Three-body hadronic molecules.

Kanchan KhemchandaniDept. 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

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

What kind of three-hadron systems?

Attractive!!!

(1)X(2175) in f0

(2) Y(4260) in J/

(3) X(1576)in K*K

(4) Y(4660) in J/ (2s)

(5)(1650), (1600) in the K- p , .

(6) 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)

(5)(1650), (1600) in the K- p , .

(6) 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)

(5)(1650), (1600) in the K- p , .

(6) Suggestions: K N exotic states

Why study them?

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

(1)X(2175) in f0

(2) Y(4260) in J/

(3) X(1576)in K*K

(4) Y(4660) in J/ (2s)

(5)(1650), (1600) in the K- p , .

(6) 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)

(5)(1650), (1600) in the K- p , .

(6) 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)

(5)(1650), (1600) in the K- p , .

(6) Suggestions: K N exotic states

Why study them?

Belle Collaboration, PRL 99 (2007).

(1)X(2175) in f0

(2) Y(4260) in J/

(3) X(1576)in K*K

(4) Y(4660) in J/ (2s)

(5)(1650), (1600) in the K- p , .

(6) Suggestions: K N exotic states

Why study them?

Eef Van Beveren, X. Liu, R.Coimbra, G.Rupp, Europhys.Lett.85 (2009)

Guo, Hanhart and Meissner, PLB 665 (2008).

(1)X(2175) in f0

(2) Y(4260) in J/

(3) X(1576)in K*K

(4) Y(4660) in J/ (2s)

(5)(1650), (1600) in the K- p , .

(6) Suggestions: K N exotic states

Why study them?

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

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!

How do we study them?

.............´´´´ 221211111 GVVgVGVGVGVGV

........´´......´´´´ 221211111 VGVgVGVGVGVGV

........´´......´´´´ 221211111 VGVgVGVGVGVGV

Chiral amplitudes

........´´......´´´´ 221211111 VGVgVGVGVGVGV

Chiral amplitudes

........´´......´´´´ 221211111 VGVgVGVGVGVGV

Chiral amplitudes

........´´......´´´´ 221211111 VGVgVGVGVGVGV

offjkoni VsVV )(

Chiral amplitudes

........´´......´´´´ 221211111 VGVgVGVGVGVGV

offjkoni VsVV )(

Chiral amplitudes

........´´......´´´´ 221211111 VGVgVGVGVGVGV

offjkoni VsVV )(

offij Vg /1

All other such terms

All other such terms

Exact ANALYTIC cancellation in theSU(3) limit!!!

All other such terms

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

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

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

K ,,f0

Which systems did we study and what do we find?

2M-1B with S= -1

K

N

,,f0(1405)

Which systems did we study and what do we find?

2M-1B with S= -1

K

N

,,f0(1405)N*(1535)

Which systems did we study and what do we find?

2M-1B with S= -1

S-wave K

N

,,f0(1405)N*(1535)

Which systems did we study and what do we find?

2M-1B with S= -1

S-wave K

N

,,f0(1405)N*(1535)

Results: 2M-1B system with S=0

Σ(1620)

Σ(1660)

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)

(MeV)

Γ(this work)

(MeV)

Isospin = 1

Σ(1560) 10-100 1590 70

Σ(1620) 10-100 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) 50-250 1740 20

Martinez Torres, Khemchandani, oset, PRC Rapid Communication 77 (2008); EPJA 35 (2008).

2M-1B with S= 0

00

00000

0000000

,,,

,,,,,

,,,,

KnpK

KKnnK

KKnp

,,f0N N*(153

5)

Γ(PDG)(MeV)

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

Γ(PDG)(MeV)

N*(1710) 50-250

N*(2100) 50-360

Δ(1750)50-300

Δ(1910) 190-270

N N

experimental amplitudes

Γ(PDG)(MeV)

N*(1710) 50-250

N*(2100) 50-360

Δ(1750)50-300

Δ(1910) 190-270

N N

Γ(PDG)(MeV)

N*(1710) 50-250

N*(2100) 50-360

Δ(1750)50-300

Δ(1910) 190-270

N N

N*(1650)

Γ(PDG)(MeV)

N*(1710) 50-250

N*(2100) 50-360

Δ(1750)50-300

Δ(1910) 190-270

N N

N*(1650)

K

Γ(PDG)(MeV)

N*(1710) 50-250

N*(2100) 50-360

Δ(1750)50-300

Δ(1910) 190-270

N N

N*(1650)

K

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

Martinez Torres, Khemchandani , Oset PRC 79 (2009)

Ref: CLAS Collaboration, PRC 73, 035202 (2006) [arXiv:nucl-ex/0509033].

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

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

3M systems

Martinez Torres, Khemchandani, Oset PRD 78

(2008).

3M systemsY(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 ….