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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
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.
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
Low lying axial vector meson,
a1,b1, … are generated
Novelty of Roca, Oset, Singh : Two K1(1270) states are generated
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
R.Molina, D. Nicmorus, E. O. PRD (08)
Spin projectors neglecting q/MV, in L=0
Bethe Salpeter eqn.
G is the ρρ propagator
ππ box provides
Note: In the I=2 (exotic channel) one has a net repulsion. No poles appear
for dynamical reasons.
f0, f2 that
Belle finds the
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
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
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.
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
This is the parameter of the theory
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
D0*(2400), X(3872) …. Daniel Gamermann PRD,E.P.J.A 2007,08,09
Phys. Rev D 2009
D* Dbar*, Ds* Dsbar* and other VV (noncharmed) coupled channels
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
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.
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
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.