We study $S$-wave interactions of the baryon decuplet with the octet of
pseudoscalar mesons using the lowest order chiral Lagrangian. We find two bound
states in the SU(3) limit corresponding to the octet and decuplet
representations. These are found to split into eight different trajectories in
the complex plane when the SU(3) symmetry is broken gradually. Finally, we are
able to provide a reasonable description for a good number of 4-star
${{3/2}}^-$ resonances listed by the Particle Data Group. In particular, the
$\Xi(1820)$, the $\Lambda(1520)$ and the $\Sigma(1670)$ states are well
reproduced. We predict a few other resonances and also evaluate the couplings
of the observed resonances to the various channels from the residues at the
poles of the scattering matrix from where partial decay widths into different
channels can be evaluated.Comment: Contribution to the HADRON05 Conference, Rio de Janeiro, September
  200

Oset, E.

Sarkar, S.

Vacas, M. J. Vicente

English

arXiv

E. Oset

Crossref

Baryonic Resonances from the Interactions of the Baryon Decuplet and Meson Octet

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Baryonic Resonances from the Interactions of the Baryon
Decuplet and Meson Octet
E. Oset, S. Sarkar and M. J. Vicente Vacas
October 3, 2018
Departmento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC,
Institutos de Investigación de Paterna, Aptd. 22085, 46071 Valencia, Spain
Abstract
We study S-wave interactions of the baryon decuplet with the octet of pseudoscalar
mesons using the lowest order chiral Lagrangian. We find two bound states in the SU(3)
limit corresponding to the octet and decuplet representations. These are found to split
into eight different trajectories in the complex plane when the SU(3) symmetry is broken
gradually. Finally, we are able to provide a reasonable description for a good number of 4-star
3
2
−
resonances listed by the Particle Data Group. In particular, the Ξ(1820), the Λ(1520)
and the Σ(1670) states are well reproduced. We predict a few other resonances and also
evaluate the couplings of the observed resonances to the various channels from the residues
at the poles of the scattering matrix from where partial decay widths into different channels
can be evaluated.
1 Introduction
The introduction of unitary techniques in a chiral dynamical treatment of the meson baryon
interaction has been very successful. It has lead to good reproduction of meson baryon data
with a minimum amount of free parameters, and has led to the dynamical generation of many
1
low lying resonances which qualify as quasibound meson baryon states [1, 2, 3]. In particular,
the application of these techniques to the s-wave scattering of the baryon octet and the
pseudoscalar meson octet have led to the successful description of many JP = 1
2
−
resonances
like the N∗(1535), the Λ(1405), the Λ(1670), the Σ(1620) and the Ξ(1620) [4, 5, 6, 7, 8].
Naively one may expect that this scheme is not suitable for studying d-wave resonances due
to a large number of unknown parameters in the corresponding chiral Lagrangian. However
d-wave resonances could be studied in s wave interactions of the meson octet with the baryon
decuplet [9], in which case chiral dynamics is quite predictive. The fact that some well known
d wave resonances like the N∗(1520), N∗(1700), ∆(1700) have very large branching ratios to
the Nππ channel though the Nπ channel is favoured by phase space, lends support to this
scheme.
2 Baryon Decuplet-Meson Octet Interaction: Re-
sults and Discussion
We have performed a systematic study [10] of the s-wave interaction of the baryon decuplet
with the meson octet taking the dominant lowest order chiral Lagrangian, which accounts
for the Weinberg Tomozawa term. In this talk we will present the main results of this work.
The tree-level scattering amplitude involving the baryon decuplet and the pseudoscalar
octet is used as the kernel of the Bethe Salpeter equation to obtain the transition matrix
fulfilling exact unitarity in coupled channels. In this approach, the only free parameter is
the subtraction constant in the dimensionally regularized meson baryon loop function for
which we took a natural size value. We have looked in detail at the 3
2
−
resonances which are
generated dynamically by this interaction, by searching for poles of the transition matrix in
the complex plane in different Riemann sheets. The search was done systematically, starting
from an SU(3) symmetric situation where the masses of the baryons are made equal and
the same is done with the masses of the mesons. In this case we found attraction in an
octet, a decuplet and the 27 representation, while the interaction was repulsive in the 35
representation. In the SU(3) symmetric case all states of the SU(3) multiplet are degenerate
and the resonances appear as bound states with no width. As we gradually break SU(3)
symmetry by changing the masses, the degeneracy is broken and the states with different
2
1350 1450 1550 1650 1750 1850 1950 2050 2150
 Re zR (MeV)
0
50
100
150
200
 −
Im
 z
R
 (
M
eV
)
S=0, I=1/2
S=−1, I=1
S=−1, I=0
S=−2, I=1/2
 Octet
? (1673)
M 0=1382 MeV
m0=368 MeV
1350 1450 1550 1650 1750 1850 1950 2050 2150
 Re zR (MeV)
0
50
100
150
200
−
Im
 z
R
 (
M
eV
)
S=0, I=3/2
S=−1, I=1
S=−2, I=1/2
S=−3, I=0
 Decuplet
?
(1738)
M 0=1382 MeV
m0=368 MeV
Figure 1: Trajectories of the poles in the scattering amplitudes for different values of the SU(3)
breaking parameter.
strangeness and isospin split apart generating pole trajectories in the complex plane which
