Sum rules for Y-family formation in e+e--annihilation

In the framework of quantum chromodynamics a prediction is obtained for the integral μ-2∫Rb(s)exp[(My2 -s)/μ2]ds, involving the contribution Rb(s) from states containing the b and anti b quarks to the quantity R measured in the e+e- annihilation, in dependence of the parameter μ. The region μ = 2-3.7.7 GeV is analysed, where the integral is saturated by the contributions from the Y and Y' resonances. The theoretical result is in a reasonable agreement with the available experimental data if the b quark mass is m = 4.65 +- 0.05 GeV. In the region of the μ parameter considered the gluon exchange effects at short distances renormalize the theoretical prediction by a factor of 2-8 (depending on μ) as compared to the result for free quarks. Therefore, the existent agreement with the experimental data is by no means trivial and is a clear evidence to the existence of the gluon exchange at short distances. (orig.)