Measurement of the rate of $b\overline{b} b\overline{b}$ events in hadronic Z decays and the extraction of the gluon splitting into $b\overline{b}$

The rate $Z \rightarrow b\overline{b}b\overline{b}$ was measured using about $2 x 10^6$ hadronic decays collected by the DELPHI experiment in 1994 and 1995. Events were forced into 3-jets with $y_{min} > 0.06$ and a b-tag was required for every jet. The rate was measured to be: $R_{4b} = BR(Z \to b\overline{b}b\overline{b}) / BR(Z \to hadrons) = (6.0 +- 1.9(stat) +- 1.4(syst.)) x 10^{-4}$ where the invariant mass of every $b\overline{b}$ system is above twice the b quark mass. Using the value of $R_{4b}$ the probability of secondary production of a $b\overline{b}$ pair from a gluon per hadronic $Z$ decay, $g_{bb}$, was extracted and found to be: $g_{bb} = (3.3+-1.0(stat.) +- 0.8(syst.)) x 10^{-3}$.