Measurement of\(\Gamma (Z^0 \to b\bar b)/\Gamma (Z^0 \to hadrons)\) using impact parameters and leptons

A measurement of\(\Gamma _{b\bar b} /\Gamma _{had} \equiv \Gamma (Z^0 \to b\bar b)/\Gamma (Z^0 \to hadrons)\) is presented using a “mixed tag” method involving the identification of\(Z^0 \to b\bar b\) events by two different techniques. The first uses the large impact parameterof tracks emerging from the decay ofb-flavoured hadrons and the second their semi-leptonic decay. The identification efficiencies are measured from the data using all possible combinations of the two tags in opposite hemispheres. The method is therefore insensitive to Monte Carlo modelling of bottom quarkproduction and ofb-flavoured hadron production and decay properties, and depends only weakly on the simulation of the detector. The data sample collected by OPAL at LEP in 1990 and 1991 is considered. The result is: $$\frac{{\Gamma _{b\bar b} }}{{\Gamma _{had} }} = 0.218 \pm 0.006(stat) \pm 0.007(syst) \pm 0.007(\Gamma _{c\bar c} /\Gamma _{had} ),$$ where the systematic uncertainty due to the charm quarkpartial width has been separated from the other systematic uncertainties. Combination with previous OPAL measurements gives: $$\frac{{\Gamma _{b\bar b} }}{{\Gamma _{had} }} = 0.220 \pm 0.004(stat) \pm 0.006(syst) \pm 0.006(\Gamma _{c\bar c} /\Gamma _{had} ),$$