Speaker
Tobias Isken
(G)
Description
I present a dispersion-theoretical analysis of the strong three-body decays in the $\eta$ and $\eta'$ sector. Based on analyticity and unitarity the dispersion relations resum the leading $\pi\pi$- and $\pi\eta$-rescattering effects to all orders, with the resulting amplitudes being solely dependent on the respective two-body scattering phase shifts. Due to the small available phase space only three decay channels are physically allowed: the two isospin breaking transitions $\eta/\eta'\to3\pi$ and the isospin conserving transition $\eta'\to\pi\pi\eta$. Combining our dispersive representation of $\eta\to3\pi$ with ChPT constraints, a fit to the high-statistics A2 and KLOE-2 Dalitz-plot distributions enables us to extract the light-quark mass double ratio $Q$. We update our previous analysis of $\eta'\to\pi\pi\eta$ by performing fits to new high-statistics measurements from A2 and BESIII. For the process $\eta'\to3\pi$, we include both elastic two-pion rescattering corrections to the isospin-breaking decay amplitude as well as the inelastic effect due to an isospin-conserving decay $\eta'\to\pi\pi\eta$ and subsequent isospin-breaking $\pi\eta\to\pi\pi$ rescattering. In this way, the inelastic contribution to the unitarity relation connects all three decays. The resulting dispersive description of $\eta'\to3\pi$ is fitted to the first available measurements of the Dalitz-plot distributions from BESIII.
Primary author
Tobias Isken
(G)
Co-authors
Andrzej Kupsc
(Uppsala University)
Bastian Kubis
(Bonn University)
Peter Stoffer
(Zürich University)
