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Extracting $\pi\pi$ $S$-wave scattering lengths from cusp effect in heavy quarkonium dipion transitions
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abstract
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 measure $\pi\pi$ $S$-wave scattering lengths. Employing a non-relativistic effective field theory, we discuss the possibility of extracting the scattering lengths in heavy quarkonium $\pi^0\pi^0$ transitions. The transition $\Upsilon(3S)\to\Upsilon(2S)\pi^0\pi^0$ is studied in details. We discuss the precision that can be reached in such an extraction for a certain number of events.
Forward citations
Cited by 2 Pith papers
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Low-energy scattering of the $J/\psi \pi$ and $J/\psi K$ system
First dispersive upper-bound estimates for J/ψπ and J/ψK scattering lengths, with soft-gluon exchange dominating the coupled-channel mechanism.
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Role of electromagnetic corrections in the $\pi\pi$ distributions of $\psi^\prime \to J/\psi \pi \pi$
Electromagnetic corrections alter the π⁺π⁻-threshold cusp magnitude by ~2–3% in ψ′→J/ψπ⁰π⁰, so they must be included for precision extraction of S-wave ππ scattering lengths.
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