High-precision particle mass measurements using the KEDR detector at the VEPP-4M collider

A review is presented of experiments performed using the KEDR detector at the VEPP-4M accelerator complex for the precise measurement of particle masses. The resonant depolarization method, proposed in 1975 at the G I Budker Institute of Nuclear Physics of the RAS Siberian Branch for measuring beam energy, has undergone further development in the experiments described; an unprecedented accuracy of $5\times 10^{-7}$ has been achieved. Application of this method together with measurement of the Compton backscattering energy allowed a series of experiments to be carried out which have provided the world's most accurate mass values for the ${\rm J}/{\rm \psi}$, $\rm {\psi(2S)}$, $\rm {\psi(3770)}$, and ${\rm D}^{\pm }$ mesons for the $\rm {\tau}$-lepton.