Upon the determination of heavy quark fragmentation functions ine + e − annihilation

Abstract

Results on the fragmentation of heavy quarks from analyses of inclusive lepton production ine + e − annihilation are studied. The use of various fragmentation variables is closely examined and their differences resolved, providing a common basis for comparison of experimental results. The mean value of the fraction of available energy-momentum carried by the primary heavy hadron, defined as $$z = \frac{{(E + p_\parallel )_{hadron} }}{{(E + p)_{quark} }},$$ is determined to be 〈z〉=0.67±0.02±0.02 and 〈z〉b=0.83±0.01±0.02 for an unknown mixture of charmed and bottom flavoured hadrons respectively. The corresponding values of the parameterɛ Q of the Peterson fragmentation function are $$\varepsilon _c = 0.06_{ + 0.02 + 0.02}^{ - 0.01 - 0.01} and \varepsilon _b = 0.06_{ + 0.001 + 0.02}^{ - 0.001 - 0.02} .$$ The ratioɛ c /ɛ b can be approximately related toM 2 /M 2 giving a value of 10 −2−4 +4+5 , in agreement with an expectation of ∼10. Measurements of the charged multiplicity of hadronic events containing heavy quark jets are investigated in terms of the mean value ofz.