Calculation of Quarkonium Spectrum and $m_b,m_c$ to Order ${\alpha }_s^4$

We include two loop, relativistic one loop and second order relativistic tree level corrections, plus leading nonperturbative contributions, to obtain a calculation of the lower states in the heavy quarkonium spectrum correct up to, and including, $O({\alpha }_s^4)$ and leading ${\mathrm{\Lambda }}^4\mathrm{/}{m}^4$ terms. This allows us, in particular, to obtain a model independent determination of the pole masses of the $b,c$ quarks, $$m_b=5015_{-70}^{+110}mev;m_c=1884_{-133}^{+222}mev$$ to which correspond the $\overline{\text{MS}}$ masses, $${\bar{m}}_b({\bar{m}}_b^2)=4453_{-32}^{+50}mev;{\bar{m}}_c({\bar{m}}_c^2)=1547_{-102}^{+169}mev\mathrm{.}$$ The decay $\mathrm{\Gamma }(\mathrm{{\rm Y}}\to e^{+}{e}^{-})$ is found in agreement with experiment, $$\mathrm{\Gamma }(\mathrm{{\rm Y}}\to e^{+}{e}^{-})=1.135_{-0.29}^{+0.27}kev(\text{exp.}=1.320\pm 0.04kev),$$ and the hyperfine splitting is predicted to be $$M(\mathrm{{\rm Y}})-M(\eta )=48.5_{-12.2}^{+15.7}mev\mathrm{.}$$