SLAC-PUB-1739 April 1976 0) MODELFOR LOWENERGYKAON-NUCLEON INTERACTION IN THE I = 0 STATE* Pontiflcia Universidade S.C.B. Andrade Cato/lica, Rio de Janeiro, Brazil E. M. Ferreira <a href="/keyword/stanford-linear-accelerator/" ><a href="/keyword/stanford-linear/" >stanford linear</a> accelerator</a> Center Stanford University, Stanford, California and Pontifi&lt;ia Universidade Catdlica, Rio de Janeiro, 94305 Brtizil (Contributed to the titernational Topical Conference on Meson Nuclear Carnegie-Mellon University, Pittsburgh, PA., May 24-28, 1976.) Physics, * Work supported by the Energy Research and Development Administration. MODEL FOR LOW ENERGY KAON-NUCLEON IN THE I = 0 STATE* CI INTERACTION S. C. B. Andrade and E. M, Ferreira** Pontiffcia Universidade Cat'olica, Rio de Janeiro, Brazil Unitary Pad6 approximants were recently used1 to build a model for the low energy kaon-nucleon interaction. The model is based on a Lagrangian 9 int = { -bzNAK Gy5AKf + &amp;y5AKo) + h. c.} + ~-ig~K(-$5ZoK++&amp;$5Zko C-K+)+h. c . } +h{ pp~`K'~~n~ K++~~`K'+~p~oKo)) (1) +iiy5~&quot;Ko-$2iiy5 written in terms of nucleon, hyperon, and kaon fields, and consisting of the usual Yukawa terms CgNAK and g=) and of the contact interaction (coupling constant h) acting directly only on the I = 1 state of the KN system. The amplitudes are calculated starting from the first diagonal Pad6 approxThis procedure guarantees the Simant to each partial wave amplitude. matrix unitarity , and the model achieved remarkable success when applied to the I = 1 state of the kaon-nucleon system. As an extension of that work, we have now applied the model to study the KN interaction in the isospin I = 0 state. To obtain the [ 1, l] Pad6 approximant we must evaluate all Feynman diagrams up to fourth order. The Yukawa coupling constants occur in the final expressions only through the ef-. fective coupling constant 2 = @NAK - 3&amp;J&amp;4* (0) with 77LY 0.97. Once the scattering length as - -0.3f in the I = 1 state is given, A is fixed in terms of an effective coupling G2 defined by the combination and then G2 can be determined by fittiy the other K+p scattering data. It is commonly accepted that the value of G lies somewhere in the interval from 10 to 20. Thus g2 becomes the-only free parameter for the description of The present knowledge of the values of the Yukawa the I = 0 interaction. coupling constants indicates that 0 &lt; $ c G . We have obtained for the I = 0 state an s-wave scattering length of.about -0.4 fermi, and positive p112 and negaye p3/2 phase shif$s , wit: typical (i&gt;2'=+0. 08 and a( ) = -0.02 (fermi) for G = g2 = scattering lengths ap p3/2 = 15. These results may b compared to the solutions of phase shift analysis by B. C. Wilson et al, 3 Their preferred sets present also negative swave shifts while both p1/2 and p3/2 phases are positive. Figure 1 shows the values of the differential crosg section for elastic K'n - K'h scattering, as extracted from results of K d scattering experiments , 2 together with the predictions from our model. The differential * Work partially supported by Energy Research and Development Administration. **Present address : <a href="/keyword/stanford-linear-accelerator/" ><a href="/keyword/stanford-linear/" >stanford linear</a> accelerator</a> Center, Stanford, CA 94305. -l- polarization observed3 in K+d - K'PP at 600 MeV/c is well reproduced by our calculations, as shown in Fi Q 2, Figure 3 shows the experimental results on K+d total cross section, together with our results. &amp;me of the noted discrepan3.0 [ I I I cies can be attributed to the way 530 MeV/c 2.5 _ K+n-K+n Kip and &amp;d experiments have been analyzed to produce the I=6 Y I_ 2.0 5 data, but we must also point out the deficiencies of the model, which does not include pions exE 15c: * t 1 plicitly and represents all kinds of short range forces by the contact term in the Lagrangian. On the whole, however, we I I I 0' think that the model reaches rela0.5 1.0 - 0.5 0 -1.0 tive success e Without free pa1.1.11 cos kll. rameters, we have predicted the...