A. Pineda et Fj. Yndurain, Remarks on "Calculation of the quarkonium spectrum and m(b), m(c) to orderalpha(4)(s)" - art. no. 077505, PHYS REV D, 6107(7), 2000, pp. 7505
In a recent paper, we included two-loop, relativistic one-loop, and second-
order relativistic tree level corrections, plus leading nonperturbative con
tributions, to obtain a calculation of the lower states in the heavy quarko
nium spectrum correct up to, and including, O(alpha(s)(4)) and leading Lamb
da(4)/m(4) terms. The results were obtained with, in particular, the value
of the two-loop static coefficient due to Peter; this has been recently cha
llenged by Schroder. In our previous paper we used Peter's result; in the p
resent 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(1) is only one amon
g the various O(alpha(s)(4)) contributions. With Schroder's expression we n
ow have m(b) = 5001 (-66) (+104) MeV, (m) over bar(b)((m) over bar(b)(2)) =
4454 (-29) (+45) MeV, m(c) = -1866 (-133) (+215) MeV, (m) over bar(c)((m)
over bar(c)(2) = 1542 (-104) (+163) MeV. Moreover, Gamma(Y --> e(+) e(-)) =
1.07 +/- 0.28 keV(expt = 1.320 +/- 0.04 keV) and the hyperfine splitting i
s predicted to be M(Y)-M(eta) = 47 (-13) (+15) MeV.