Applicability limits of the Standard Model (SM) of electroweak interactions and search for novel phenomena beyond the SM which indicate existence of new physics are issues of great importance in modern Elementary Particle Physics. Along with the search for and investigations of new processes at the recently created accelerators, the signals of this new physics could be found during a close high-precision research of well-known processes, including rare ones.

The precision of rare processes has been increased by 12 orders of magnitude over the last 50 years. It became possible due to both improvements of the measurement methodology and progress in designing new high-current accelerators. Several periods can be distinguished in the history of the study of rare muon and pion processes: investigations of cosmic muons, of stopped accelerator pions and muon beams (meson factories).
At DLNP, JINR, the research started with the pion beta decay observation at the synchrocyclotron, and continued in the Sector led by S.M. Korenchenko. The investigations are now being carried out by the lab stuff members within the preparation for upcoming experiments at external accelerators: COMET (J-park, Japan) and Mu2e (FNAL) to search for the μ-е conversion, and the MEG-II experiment to study µ+ → e+γ decay at the Paul Scherrer Institute.