Meson and Baryon Resonances from the interaction of vector mesons

Hidden gauge formalism for vector mesons, pseudoscalars and photonsDerivation of chiral Lagrangians

Vector-pseudoscalar interactions. The case for two K1 axial vector statesVector-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

E. Oset , R. Molina, L.S. Geng, D. Nicmorus, T. BranzIFIC and Theory Department, Valencia

Hidden gauge formalism for vector mesons, pseudoscalars and photonsBando 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 vectormesons 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/MV=0 one obtains the Chiral Lagrangians used by Lutz and Kolomeitsev (04) Roca, Oset, Singh (05)

Novelty of Roca, Oset, Singh : Two K1(1270) states are generated

Low lying axial vector meson,a1,b1, … are generated

V from LagrangianG: pseudoscalar-vectorpropagator

Geng, E.O., Roca, OllerPRD(07) (theory)

The higher mass oneCouples 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/MV, 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 providesImaginary part

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

Two I=0 states generatedf0, f2 that we associate to f0(1370)and f2(1270)

Belle finds thef0(1370) around1470 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 theρρ channel from the residues at the pole of the scattering matrix

Exp (PDG): Г( f2(1270)) = 2.6 ± 0.24 KeV

Belle

CrystalBall

= 0.25

Generalization to coupled channels: L. S. Geng , E.O, Phys Rev D 09

The f2(1270) is not changed by the additionof new channels, but a new resonance appears can be associated to f ‘2(1525)

Exp: Г (f ‘2(1525)) = 76 MeV

Exp :Г( f2(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=1PP needs L=1 to match J=1, but thenP=-1. The width is smallit comes only from K* K*bar ( a convolutionover 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 :

f0(1710) 0.056 KeV PDG: < 0.289 KeV

f’2(1525) 0.051 KeV PDG: 0.081±0.009 KeV

L.S. Geng, T. Branz, 09

Study of the J/psi decay into Φ, ω + ResonanceA. Martinez, Geng, Dai, Sun, Zou, E. O. , good rates obtained

Study of the J/psi decay into γ + ResonanceGeng, 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

D2*(2460) Г=43 MeVNew

D*(2640) ?I(JP)=1/2(??)Г<15 MeV

VV in L=0has P=+Decay into π D forbiddensince L’ shouldbe equal to S=1and this has negative parity

We also allow for decay into π Dρ D* interaction, R. Molina, H. Nagahiro,A. Hosaka, E.O, PRD 2009

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

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

Extension to the baryon sector

q

In the approximation q2/MV2= 0 one recovers the chiral Lagrangians

Weinberg-Tomozawa term.

Vector propagator 1/(q2-MV2)

> 200 works

Kolomeitsev et alSarkar et al

New: A. Ramos, E. O.

New: J. Vijande, P. Gonzalez. E.OSarkar, Vicente Vacas, B.X.Sun, E.O

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 transversevectors. Then ∂ν becomes three momentum which is neglected. Vv corresponds to the exchanged vector. complete analogy to VPPExtra εμεμ = -εiεi but the interaction is formally identical to the case of PBPB In the same approximation only γ0 is kept for the baryons the spindependence is only εiεi and the states are degenerate in spin 1/2 and 3/2

K0 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 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 onSU(6) symmetry of flavor and spin. The two approaches are not equivalent.

We solve the Bethe Salpeter equation incoupled channels Vector-Baryon octet.

T= (1-GV) -1 V

with G the loop function of vector-baryon

Apart from the peaks, poles are searchedIn 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 yetconsidered.

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 interactionP. 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=3/2I=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 MeVfound in the entries of N* states with these quantum numbers around 2100 MeV

Extension to theoctet of vectorsand decuplet ofBaryonsS. Sarkar, Bao Xi SunE. O, M.J. Vicente Vacas09

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.