Hadronic Atoms in QCD

TL;DR

This paper develops a non-relativistic effective Lagrangian method within QCD to analyze hadronic atom observables, providing a way to extract pi-pi scattering lengths from atom decay measurements.

Contribution

It introduces a formalism to calculate hadronic atom properties including isospin breaking effects, enabling precise extraction of scattering lengths from experimental data.

Findings

Derived a general expression for pi+pi- atom decay width.

Included leading and next-to-leading order isospin breaking terms.

Facilitated the determination of pi-pi scattering length differences.

Abstract

We propose a non relativistic effective Lagrangian approach to study hadronic atom observables in the framework of QCD (including photons). We apply our formalism to derive a general expression for the width of the pi+pi- atom decaying into two neutral pions. It contains all terms at leading and next-to-leading order in isospin breaking. The result allows one to evaluate the combination a0-a2 of pi-pi S-wave scattering lengths from pi+pi- atom lifetime measurements, like the one presently performed by the DIRAC expeiment at CERN.