Meson and Baryon Resonances from the interaction of vector mesons

1. E. Oset , R. Molina, L.S. Geng, D. Nicmorus, T. Branz IFIC and Theory Department, Valencia Meson and Baryon Resonances from the interaction of vector mesons Hidden gauge formalism for vector mesons, pseudoscalars and photons Derivation of chiral Lagrangians Vector-pseudoscalar interactions. The case for two K1 axial vector states Vector-vector interaction. New meson resonances, f0, f2, …. Vector baryon molecules: from octet of vectors and octet of baryons from octet of vectors and decuplet of baryons

2. Hidden gauge formalism for vector mesons, pseudoscalars and photons Bando et al. PRL, 112 (85); Phys. Rep. 164, 217 (88)

4. This work stablishes the equivalence of the chiral Lagrangians using antisymmetric formalism for vector mesons and the hidden gauge approach that uses the vector formalism. In addition the hidden gauge formalism provides the interaction of vector mesons among themselves and with baryons.

5. SeepracticalFeyman rules in Nagahiro, Roca, Hosaka, E.O. Phys. Rev. D 2009

6. Vector-pseudoscalar interaction: in the approximation q/MV=0 one obtains the Chiral Lagrangians used byLutz and Kolomeitsev (04) Roca, Oset, Singh (05) V from Lagrangian G: pseudoscalar-vector propagator Low lying axial vector meson, a1,b1, … are generated Novelty of Roca, Oset, Singh : Two K1(1270) states are generated

7. Experimental support for the two K1 states Exp. Daum, NPB (81) Geng, E.O., Roca, Oller PRD(07) (theory) The higher mass one Couples strongly to ρK The lower mass one Couples strongly to K* π The peaks of the ρK and K* π are separated by about 100 MeV

9. Rho-rho interaction in the hidden gauge approach R.Molina, D. Nicmorus, E. O. PRD (08) + V= + Spin projectors neglecting q/MV, in L=0 Bethe Salpeter eqn. G is the ρρ propagator

10. Extra contributions evaluated

11. Real parts small. ππ box provides Imaginary part

12. Note: In the I=2 (exotic channel) one has a net repulsion. No poles appear for dynamical reasons.

13. Two I=0 states generated f0, f2 that we associate to f0(1370) and f2(1270) Belle finds the f0(1370) around 1470 MeV

14. Can one make more predictions concerning these states? γγ decay: Yamagata, Nagahiro,E.O., Hirenzaki, PRD (2009)) The approach allows one to get the coupling of the Resonance to the ρρ channel from the residues at the pole of the scattering matrix Belle Crystal Ball = 0.25 Exp (PDG): Г( f2(1270)) = 2.6 ± 0.24 KeV

15. Generalization to coupled channels: L. S. Geng , E.O, Phys Rev D 09 Attraction found in many channels The f2(1270) is not changed by the addition of new channels, but a new resonance appears can be associated to f ‘2(1525) Exp :Г( f2(1270))= 185 MeV Exp: Г (f ‘2(1525)) = 76 MeV

16. For S=1 there is no decay into pseudoscar-pseudoscalar. Indeed, V V in L=0 has P=+. J=S=1 PP needs L=1 to match J=1, but then P=-1.  The width is small it comes only from K* K*bar ( a convolution over the mass distribution of the K*’s is made)

19. Note broad peak around 1400 MeV with I=2. A state there is claimed in the PDG. But we find no pole since the interaction is repulsive. No exotics.

