Determination of semi-muonic branching ratios and fragmentation functions of heavy quarks ine + e ? annihilation at $$\langle \sqrt s \rangle $$ =34.6 GeV

Muon inclusive multihadronic final states ine + e − annihilation at $$\langle \sqrt s \rangle $$ =34.6 GeV, collected by the JADE detector at PETRA, have been analysed in terms of the semi-muonic branching ratios and fragmentation functions of heavy quarks. Defining the fragmentation variable, ζ, as $$z = \frac{{\left( {E + p_\parallel } \right)_{hadron} }}{{\left( {E + p} \right)_{quark} }}$$ we find =(77±3±5)% and =(86±4±5)%. The corresponding semi-muonic branching ratios are measured to be BR(c→μv μ X)=7.8±1.5±2)% and BR (b→μv μ X)=(11.7±1.6±1.5)%. Defining ζ as $$x_E = \frac{{E_{hadron} }}{{E_{beam} }}$$ we observe an expected softening effect in the fragmentation due mainly to gluon emission, but find that this definition leads to semi-muonic branching ratiomeasurements which are strongly affected by uncertainties in the fragmentation process and the WCD calculation.