Exchange degeneracy from FESR and the Y-resonances

We assume tha t the K,N ~ system does not conta in resonances (at least in a first approximat ion) (*). We fur ther assume tha t forces axe due to one-part icle exchanges. (This corresponds to the assumption of resonance sa tura t ion in the F E S R . ) U n d e r these assumptions the channel ] ~ \ " ~ K&' , considered by itself (without coupled channels), contains only ~ direct forces ~, 4.e. meson exchanges, bu t no ~ exchange forces ~), i .e . no baryon exchanges, because there is no baryon wi th the quan tum numbers of (K.,\~). If there are only direct forces, ~hey genera te resonances which lie on one t r a j ec to ry 's+ and/or 1⁄2-, 23+, ~ . . . The couplings of each for even and odd l, e .g . , }+, } , s . . . . sequence are g iven by one residue hmc t ion . Bu t in our case there exist impor t an t other channels which couple to IXA ~, namely A~. and Z~. In these o ther channels there are bo th types of forces, meson exchange and baryon exchange. The same is t rue for iQV---~ (A or Z)r:. i n the eoupled-chamml case the difference be tween var ious dynamica l seheines becomes impor tan t . If we do an N / D bootstrap, we conclude tha t there is no reason to have any type of exchange degeneracy, because some of the channels have bo th types of forces. And because of nn i t a r i ty this breaking of exchange degeneracy propagates into all coupled channels. On the o ther hand, in a F E S R boots t rap scheme (~) i t is r igorously possible to consider each ampl i tude separately, f~.V elastic, =Z elastic, IX,.\~ ~ =Z, etc. ; and i t i lnmedia te ly follows (assuming resonance saturat ion) t ha t an F E S R boots t rap scheme predicts tha t the ¥*-resonanees as observed in K . \ ' ~ ] ( ~ \ " are exchange degenerate (in ~ and fl, i .e . in mass and coupling strength). Le t us tes t this predic t ion exper imenta l ly . We consider the ] ~ in the Rosenfeld table. Fi rs t we not ice the beaut i ful exchange-degenera te sequence which starts wi th the A ( l l l 5 ) : 1_+ a5+ 72 ,~ , u ,~ ,-~+(?). This is shown in Fig. la .