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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

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meson and baryon resonances from the interaction of vector mesons

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


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.


SeepracticalFeyman 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 byLutz and Kolomeitsev (04)

Roca, Oset, Singh (05)

V from Lagrangian

G: pseudoscalar-vector


Low lying axial vector meson,

a1,b1, … are generated

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


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


Rho-rho interaction in the hidden gauge approach

R.Molina, D. Nicmorus, E. O. PRD (08)




Spin projectors neglecting q/MV, in L=0

Bethe Salpeter eqn.

G is the ρρ propagator


Real parts small.

ππ 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


f0, f2 that

we associate

to f0(1370)

and f2(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




= 0.25

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


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


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.


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

Phys.Lett. B (2009)

SU(3) singlet

This is the parameter of the theory


ρ D* interaction, R. Molina, H. Nagahiro,

A. Hosaka, E.O, PRD 2009

We also allow for decay into π D

D*(2640) ?


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


Г=43 MeV



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

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.


Kolomeitsev et al

Sarkar et al

New: J. Vijande, P. Gonzalez. E.O

Sarkar, Vicente Vacas, B.X.Sun, E.O

vector octet baryon octet interaction
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


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.


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


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




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


S. Sarkar, Bao Xi Sun

E. O, M.J. Vicente Vacas




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.