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{}γ₁^[μ...γn]^μq 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 fB*/fB =1-2αₛ(mb)/3{π}-Kb{{{α}}}ₛ²$/${{{π}}}²$ +O(${{{α}}}ₛ³$,1/${m}b$) is ${K}b$=83/12+4/81${{{π}}}²$+2/27${{{π}}}²ln2-1/9ζ(3)-19/54{N}ₗ$ +${{{Δ}}}c$=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 ${{{β}}}₀$=11=2/3${N}ₗ$. Consistent cancellation between infrared- and ultraviolet-renormalon ambiguities is demonstrated.