lead us to the physical situation in the final point, as seen in fig. 1. This systematic search
allows us to trace the poles to their SU(3) symmetric origin, although there is a mixing
of representations when the symmetry is broken. In addition we also find poles which only
appear for a certain amount of symmetry breaking and thus have no analog in the symmetric
case.
The search for poles is an ideal technique to identify resonances in addition to visual
inspection of the amplitudes. On the other hand, in ref. [9] the speed plot technique is used
to identify resonances. However, the speed plot, involving derivatives of the amplitudes, pro-
duces artificial peaks at the thresholds of new channels, because the cusp of the amplitudes,
and should not be used there. Neglecting this fact, some peaks which are actually reflections
of cusps in the speed plot are misidentified as resonances in [9] while we do not find poles,
not even making reasonable changes in the input data.
We have also evaluated the residues of the poles from where the couplings of the resonances
to the different coupled channels were found and this allowed us to make predictions for
partial decay widths into a decuplet baryon and a meson. There is very limited experimental
information on these decay channels but, even then, it represents an extra check of consistency
of the results which allowed us to more easily identify the resonances found with some
resonances known, or state that the resonance should correspond to a new resonance not yet
3
1300 1500 1700 1900 2100
ECM (MeV)
0
0.01
0.02
0.03
0.04
0.05
0.06
|T
|2  
(1
/M
eV
2 )
∆π
Σ*K
∆π (with width)
Σ*K (with width)
(S,I)=(0,1/2)
N
*
(1520)
1300 1500 1700 1900 2100
ECM (MeV)
0
0.001
0.002
0.003
0.004
0.005
|T
|2  
(1
/M
eV
2 )
∆π
Σ*K
∆η
(S,I)=(0,3/2)
∆(1700)
∆ (?)
1300 1500 1700 1900 2100
ECM (MeV)
0
0.005
0.01
0.015
0.02
0.025
|T
|2  
(1
/M
eV
2 )
Σ∗ π
Ξ*K
(S,I)=(−1,0)
Λ(1520)
1300 1500 1700 1900 2100
ECM (MeV)
0
0.2
0.4
0.6
0.8
1
|T
|2  
(1
/M
eV
2 )
∆K
Σ∗ π
Σ∗ η
Ξ*K
(S,I)=(−1,1) −
Σ(1670)
Σ(1940)
1300 1500 1700 1900 2100
ECM (MeV)
0
0.05
0.1
0.15
|T
|2  
(1
/M
eV
2 )
Σ*K
Ξ∗ π
Ξ∗ η
ΩK
(S,I)=(−2,1/2) −
Ξ(1820)
Ξ (?)
1300 1500 1700 1900 2100
ECM (MeV)
0
0.02
0.04
0.06
0.08
|T
|2  
(1
/M
eV
2 )
Ξ*K
Ωπ
(S,I)=(−3,0) −
Ω (?)
Figure 2: Amplitudes for 3/2− resonances generated dynamically in decuplet baryon - pseudoscalar
octet interactions.
4
reported in the Particle Data Book (PDB). In particular, in view of the information of the
pole positions and couplings to channels we could associate some of the resonances found
to the N∗(1520), ∆(1700), Λ(1520), Σ(1670), Σ(1940), Ξ(1820) resonances tabulated in the
PDB. We could also favour the correspondence of a resonance found in S = −3, I = 0 to the
Ω(2250) on the basis of the quantum numbers, position and compatibility of the partial decay
width found with the total width of the Ω(2250). The scattering amplitudes for different
values of strangeness and isospin as a function of the C.M. energy are shown in fig. 2.
We also found several extra resonances, well identified by poles in the complex plane
which do not have a correspondent one in the PDB. Some of them are too broad, which
could justify the difficulty in their observation, but two other resonances, the ∆(1500) with
a width around 300 MeV and the Ξ(2160) with a width of about 40 MeV stand much better
chances of observation. The first one because of its large strength in the ∆π channel and the
second one because of its narrowness.
In addition, our study produces couplings of the resonances to baryon-meson channels
which could facilitate the identification when further information on these branching ratios
is available. We have found that in some cases the dynamically generated resonances couple
very strongly to some channels with the threshold above the resonance energy, which makes
them qualify as approximately single channel quasibound meson-baryon states.
Lastly, we mention the very interesting case concerning the ∆K resonance [11] found in
S = 1, I = 1 which shows up as a pole in the unphysical Riemann sheet and leads to ∆K
cross sections much larger than the corresponding ∆K cross sections in I = 2. We suggest
that these two cross sections could be seen in ∆K production in pp → Λ∆K and pp → Σ∆K
reactions and could provide evidence for this new ’exotic pentaquark’ state, although its
structure is more efficiently taken into account in the meson baryon picture where it has
been generated. This state, however, appears as a broad bump above the K∆ threshold
and its strength is also tied to details of the interaction. Hence, the ultimate fate of this
resonance is difficult to predict at the present stage.
Acknowledgments: This work is partly supported by DGICYT contracts BFM2002-
01868, and the E.U. EURIDICE network contract HPRN-CT-2002-00311. This research is
part of the EU Integrated Infrastructure Initiative Hadron Physics Project under contract
5
number RII3-CT-2004-506078.
References
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and W. Weise, Nucl. Phys. A 612 (1997) 297.
[2] E. Oset and A. Ramos, Nucl. Phys. A 635 (1998) 99.
[3] J. A. Oller and U.-G. Meißner, Phys. Lett. B 500 (2001) 263.
[4] T. Inoue, E. Oset and M. J. Vicente Vacas, Phys. Rev. C 65 (2002) 035204.
[5] D. Jido, J. A. Oller, E. Oset, A. Ramos and U. G. Meissner, Nucl. Phys. A 725 (2003)
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[6] C. Garcia-Recio, J. Nieves, E. Ruiz Arriola and M. J. Vicente Vacas, Phys. Rev. D 67
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6


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