Investigation of the chiral anomaly<i>γ→3π</i>in pion pair production by pion in the nuclear Coulomb field

The vertex \ensuremath{\gamma}\ensuremath{\rightarrow}3\ensuremath{\pi} has been investigated in the reaction of pion pair production by pions in the nuclear Coulomb field, ${\ensuremath{\pi}}^{\ensuremath{-}}$+(Z,A)\ensuremath{\rightarrow}${\ensuremath{\pi}}^{\ensuremath{-}}$+${\ensuremath{\pi}}^{0}$+(Z,A), in the region of low-invariant-mass ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$${\ensuremath{\pi}}^{0}$ pairs. The experiment has been carried out in the 40-GeV pion beam of the IHEP accelerator (Serpukhov) with the SIGMA spectrometer. We have measured for the first time the cross section of the reaction in the region of momentum transfer squared ${q}^{2}$2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ (GeV/c${)}^{2}$, \ensuremath{\sigma}/${Z}^{2}$=1.63\ifmmode\pm\else\textpm\fi{}0.23\ifmmode\pm\else\textpm\fi{}0.13 nb, and the \ensuremath{\gamma}\ensuremath{\rightarrow}3\ensuremath{\pi} coupling constant ${F}^{3\ensuremath{\pi}}$=12.9\ifmmode\pm\else\textpm\fi{}0.9\ifmmode\pm\else\textpm\fi{}0.5 ${\mathrm{GeV}}^{\mathrm{\ensuremath{-}}3}$, where the first (second) error is statistical (systematic). The obtained result agrees with the calculations based on the Wess-Zumino-Witten effective Lagrangian. The hypothesis of chiral anomalies and the color-SU(3) quark symmetry are confirmed.