Determination of $\pi\pi$ scattering lengths from measurement of $\pi^+\pi^-$ atom lifetime

TL;DR

The paper reports a precise measurement of the $$ scattering length difference using $$ atom lifetime data, testing predictions of Chiral Perturbation Theory with improved experimental accuracy.

Contribution

It presents the first high-precision measurement of the $$ scattering length difference from $$ atom lifetime, enhancing the experimental validation of theoretical models.

Findings

Measured $|a_0 - a_2|$ with 4% precision

Provided a critical test of Chiral Perturbation Theory

Achieved significant improvement in lifetime measurement accuracy

Abstract

The DIRAC experiment at CERN has achieved a sizeable production of $\pi^+\pi^-$ atoms and has significantly improved the precision on its lifetime determination. From a sample of 21227 atomic pairs, a 4% measurement of the S-wave $\pi\pi$ scattering length difference $|a_0-a_2| = (.0.2533^{+0.0080}_{-0.0078}|_\mathrm{stat}.{}^{+0.0078}_{-0.0073}|_\mathrm{syst})M_{\pi^+}^{-1}$ has been attained, providing an important test of Chiral Perturbation Theory.