[en] Theoretical investigation of γ resonance production in the e⁺e^- annihilation is presented. For this purpose vacuum polarization by vector (electromagnetic) current of b quarks is considered. The calculation of the amplitude of the process leads to the sum rules for γ resonance production. The L-transform of the vacuum polarization amplitudes is discussed. It is shown that agreement of theoretical prediction with experimental data is fulfilled for the b quark mass m=4.65+-0.05 GeV. It is evident for reality of gluon exchange at short distances