Abstract
We present and discuss a non-expensive mechanical experiment which is very suitable for a classroom demonstration of the fold catastrophe behaviour. The apparatus consists of a bar attached ...to a pulley, to which a hanging body is connected by means of a thread wrapped around its rim. The system may perform stable oscillations or, else, the body may continuously fall down, while the pulley executes a sequence of 360° rotations. This behaviour is analysed in connection with the shape of the potential, which is a good example of a fold catastrophe potential. For the system to perform stable oscillations, that shape reminds a clothes washboard, with local maxima and minima, a potential well known in superconducting quantum computing. We provide some hints for the instructor to explore the device in lab classes.
.
We apply a coupled-channel formalism incorporating quasi-bound quark-model states to calculate pion scattering into
,
and
channels, as well
,
,
, and
photoproduction processes. The meson-baryon and ...photon-baryon vertices are determined in a
SU
(3) version of the Cloudy Bag Model. Our model predicts sizable amplitudes in the P
11
, P
13
, P
33
and S
11
partial waves in agreement with the latest MAID isobar model and the recent partial-wave analyses of the Bonn-Gatchina group. We are able to give a quark-model explanation for the apparent resonance near 1685 MeV in the
channel.
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Roper resonances in chiral quark models Golli, B.; Širca, S.
The European physical journal. A, Hadrons and nuclei,
12/2008, Volume:
38, Issue:
3
Journal Article
Peer reviewed
We derive a method to calculate the multi-channel
K
-matrix applicable to a broad class of models in which mesons linearly couple to the quark core. The method is used to calculate pion scattering ...amplitudes in the energy region of low-lying P11 and P33 resonances. A good agreement with experimental data is achieved if in addition to the elastic channel we include the
and
N
(
channels where the
-meson models the correlated two-pion decay. We solve the integral equation for the
K
-matrix in the approximation of separable kernels; it yields a sizable increase of the widths of the
(1232) and the
N
(1440) resonances compared to the bare quark values.
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We present a method to calculate pion electro-production amplitudes in a coupled-channel framework incorporating quasi-bound quark-model states. The method offers a clear prescription how to extract ...the resonant part of the amplitudes, even in the presence of different decay channels and a strong mixing of neighbouring resonances. The method is applied to the calculation of the M
1-
and the S
1-
amplitudes in the
P
11 partial wave in a simple chiral quark model. A good agreement with the observed M
1-
amplitude is found with a significant contribution from the pion cloud. The same effect is also prominent in the S
1-
amplitude but a rather uncertain data prevent us to draw a definitive conclusion.
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The mechanism for the formation of the
Λ
(
1405
)
resonance is studied in a chiral quark model that includes quark-meson as well as contact (four point) interactions. The negative-parity
S
-wave ...scattering amplitudes for strangeness
-
1
and 1 are calculated within a unified coupled-channel framework that includes the
KN
,
K
¯
N
,
π
Σ
,
η
Λ
,
K
Ξ
,
π
Λ
, and
η
Σ
channels and possible genuine three-quark bare singlet and octet states corresponding to
1
2
-
resonances. It is found that in order to reproduce the scattering amplitudes in the
S
01
partial wave it is important to include the pertinent three-quark octet states as well as the singlet state, while the inclusion of the contact term is not mandatory. The Laurent-Pietarinen expansion is used to determine the
S
-matrix poles. Following their evolution as a function of increasing interaction strength, the mass of the singlet state is strongly reduced due to the attractive self-energy in the
π
Σ
and
K
¯
N
channels; when it drops below the
KN
threshold, the state acquires a dominant
K
¯
N
component which can be identified with a molecular state. The attraction between the kaon and the nucleon is generated through the
K
¯
N
Λ
∗
interaction rather than by meson-nucleon forces.
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The meson scattering and electroproduction amplitudes in the
D
13 ,
D
33 and
D
15 partial waves are calculated in a coupled-channel formalism incorporating quasi-bound quark-model states, extending ...our previous studies of the
P
11 ,
P
33 and
S
11 partial waves. The vertices of the baryon-meson interaction including the
s
- and
d
-wave pions and
-mesons, the
s
-wave
-meson, and the
s
- and
p
-wave
-mesons are determined in the Cloudy Bag Model, with some changes of the parameters to reproduce the widths of the resonances. The helicity amplitudes and the electroproduction amplitudes exhibit consistent behavior in all channels but tend to be too weak compared to the experiment. We discuss possible origins of this discrepancy which arises also in the constituent quark model calculations.
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We present a method that incorporates solutions of a broad class of quark models into the coupled-channel formalism for the
K
matrix. The method is applied to the calculation of the
P
11 and
P
33 ...scattering amplitudes in the region of the
N
(1440) and Δ(1600) resonances. Solving the Lippmann-Schwinger equation for the
K
matrix we find a strong enhancement of the bare quark-model meson-baryon coupling constants consistent with the values used in effective Lagrangian approaches.
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