1. Three-body hadronic molecules.
Kanchan Khemchandani
Dept. de Física, Universidade de Coimbra.
The 5-th International Conference on Quarks and Nuclear Physics,
Beijing , September 21－26, 2009

2. In Collaboration with: Alberto Martinez Torres and Eulogio Oset IFIC-Univ. de Valencia, Spain

3. What kind of three-hadron systems?
Meson Meson Meson = 3M
Meson Meson Baryon = 2M-1B

4. What kind of three-hadron systems?
Meson Meson Meson = 3M
Meson Meson Baryon = 2M-1B

5. What kind of three-hadron systems?
Meson Meson Meson = 3M
Meson Meson Baryon = 2M-1B
Attractive!!!

6. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states

7. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
BABAR Collaboration, Phys.Rev.D74:091103,2006,
,Phys.Rev.D76:012008,2007
BES Collaboration Phys.Rev.Lett.100:102003,2008

8. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
Belle Collaboration, PRL 99 (2007) ,
BABAR Collaboration, PRL 95 (2005),
CLEO Collaboration PRL 96 (2006), PRD 74,(2006).

9. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
BES Collaboration PRL 97 (2006).

10. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
Guo et al. Phys.Rev.D74:097503,2006.

11. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
Belle Collaboration, PRL 99 (2007).

12. Why study them? (1)X(2175) in  f0 (2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
Guo, Hanhart and Meissner, PLB 665 (2008).
Eef Van Beveren, X. Liu, R.Coimbra, G.Rupp, Europhys.Lett.85 (2009)

13. Why study them? Prakhov et. al. PRC 73 (2006), 74 (2004).
(1)X(2175) in  f0
(2) Y(4260) in J/ 
(3) X(1576)in K*K
(4) Y(4660) in J/ (2s) 
(1650), (1600) in the K- p  , .
Suggestions:  K N exotic states
Prakhov et. al. PRC 73 (2006), 74 (2004).

14. If these states couple strongly to three-hadrons
It would be difficult to see them or understand their properties in other systems

15. If these states couple strongly to three-hadrons
It would be difficult to see them or understand their properties in other systems

16. If these states couple strongly to three-hadrons
It would be difficult to see them or understand their properties in other systems
confusion !!!

18. 
= MeV

20. How do we study them? We solve the Faddeev equations
in the coupled channel approach.
For the two body interactions we use chiral Lagrangians.
While writing the three-body equations, we find a very INTERESTING RESULT in this case!

25. Chiral amplitudes

26. Chiral amplitudes

27. Chiral amplitudes

28. Chiral amplitudes

29. Chiral amplitudes

32. All other such terms

33. All other such terms

34. Exact ANALYTIC cancellation in theSU(3) limit!!!
All other such terms
Exact ANALYTIC cancellation in theSU(3) limit!!!
Khemchandani, Martinez Torres, oset EJA 37 (2008);
Martinez Torres, Khemchandani, oset PRD 78 (2008)

35. Exact ANALYTIC cancellation in theSU(3) limit!!!
All other such terms
Exact ANALYTIC cancellation in theSU(3) limit!!!
Use the onshell parts of t-matrices AND neglect the3 B forces

36. where

37. where

38. where

39. where

40. where

41. where

42. where

43. where

44. where

45. We extend the procedure for the rest of diagrams involving more than three t-matrices

46. We extend the procedure for the rest of diagrams involving more than three t-matrices

47. We extend the procedure for the rest of diagrams involving more than three t-matrices

48. Variables of the eqn: s, s23
We extend the procedure for the rest of diagrams involving more than three t-matrices
Variables of the eqn: s, s23

49. Which systems did we study and what do we find?
2M-1B with S= -1

50. Which systems did we study and what do we find?
2M-1B with S= -1

51. Which systems did we study and what do we find?
2M-1B with S= -1
,,f0
 K

52. Which systems did we study and what do we find?
2M-1B with S= -1
,,f0
 K N
(1405)

53. Which systems did we study and what do we find?
2M-1B with S= -1
,,f0
 K
N*(1535) N
(1405)

54. Which systems did we study and what do we find?
2M-1B with S= -1
,,f0
 K
S-wave
N*(1535) N
(1405)

55. Which systems did we study and what do we find?
2M-1B with S= -1
,,f0
 K
S-wave
N*(1535) N
(1405)

56. Results: 2M-1B system with S=0
Σ(1660)
Σ(1620)
R. Armenteros et al. Nucl. Phys. B 8, 183 (1968).
B. R. Martin et al, Nucl. Phys. B 127, 349 (1977).

