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

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

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

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

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

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

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

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).

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).

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.

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).

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)

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).

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

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

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

137+1405 = 1542 MeV

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!

Chiral amplitudes

Chiral amplitudes

Chiral amplitudes

Chiral amplitudes

Chiral amplitudes

All other such terms

All other such terms

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)

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

where

where

where

where

where

where

where

where

where

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

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

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

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

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

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

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

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

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

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

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

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).

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).

2M-1B with S= 0 ,,f0   N N*(1535)

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) 190-270

 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) 190-270  N   N Khemchandani, Martinez Torres, oset, EPJA 37 (2008).

 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) 190-270  N   N

 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) 190-270  N   N experimental amplitudes

 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) 190-270  N   N

 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) 190-270  N   N  N*(1650)

 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) 190-270  N   N  N*(1650)  K

 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) 190-270  N   N  N*(1650)  K

Martinez Torres, Khemchandani , Oset PRC 79 (2009) Γ(PDG) (MeV) N*(1710) 50-250 N*(2100) 50-360 Δ(1750) 50-300 Δ(1910) 190-270  N   N  N*(1650)  K + A new N*(1920)  predicted by Jido and Y. Kanada-En’yo PRC78:035203,2008

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 1920 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:0902.3633 [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, 035202 (2006) [arXiv:nucl-ex/0509033].

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).

3M systems

3M systems BaBar BES

3M systems

3M systems

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

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: 0906.5333)

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.

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 ….