A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

16 introduction
amount of resonances at first and letting a fit to existing data to decide
which of them were more active in the reaction dynamics. Obviously,
the large number of fitting parameters generates doubts about the
uniqueness of the solution obtained by this method.
Table 1: Model Kaon-Maid for Λ and Σ 0 production. Parameters of assumed
resonances.
resonance (I)J π mass( MeV) width(MeV) g1/v g2/t
K ∗ (892) 1 − 892 50 -0.787 -2.628
K1(1270) 1 + 1273 90 3.810 -2.408
N(1650) S11
N(1710) P11
N(1720) P13
N(1895) D13
∆(1900) S31
1 1 −
2 ( 2 )
1 1 −
2 ( 2 )
1 3 +
2 ( 2 )
1 3 −
2 ( 2 )
3 1 −
2 ( 2 )
−
)
1655
1710
1720
1895
1900
1910
150
100
150
370
200
250
-0.133
-0.258
-0.046
1.101
0.106
0.322
0.000
0.000
-0.614
0.634
0.000
0.000
∆(1910) P31
3 1
2 ( 2
The isobaric model by Bennhold et al. (Kaon-Maid in the following
[33]) uses spin 1/2 and 3/2 s-channel resonances, S11(1650), P11(1710),
P13(1720) and the missing resonance D13(1895) predicted by the constituent
quark model by Capstick and Roberts and calculated to
have a significant KΛ decay width. For K + Σ 0 production, the two
∆-resonances S13(1900) and P13(1910) are added. Phenomenological
form factors are used at the hadron vertexes to account for the high W
region behavior and the Haberzettl method is used to restore gauge
invariance. Kaon resonances K ∗ (890) and K1(1270) are included in the
t channel. No hyperon resonances are used in this model. Coupling
constants are obliged to fulfill the SU(3) constrains explained above.
The Kaon-Maid version used in this thesis was fitted to the older
SAPHIR data [34]
In the original Kaon-Maid model the longitudinal coupling constants
to N ∗ resonances appeared unreasonably large (see table 1), and
cut-off parameters unreasonably small. In addition, some inconsistencies
in convention for the amplitudes in the electromagnetic form
factors in the born terms and in the couplings to spin-3/2 resonances
were found and corrected. A reduced version of the model was defined
by setting these longitudinal couplings to zero.
As an example Fig. 5 shows the contributions of the different resonances
in this reduced version to the total Λ and Σ 0 cross-sections
in our kinematics (See chapter 2). We will also make use of a new
version of Kaon-Maid that uses very small longitudinal couplings. In
this version four nucleon resonances, D15(1675), D13(1700), F15(2000),
and D15(2200) were added to the previous set and the free parameters
of the model were re-fitted to describe the new world data on the