Calculation of the quarkonium spectrum and m(b), m(c) to order alpha(4)(s)

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⁡(𝛼4𝑠) and leading 𝛬4⁢/𝑚4 terms. This allows us, in particular, to obtain a model-independent determination of the pole masses of the b,c quarks, 𝑚𝑏⁢=5015+110−70⁢MeV, 𝑚𝑐⁢=1884+222−133⁢MeV, to which correspond the ¯MS masses 𝑚𝑏(𝑚2𝑏⁢)=4453+50−32⁢MeV, 𝑚𝑐(𝑚2𝑐⁢)=1547+169
−102⁢MeV. The decay 𝛤⁡(→𝛶⁢𝑒+⁢𝑒−) is found to be in agreement with experiment, 𝛤(→𝛶⁢𝑒+⁢𝑒−⁢)=1.135+0.27−0.29⁢keV (expt. =1.320 ±0.04⁢keV), and the hyperfine splitting is predicted to be 𝑀⁡(𝛶)−𝑀(𝜂⁢)=48.5+15.7−12.2⁢MeV.