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 K 1 axial vector states Vector-vector interaction. New meson resonances, f 0, f 2, …. Vector baryon molecules: from octet of vectors and octet of baryons from octet of vectors and decuplet of baryons E. Oset, R. Molina, L.S. Geng, D. Nicmorus, T. Branz IFIC and Theory Department, Valencia

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

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.

See practical Feyman rules in Nagahiro, Roca, Hosaka, E.O. Phys. Rev. D 2009

Vector-pseudoscalar interaction: in the approximation q/M V =0 one obtains the Chiral Lagrangians used by Lutz and Kolomeitsev (04 ) Roca, Oset, Singh (05) Novelty of Roca, Oset, Singh : Two K 1 (1270) states are generated Low lying axial vector meson, a 1,b 1, … are generated V from Lagrangian G: pseudoscalar-vector propagator

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 Exp. Daum, NPB (81) Experimental support for the two K1 states

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

Extra contributions evaluated

Real parts small. π π box provides Imaginary part

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

Two I=0 states generated f 0, f 2 that we associate to f 0 (1370) and f 2 (1270) Belle finds the f0(1370) around 1470 MeV

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 Exp (PDG): Г( f 2 (1270)) = 2.6 ± 0.24 KeV Belle Crystal Ball = 0.25

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

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)

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.

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

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

New results for radiative decay : f 0 (1710)  KeV PDG: < KeV f’ 2 (1525)  KeV PDG: 0.081±0.009 KeV L.S. Geng, T. Branz, 09 Study of the J/psi decay into Φ, ω + Resonance A.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

Geng,Branz, E. O. (2009)

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

Dominant

D 2 *(2460) Г=43 MeV New D*(2640) ? I(J P )=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 We also allow for decay into π D ρ D* interaction, R. Molina, H. Nagahiro, A. Hosaka, E.O, PRD 2009

Many states dynamically generated from mesons with charm, D s0 *(2317), D 0 *(2400), X(3872) …. Daniel Gamermann PRD,E.P.J.A 2007,08,09 Phys. Rev D 2009

States dynamically generated from the interaction of D* Dbar*, D s * D s bar* and other VV (noncharmed) coupled channels

Extension to the baryon sector q In the approximation q 2 /M V 2 = 0 one recovers the chiral Lagrangians Weinberg-Tomozawa term. Vector propagator 1/(q 2 -M V 2 ) > 200 works Kolomeitsev et al Sarkar et al New: A. Ramos, E. O. New: J. Vijande, P. Gonzalez. E.O Sarkar, Vicente Vacas, B.X.Sun, E.O

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

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 MeV. It is cheaper to produce one pion, or two ( 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.

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. 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

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=3/2 I=1/2

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

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

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.