Abstract
In this work we provide a dispersive analysis of pi pi rightarrow K{bar{K}} scattering. For this purpose we present a set of partial-wave hyperbolic dispersion relations using a family of hyperbolas that maximizes the applicability range of the hyperbolic dispersive representation, which we have extended up to 1.47 GeV. We then use these equations first to test simple fits to different and often conflicting data sets, also showing that some of these data and some popular parameterizations of these waves fail to satisfy the dispersive analysis. Our main result is obtained after imposing these new relations as constraints on the data fits. We thus provide simple and precise parameterizations for the S, P and D waves that describe the experimental data from K{{bar{K}}} threshold up to 2 GeV, while being consistent with crossing symmetric partial-wave dispersion relations up to their maximum applicability range of 1.47 GeV. For the S-wave we have found that two solutions describing two conflicting data sets are possible. The dispersion relations also provide a representation for S, P and D waves in the pseudo-physical region.
Highlights
Most of the data on meson-meson scattering [2,3,4,5,6,7,8,9,10] are extracted indirectly from meson-nucleon to meson-meson-nucleon reactions
In this work we have performed a dispersive study of π π → K Kscattering by means of partial-wave dispersion relations of the Roy–Steiner type, i.e. based on hyperbolic dispersion relations
We have derived a set of equations based on (s − a)(u − a) = b hyperbolae in which we have obtained the value of a that maximizes the applicability range of these hyperbolic dispersion relations
Summary
Most of the data on meson-meson scattering [2,3,4,5,6,7,8,9,10] are extracted indirectly from meson-nucleon to meson-meson-nucleon reactions. The main experimental results on π π → K Kpartial waves, that will be thoroughly analyzed in this work, were obtained in the early eighties [7,8], indirectly from π N → K K N reactions They extend from energies very close to the K Kthreshold up to 1.6 GeV. We will derive a new set of hyperbolic dispersion relations, along (s − a)(u − a) = b hyperbolas, choosing the a parameter to maximize the applicability range which allows us to use them up to 1.47 GeV This will allow us to test different and often conflicting data sets and popular parameterizations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
