Eur. Phys. J. C (2013) 73: 2284
https://doi.org/10.1140/epjc/s10052-013-2284-2

Regular Article - Theoretical Physics

Extracting ππ S-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions

¹ Institut für Theoretische Physik II, Rhur-Universität Bochum, 44780, Bochum, Germany
² Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53115, Bonn, Germany

^* e-mail: Xiao-Hai.Liu@tp2.ruhr-uni-bochum.de

Received: 18 December 2012
Published online: 26 January 2013

Abstract

Charge-exchange rescattering π ⁺ π ⁻→π ⁰ π ⁰ leads to a cusp effect in the π ⁰ π ⁰ invariant mass spectrum of processes with π ⁰ π ⁰ in the final state which can be used to measure ππ S-wave scattering lengths. Employing a non-relativistic effective field theory, we discuss the possibility of extracting the scattering lengths in heavy quarkonium π ⁰ π ⁰ transitions. The transition ϒ(3S)→ϒ(2S)π ⁰ π ⁰ is studied in detail. We discuss the precision that can be reached in such an extraction for a certain number of events.