There is no $κ(900)$

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 $qq{\bar {qq}}$. Such proposals require the existence of at least two strange isodoublets (and their antiparticles). The current PDG Tables list just one state, the $K^*_0(1430)$, while fits to data with Breit-Wigner forms and variable backgrounds can accommodate a $κ(900)$ 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 $πK$ scattering results between 825 MeV and 2 GeV to determine the number and position of resonance poles. We find that there {\bf is} a $K^*_0(1430)$, but {\bf no} $κ(900)$. The LASS data cannot rule out the possibility of a very low mass $κ$ well below 825 MeV.