MATCHING QCD AND HEAVY-QUARK EFFECTIVE THEORY HEAVY-LIGHT CURRENTS AT2 LOOPS AND BEYOND

Heavy-light QCD currents are matched with heavy-quark effective theory (HQET) currents at two loops and leading order in 1/m. A single formu la applies to all current matchings. As a byproduct, a master formula for the two-loop anomalous dimension of the QCD current (q) over bar g amma([mu 1...gamma mu n])q is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on rs prescrip tions is elucidated. Ratios of QCD matrix elements are obtained, indep endently of the three-loop anomalous dimension of HQET currents. The t wo-loop coefficient in f(B)/f(B) = 1 - 2 alpha(s)(m(b))/3 pi - K-b al pha(s)(2)/pi(2) + O(alpha(s)(3), 1/m(b)) is K-b = 83/12 + 4/81 pi(2) 2/27 pi(2) In 2 - 1/9 zeta(3) - 19/54 N-l + Delta(c) = 6.37 + Delta(c ) with N-l = 4 light flavors, and a correction Delta(c) = 0.18 +/- 0.0 1 that takes account of the nonzero ratio m(c)/m(b) = 0.28 +/- 0.03. C onvergence of the perturbative series is poor: fastest apparent conver gence would entail alpha(s)(mu) at mu = 370 MeV. ''Naive non-Abelianiz ation'' of large-N-l results, via N-l --> N-l - 33/2, gives reasonable approximations to exact two-loop results. All-order results for anoma lous dimensions and matching coefficients are obtained at large beta(0 ) = 11 - 2/3 N-l. Consistent cancellation between infrared- and ultrav iolet-renormalon ambiguities is demonstrated.