KN scattering in the nonrelativistic quark model Page: 4 of 14
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one pion exchange, is forbidden by angular quantum numbers; the lightest t-channel
exchanges possible are the vector qq states, and these are suppressed by their higher
masses. This implies that we may be able to see scattering due to quark-gluon
interactions in KN without important complications from additional mechanisms.
In this contribution we first discuss the experimental status of KN scat-
tering, following which we review theoretical studies of KN using quark and gluon
degrees of freedom. Here we primarily consider the short-ranged S-waves, which are
the relevant amplitudes for near-threshold studies at DAPHNE. Although the higher
partial waves are very interesting and exhibit large spin-orbit forces and possibly
exotic "Z*" resonances, 1) they are beyond the range of invariant mass which will
initially be accessible at DAPHNE.
2 - Experimental status of low energy KN S-wave scattering
We begin by reviewing the status of experimental KN scattering lengths (abstracted
from Barnes and Swanson 2)). Since there are unresolved disagreements between
analyses in the I=0 channel, we show all relatively recent (since 1980) single-energy
S-wave phase shifts. These are Martin and Oades 3) (Aarhus and UC London, 1980);
Watts et al. 4) (QMC and RAL, 1980); Hashimoto 5) (Kyoto and VPI, 1984); and
Hyslop et al. 6) (VPI, 1992). The I=1 data set analysed by Arndt and Roper 7) (VPI,
1985) was incorporated in the 1992 VPI analysis. Fig.1 shows these experimental
I=0 and I=1 S-wave phase shifts versus P,,= IP"I.
For I=1, the linear low energy behavior which determines the scattering
length is evident in the data, and Hyslop et al. cite a fitted value of alt = -0.33 fm.
Previous analyses (summarized by Dover and Walker 1) and Hyslop et al. 6)) have
given values between -0.28(6) fm 8) and -0.33 fm. 6, 9)
In contrast, the I=0 phase shift is not yet well determined experimentally;
evidently it is negative and somewhat weaker than I=1, but there is considerable
disagreement between analyses. Since an extrapolation of this poorly determined
quantity to threshold is problematical, the value of the I=0 KN scattering length is
not well established. Previous (favored) solutions for ai o up to 1982 are summarized
in Table 2.3 of Dover and Walker, 1) and range between +0.02 fm and -0.11 0:0 fm.
There appear to be two sets of low energy values in the data of Fig.1, a smaller
phase shift from the Aarhus-UCL and QMC-RAL collaborations and a larger one
from from the Kyoto-VPI and VPI analyses. Below P, = 0.4 Gev the Kyoto-VPI
and VPI results are larger than Aarhus-UCL and QMC-RAL by about a factor of
two. The VPI group 6) actually cite a scattering length of a4 = 0.0 fm, although
this requires rapid low energy variation below the first experimental point.
A more useful way to present the S-wave phase shift data is to show SJ/P.
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Barnes, F. E. KN scattering in the nonrelativistic quark model, article, December 31, 1995; Tennessee. (https://digital.library.unt.edu/ark:/67531/metadc665175/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.