57. Γ(PDG)
(MeV)
Peak position
(this work) Γ
Isospin = 1
Σ(1560)
10-100
1590 70
Σ(1620)
1630 39
Σ(1660)
40-200
1656 30
Σ(1770)
60-100
1790 24
Isospin = 0
Λ(1600)
50-250
1568,1700
60, 136
Λ(1810)
1740 20
Martinez Torres, Khemchandani, oset, PRC Rapid Communication 77 (2008); EPJA 35 (2008).

58. 2M-1B with S= 0
,,f0
  N
N*(1535)

59. N*(1710) 50-250 N*(2100) 50-360 Δ(1750) 50-300 Δ(1910) 190-270 Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)

60.  N   N Khemchandani, Martinez Torres, oset, EPJA 37 (2008).
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N
Khemchandani, Martinez Torres, oset, EPJA 37 (2008).

61.  N   N N*(1710) 50-250 N*(2100) 50-360 Δ(1750) 50-300 Δ(1910)
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N

62.  N   N experimental amplitudes N*(1710) 50-250 N*(2100) 50-360
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N
experimental
amplitudes

63.  N   N N*(1710) 50-250 N*(2100) 50-360 Δ(1750) 50-300 Δ(1910)
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N

64.  N   N  N*(1650) N*(1710) 50-250 N*(2100) 50-360 Δ(1750) 50-300
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N
 N*(1650)

65.  N   N  N*(1650)  K N*(1710) 50-250 N*(2100) 50-360 Δ(1750)
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N
 N*(1650)
 K

66.  N   N  N*(1650)  K N*(1710) 50-250 N*(2100) 50-360 Δ(1750)
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N
 N*(1650)
 K

67. Martinez Torres, Khemchandani , Oset PRC 79 (2009)
Γ(PDG)
(MeV)
N*(1710)
50-250
N*(2100)
50-360
Δ(1750)
50-300
Δ(1910)
 N   N
 N*(1650)
 K
+ A new N*(1920)  predicted by Jido and Y. Kanada-En’yo PRC78:035203,2008

68. exptl study going on at spring8
Indeed, there is a peak in the cross sections for the γp → K+ reaction at around 1920 MeV!
And suggestions of existence of a new resonance around MeV was made by several groups: (see: Testing the three-hadron nature of the N*(1920) resonance: A. Martinez Torres, K.P. Khemchandani, Ulf-G. Meissner, E. Oset arXiv: [nucl-th] )
We suggest to study γ p → K+ K− p reaction to test the nature of this resonance
exptl study going on at spring8
Ref: CLAS Collaboration, PRC 73, (2006) [arXiv:nucl-ex/ ].

69. Khemchandani, Martinez Torres, Oset PLB 675 (2009).
2M-1 B system with S=1
study of the possibility that the  KN could be a + bound state.
We do not find any signal around 1520 MeV but we obtain a peak around 1700 MeV with 200 MeV of width.  N
Khemchandani, Martinez Torres, Oset PLB 675 (2009).

70. 3M systems

71. 3M systems
BaBar
BES

72. 3M systems

73. 3M systems

74. Martinez Torres, Khemchandani, Oset PRD 78 (2008).
3M systems
Martinez Torres, Khemchandani, Oset PRD 78 (2008).

75. 3M systems Y(4260) 1--  strong coupling to J/
Enhancement near 1 GeV in the  invariant mass
M(J/) + M(f0(980)) +200 MeV  4260 MeV.
V(J/(K) J/(K)) = 0, proceeds through D*D and coupled channels (like in  (K)).
Calculations of J/ and J/KK  dynamical generation of a resonance near the mass of the Y(4260)(Martinez Torres, Khemchandani,Oset, arxiv: )

76. Summary and Future plans
Systems studied so far:
2M-1B with S= -1  Evidence for known 4  and two  resonances
2M-1B with S= 0  (a) Evidence for 2 N* and one  resonance. (b) prediction of a new N* around 1920 MeV.
2M-1B with S= 1  (a) No evidence for a state around 1540 MeV. (b) found a broad peak around 1700 MeV.

77. Summary and Future plans
Systems studied so far:
3M (two pseudoscalar-1vector)  (a)  and KK  X(2175) (b) J/ and J/ KK  Y(4260)
System under study: K*K, ,   to look for X(1576) and other low lying vector meson resonances.
Next projects: 2baryon-1meson, 2 vector-1pseudoscalar, 3 pseudoscalars and ….