Test of the flavour independence of $\alpha_s$ using next-to-leading order calculations for heavy quarks

We present a test of the flavour independence of the strong coupling constant for charm and bottom quarks with respect to light (uds) quarks, based on a hadronic event sample obtained with the OPAL detector at LEP. Five observables related to global event shapes were used to measure ${\alpha_s}$ in three flavour tagged samples (uds, c and b). The event shape distributions were fitted by ${\mathcal{O}(\alpha_s^2)}$ calculations of jet production taking into account mass effects for the c and b quarks. We find: $$ \alpha_s^\mathrm{c}/\alpha_s^\mathrm{uds}~ = 0.997 \pm 0.038~(stat.) \pm 0.030~(syst.) \pm 0.012~(theory)\quad \mathrm{and}$$ $$ \alpha_s^\mathrm{b}/\alpha_s^\mathrm{uds}~= 0.993 \pm 0.008~(stat.) \pm 0.006~(syst.) \pm 0.011~(theory).$