20. No claims of states there in the PDG. BEWARE: these are no poles

21. Predicted meson states from V V interaction M , Г [MeV] (M,Г) MeV

22. L.S. Geng, T. Branz, 09 New results for radiative decay : f0(1710) 0.056 KeV PDG: < 0.289 KeV f’2(1525)  0.051 KeV PDG: 0.081±0.009 KeV • Study of the J/psi decay into Φ, ω + Resonance • Martinez, Geng, Dai, Sun, Zou, E. O. , good rates obtained • Study of the J/psi decay into γ+ Resonance • Geng, Guo, Hanhart, Molina, E.O., Zou, good rates obtained

23. Geng,Branz, E. O. (2009)

25. Phys.Lett. B (2009) SU(3) singlet This is the parameter of the theory

27. Dominant

29. ρ D* interaction, R. Molina, H. Nagahiro, A. Hosaka, E.O, PRD 2009 We also allow for decay into π D D*(2640) ? I(JP)=1/2(??) Г<15 MeV VV in L=0 has P=+ Decay into π D forbidden since L’ should be equal to S=1 and this has negative parity D2*(2460) Г=43 MeV New

30. Many states dynamically generated from mesons with charm, Ds0*(2317), D0*(2400), X(3872) …. Daniel Gamermann PRD,E.P.J.A 2007,08,09 Phys. Rev D 2009

31. States dynamically generated from the interaction of D* Dbar*, Ds* Dsbar* and other VV (noncharmed) coupled channels

32. Extension to the baryon sector Vector propagator 1/(q2-MV2) In the approximation q2/MV2= 0 one recovers the chiral Lagrangians Weinberg-Tomozawa term. > 200 works New: A. Ramos, E. O. q Kolomeitsev et al Sarkar et al New: J. Vijande, P. Gonzalez. E.O Sarkar, Vicente Vacas, B.X.Sun, E.O

33. Vector octet – baryon octet interaction Vν cannot correspond to an external vector. Indeed, external vectors have only spatial components in the approximation of neglecting three momenta, ε0= k/M for longitudinal vectors, ε0=0 for transverse vectors. Then ∂ν becomes three momentum which is neglected.  Vv corresponds to the exchanged vector.  complete analogy to VPP Extra εμεμ = -εiεi but the interaction is formally identical to the case of PBPB In the same approximation only γ0 is kept for the baryons  the spin dependence is only εiεi and the states are degenerate in spin 1/2 and 3/2 K0 energy of vector mesons

34. Philosophy behind the idea of dynamically generated baryons: The first excited N* states: N*(1440)(1/2^+) , N*(1535) (1/2^-). In quark models this tells us the quark excitation requires 500-600 MeV. It is cheaper to produce one pion, or two (140-280 MeV), if they can be bound. But now we will bind vector mesons There is another approach for vector-baryon by J. Nieves et al. based on SU(6) symmetry of flavor and spin. The two approaches are not equivalent.

35. Octet of vectors-Octet of baryons interaction A. Ramos, E. O. (2009) Attraction found in I=1/2,S=0 ; I=0,S=-1; I=1,S=-1; I=1/2,S=-2 Degenerate states 1/2- and 3/2- found We solve the Bethe Salpeter equation in coupled channels Vector-Baryon octet. T= (1-GV) -1 V with G the loop function of vector-baryon Apart from the peaks, poles are searched In the second Riemann sheet and pole positions and residues are determined. The G function takes into account the mass distribution of the vectors (width). Decay into pseudoscalar-baryon not yet considered.

39. ρΔ interaction P. Gonzalez, E. O, J. Vijande, Phys Rev C 2009 Complete analogy to the case of pseudoscalar-baryon decuplet studied in Kolomeitsev et al 04, Sarkar et al 05 I=1/2 I=3/2

40. We get now three degenerate spin states for each isospin, 1/2 or 3/2 For I=1/2 the candidates could be a block of non catalogued states around 1900 MeV found in the entries of N* states with these quantum numbers around 2100 MeV

41. Extension to the octet of vectors and decuplet of Baryons S. Sarkar, Bao Xi Sun E. O, M.J. Vicente Vacas 09

43. Conclusions Chiral dynamics plays an important role in hadron physics. Its combination with nonperturbative unitary techniques allows to study the interaction of hadrons. Poles in amplitudes correspond to dynamically generated resonances. Many of the known meson and baryon resonances can be described in this way. The introduction of vector mesons as building blocks brings a new perspective into the nature of higher mass mesons and baryons. Experimental challenges to test the nature of these resonances looking for new decay channels or production modes.