XVIII International Conference on Hadron Spectroscopy and Structure (HADRON2019)

Since 2010 the VEPP-2000 electron-positron collider has been operated at Budker Institute of Nuclear Physics in the center-of-mass (c.m.) energy range from $\sqrt{s}=320$ MeV to $2000$ MeV. VEPP-2000 has two interaction regions in which the Cryogenic Magnetic Detector (CMD-3) and the Spherical Neutral Detector (SND) are installed. Production of four charged pions in $e^+ e^-$ annihilation has been studied before with good statistics at the CMD-2 and SND detectors as well as using initial-state radiation (ISR) with BaBar at which a low systematic uncertainty of about 3% was achieved for the $e^+ e^- \to \pi^{+}\pi^{-}\pi^{+}\pi^{-}$ cross section in the wide c.m. energy range. In this work the cross section of the process $e^+ e^- \to \pi^{+}\pi^{-}\pi^{+}\pi^{-}$ has been measured using an integrated luminosity of 168 pb$^{-1}$ collected with the CMD-3 detector in the c.m. energy range 650-2000 MeV. Also studied are the internal dynamics of four-pion production. High-precision measurements of various hadronic cross sections are of great interest in relation with the problem of the muon anomalous magnetic moment g-2. The $e^+ e^- \to \pi^{+}\pi^{-}\pi^{+}\pi^{-}$ cross section can be also used to test relations between $e^+e^-$ annihilation and $\tau$ lepton decays based on conservation of vector current.