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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IFIC and Theory Department, Valencia
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
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 Lagrangians using practicalFeyman rules in
Nagahiro, Roca, Hosaka, E.O.
Phys. Rev. D 2009
Vector-pseudoscalar interaction Lagrangians using : in the approximation q/MV=0 one obtains the
Chiral Lagrangians used byLutz and Kolomeitsev (04)
Roca, Oset, Singh (05)
V from Lagrangian
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 Lagrangians using
Exp. Daum, NPB (81)
Geng, E.O., Roca, Oller
The higher mass one
Couples strongly to ρK
The lower mass one
Couples strongly to
The peaks of the ρK and
K* π are separated by about 100 MeV
Rho-rho interaction in the hidden gauge approach Lagrangians using
R.Molina, D. Nicmorus, E. O. PRD (08)
Spin projectors neglecting q/MV, in L=0
Bethe Salpeter eqn.
G is the ρρ propagator
Extra contributions evaluated Lagrangians using
Real parts small. Lagrangians using
ππ box provides
Note: In the I=2 (exotic channel) one has a net repulsion. No poles appear
for dynamical reasons.
Two I=0 states No poles appear
f0, f2 that
Belle finds the
Can one make more predictions concerning these states? No poles appear
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( f2(1270)) = 2.6 ± 0.24 KeV
Generalization to coupled channels No poles appear : 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
Exp :Г( f2(1270))= 185 MeV
Exp: Г (f ‘2(1525)) = 76 MeV
For S=1 there is no decay into No poles appear
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. claimed in the BEWARE: these are no poles
Predicted meson states from V V interaction claimed in the
M , Г [MeV]
L.S. Geng, T. Branz, 09 claimed in the
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
Geng,Branz, E. O. (2009) claimed in the
Phys.Lett. B (2009) claimed in the
This is the parameter of the theory
Dominant claimed in the
ρ claimed in the D* interaction, R. Molina, H. Nagahiro,
A. Hosaka, E.O, PRD 2009
We also allow for decay into π D
VV in L=0
π D forbidden
since L’ should
be equal to S=1
and this has
Many states dynamically generated from mesons with charm, D claimed in the s0*(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 claimed in the
D* Dbar*, Ds* Dsbar* and other VV (noncharmed) coupled channels
Extension to the baryon sector claimed in the
Vector propagator 1/(q2-MV2)
In the approximation q2/MV2= 0 one recovers the chiral Lagrangians
> 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
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 PBPB
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 claimed in the :
The first excited N* states: N*(1440)(1/2^+) , N*(1535) (1/2^-).
In quark models this tells us the quark excitation requires
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 claimed in the 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
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
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 1/2 or 3/2
octet of vectors
and decuplet of
S. Sarkar, Bao Xi Sun
E. O, M.J. Vicente Vacas
Conclusions 1/2 or 3/2
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.