On the R and R, Ratios at the Five-Loop Level of Perturbative &CD*

We study perturbative QCD at the five-loop level. In particular we consider R = ctot( eSe+ hadrons)/a( e+e+ p+p-) and R, = I’(7 + v + hadrons)/I’(r + evv). We use our method to estimate the five-loop coefficients. As a result, we obtain cys(Mz) = 0.1186(11) and a,(34 GeV) = 0.1396(16), which are accurate at the 1% level. We also find R = 3.8350(18) which is consistent with R, and is accurate to 0.05%. 1 Submitted to Physical Review Letters. * Work supported by the Department of Energy, contract DE-AC03-76SF00515.