three-body hadronic molecules
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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 ….