GLUON SPLITTING INTO A PAIR OF HEAVY QUARKS IN E(-) ANNIHILATION()E()

The cross section for the process (+)e(-) --> q (q) over bar Q (Q) ove r bar, where Q is a heavy quark (c or b), and q is one of the quarks u , d, s, c, and b, is calculated in perturbative QCD. The mean multipli city of c (c) over bar pairs in the process e(+)e(-) --> q (q) over ba r c (c) over bar is found to be n(c (c) over bar) = 2.54 x 10(-2). For the characteristic virtuality Q(2) in the definition of alpha(s) for processes of the above type, comparison with experimental data yields Q(2) = 4m(Q)(2), where 2m(Q) is the mass of the emitted quark pair. Wi th alpha(s) taken at the virtuality of Q(2) = 4m(b)(2) for the b (b) o ver bar case, it is found that the ratio of the cross section for the production of the additional b (b) over bar pair to that for b (b) ove r bar production at the Z(0)-boson peak is sigma(addb (b) over bar)/si gma(b (b) over bar) = 0.99%. The differential distributions of b quark s and B mesons are used to study whether the additional b (b) over bar pairs from e(+)e(-) --> q (q) over bar b (b) over bar events contribu te to R-b (b over bar).