * ) (Λc) B.E. thr. anti-D 12 C ( Λc 12 C) s.p.s. (n 2S+1 L J ) of anti-D ( * ) (Λc) → Λ, λ 1, λ 2 (m Q ) @n 2S+1 L J scale anomaly, chromoelectric gluon, chromomagnetic gluon for each s.p.s. Q gluon E a, B a g.s. e.s. j-1/2 j+1/2 Gluon dynamics can be probed for each s.p.s. !?

39. 3. Anti-D (B) meson in nuclear medium Gluon dynamics in “single particle state” in atomic nuclei with anti-D ( * ) (Λc) B.E. thr. anti-D 12 C ( Λc 12 C) s.p.s. (n 2S+1 L J ) of anti-D ( * ) (Λc) → Λ, λ 1, λ 2 (m Q ) @n 2S+1 L J scale anomaly, chromoelectric gluon, chromomagnetic gluon for each s.p.s. Q gluon E a, B a g.s. e.s. j-1/2 j+1/2 Heavy hadron mass spectrum Gluon dynamics can be probed for each s.p.s. !?

40. 3. Anti-D (B) meson in nuclear medium chromomagnetic gluonchromoelectric gluon → enhanced → suppressed Cf. Yamaguchi’s presentation Few-body calculations Two-body S.Y., K.Sudoh, Phys. Rev. D80, 034008 (2009) Y.Yamaguchi, S.Ohkoda, S.Y., A.Hosaka, Phys. Rev. D84, 014032 (2011); ibid. 85, 054003 (2013) Three-body Y.Yamaguchi, S.Y., A.Hosaka, arXiv:1309.4324 [nucl-th]

41. 4. Summary & perspectives We discussed charm (bottom) hadron mass in nuclear medium. By probing of P ( * ) meson mass in nuclear matter, we find... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. We considered 1/m Q expansion up to O(1/m Q ). Experimental studies for charmed nuclei at J-PARC and GSI-FAIR.

42. 4. Summary & perspectives We discussed charm (bottom) hadron mass in nuclear medium. By probing of P ( * ) meson mass in nuclear matter, we find... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. We considered 1/m Q expansion up to O(1/m Q ). Experimental studies for charmed nuclei at J-PARC and GSI-FAIR.

43. 4. Summary & perspectives We discussed charm (bottom) hadron mass in nuclear medium. By probing of P ( * ) meson mass in nuclear matter, we find... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. We considered 1/m Q expansion up to O(1/m Q ). Experimental studies for charmed nuclei at J-PARC and GSI-FAIR.

44. 4. Summary & perspectives We discussed charm (bottom) hadron mass in nuclear medium. By probing of P ( * ) meson mass in nuclear matter, we find... (1) Scale anomaly from QCD is suppressed. (2) Chromoelectric gluons are enhanced. (3) Chromomagnetic gluons are suppressed. Experimental studies for charmed nuclei at J-PARC and GSI-FAIR. We considered 1/m Q expansion up to O(1/m Q ). “Gluons” can be researched in charm/bottom systems !!

45. Quarks & Gluons Chiral symmetry m→0

46. Chiral symmetry Heavy quark symmetry Quarks & Gluons m→0m→∞

50. D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel D and nucleon `Exotic channel‘ 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 SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) Yamaguchi, Ohkoda, SY, Hosaka, arXiv:1301.4557 [hep-ph]

51. D*+N (2947 MeV) D+N (2803 MeV) Only DN and D*N channel D and nucleon `Exotic channel‘ C<0 What is D/D-nucleon interaction ? cqqq q SY and Sudoh, PRD80, 034008 (2009) Yamaguchi, Ohkoda, SY, Hosaka, PRD84, 014032 (2011) Yamaguchi, Ohkoda, SY, Hosaka, PRD85, 054003 (2012) 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 Yamaguchi, Ohkoda, SY, Hosaka, arXiv:1301.4557 [hep-ph]