ExtractingRbandRcwithout Flavor Tagging

We note that a flavor tagging independent measurement of the branching fractions $R_b$ and $R_c$ may be obtained from the width of hadronic $Z$ decays with a prompt photon, ${\Gamma }_{q\overline{q}\gamma }$, and an additional theoretical assumption. We find that the current value of ${\Gamma }_{q\overline{q}\gamma }$ supports the direct measurements and favors generation-blind corrections to quark widths. An updated measurement of ${\Gamma }_{q\overline{q}\gamma }$ with the currently available LEP data will provide an even stronger constraint.