Study of low-energy QCD in meson reactions with the Coulomb field of atomic nuclei

This paper reviews the development of theoretical and experimental studies of low-energy QCD parameters starting from early investigations at the JINR Laboratory of Theoretical Physics and ending with modern measurements at CERN. We summarize the historical background and the pioneering theoretical approaches used at JINR to calculate meson parameters in various hadronic models which have laid the foundation for the experimental proposal to investigate the pion polarizability via radiative scattering off nuclei. The first observation of the Compton effect on the pion and the first measurements of the charged pion polarizability and the γ → 3π constant performed with the U-70 accelerator are discussed as key milestones enabling quantitative studies of the meson structure and highlighting their impact on the low-energy QCD phenomenology. Continued advances in theoretical predictions have underscored the need for higher-precision experimental data and motivated new measurements carried out with pion beams in the COMPASS experiment at CERN. Finally, we outline the prospects for future studies within the AMBER experiment where kaon beams will enable a precision determination of kaon polarizabilities and related low-energy constants further advancing our understanding of dynamics of the strong interaction.