Extracting $\pi \pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions

Xiao-Hai Liu, Feng-Kun Guo, Evgeny Epelbaum

Charge-exchange rescattering ${\pi }^{+}{\pi }^{-}\to {\pi }^0{\pi }^0$ leads to a cusp effect in the ${\pi }^0{\pi }^0$ invariant mass spectrum of processes with ${\pi }^0{\pi }^0$ in the final state which can be used to me…