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

TL;DR

This paper proposes a method using the cusp effect in heavy quarkonium decays to precisely measure $\pi ext{-}\pi$ $S$-wave scattering lengths, employing non-relativistic effective field theory.

Contribution

It introduces a novel approach to extract $\pi ext{-}\pi$ scattering lengths from heavy quarkonium dipion transitions using the cusp effect and non-relativistic effective field theory.

Findings

Demonstrates the feasibility of extracting scattering lengths from $$ transitions.

Analyzes the precision achievable with current experimental data.

Provides detailed study of the $S o2S ext{ }$ transition.

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.