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Three-body hadronic molecules.

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.

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Three-body hadronic molecules.

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  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 OsetIFIC-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. (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 Whystudythem?

  7. (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 Whystudythem? BABAR Collaboration, Phys.Rev.D74:091103,2006, ,Phys.Rev.D76:012008,2007 BES Collaboration Phys.Rev.Lett.100:102003,2008

  8. (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 Whystudythem? Belle Collaboration, PRL 99 (2007) , BABAR Collaboration, PRL 95 (2005), CLEO Collaboration PRL 96 (2006), PRD 74,(2006).

  9. (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 Whystudythem? BES Collaboration PRL 97 (2006).

  10. (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 Whystudythem? Guo et al. Phys.Rev.D74:097503,2006.

  11. (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 Whystudythem? Belle Collaboration, PRL 99 (2007).

  12. (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 Whystudythem? Guo, Hanhart and Meissner, PLB 665 (2008). Eef Van Beveren, X. Liu, R.Coimbra, G.Rupp, Europhys.Lett.85 (2009)

  13. (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:  KN exotic states Whystudythem? 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 !!!

  17. 137+1405 = 1542 MeV

  18. 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!

  19. Chiral amplitudes

  20. Chiral amplitudes

  21. Chiral amplitudes

  22. Chiral amplitudes

  23. Chiral amplitudes

  24. All other such terms

  25. All other such terms

  26. 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)

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

  28. where

  29. where

  30. where

  31. where

  32. where

  33. where

  34. where

  35. where

  36. where

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

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

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

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

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

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

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