Matching QCD and heavy-quark effective theory heavy-light currents at two 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 formula applies to all current matchings. As a by-product, a master formula for the two-loop anomalous dimension of the QCD current q¯γ^[μ₁...γ^μ_n]q is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on γ₅ prescriptions is elucidated. Ratios of QCD matrix elements are obtained, independently of the three-loop anomalous dimension of HQET currents. The two-loop coefficient in f^*_B/f_B =1-2α_s(m_b)/3π-K_bα²_s/π² +O(α³_s,1/m_b) is K_b=83/12+4/81π²+2/27π²ln2-1/9ζ(3)-19/54N_l +Δ_c=6.37+Δ_c, with N_l=4 light flavors, and a correction Δ_c=0.18+/-0.01 that takes account of the nonzero ratio m_c/m_b=0.28+/-0.03. Convergence of the perturbative series is poor: the fastest apparent convergence would entail α_s(μ) at μ=370 MeV. ``Naive non-Abelianization'' of large-N_l results, via N_l-->N_l-33/2, gives reasonable approximations to exact two-loop results. All-order results for anomalous dimensions and matching coefficients are obtained at large β₀=11=2/3N_l. Consistent cancellation between infrared- and ultraviolet-renormalon ambiguities is demonstrated.