Remarks on "Calculation of the quarkonium spectrum and $m_{b}$, $m_{c}$ to order $\alpha_{s}^{4}$"

In a recent paper, we included 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 /sub s//sup 4/) and leading Lambda /sup 4//m/sup 4/ terms. The results were obtained with, in particular, the value of the two- loop static coefficient due to Peter; this has been recently challenged by Schroder. In our previous paper we used Peter's result; in the present one we now give results with Schroder's, as this is likely to be the correct one. The variation is slight as the value of b/sub 1/ is only one among the various O( alpha /sub s//sup 4/) contributions. With Schroder's expression we now have m/sub b/=5001 /sub -66//sup +104/ MeV, m/sub b/(m/sub b//sup 2/)=4454/sub -29//sup +45/ MeV, m/sub c/=1866/sub -133//sup +215/ MeV, m/sub c/(m/sub c //sup 2/)=1542/sub -104//sup +163/ MeV. Moreover, Gamma ( Upsilon to e/sup +/e/sup -/)=1.07+or-0.28 keV(expt=1.320+or-0.04 keV) and the hyperfine splitting is predicted to be M( Upsilon )-M( eta )=47/sub -13//sup +15/ MeV. (10 refs).