Using Heavy Quark Fragmentation into Heavy Hadrons to Determine QCD Parameters and Test Heavy Quark Symmetry

We present a detailed analysis of the use of heavy quark fragmentation into heavy hadrons for testing the heavy quark effective theory through comparison of the measured fragmentation parameters of the $c$ and $b$ quarks. Our analysis is entirely model independent. We interpret the known perturbative evolution in a way useful for exploiting heavy quark symmetry at low energy. We first show consistency with perturbative QCD scaling for measurements done solely with $c$ quarks. We then apply the perturbative analysis and the heavy quark expansion to relate measurements from ARGUS and LEP. We place bounds on a nonperturbative quark mass suppressed parameter, and compare the values for the $b$ and $c$ quarks. We find consistency with the heavy quark expansion but fairly sizable QCD uncertainties. We also suggest that one might reduce the systematic uncertainty in the result by not extrapolating to low $z$.