There is no $\kappa (900)$

Abstract

In the I=0 sector there are more scalar mesons than can fit in one $q\bar{q}$ nonet. Consequently, many have claimed that there is in fact more than one multiplet, perhaps both $q\bar{q}$ and $qq\overline{qq}$. Such proposals require the existence of at least two strange isodoublets (and their antiparticles). The current PDG Tables list just one state, the $K_0^{\ast }(1430)$, while fits to data with Breit-Wigner forms and variable backgrounds can accommodate a $\kappa (900)$ too. Whether a state exists in the spectrum of hadrons is not a matter of ability to fit data along the real energy axis, but is completely specified by the number of poles in the complex energy plane. Here we perform a model-independent analytic continuation of $\pi K$ scattering results between 825 MeV and 2 GeV to determine the number and position of resonance poles. We find that there {\bf is} a $K_0^{\ast }(1430)$, but {\bf no} $\kappa (900)$. The LASS data cannot rule out the possibility of a very low mass $\kappa$ well below 825 MeV.

Comments: 19 pages, 5 figures Version to be published in Nuclear Physics A containing new figures and additional entries in tables to clarify the role played by near threshold $\pi K$ scattering$ below the energy explored by the SLAC LASS experiment