Matching QCD and heavy-quark effective theory heavy-light currents at two loops and beyond
- Physics Department, Open University, Milton Keynes, MK7 6AA (United Kingdom)
Heavy-light QCD currents are matched with heavy-quark effective theory (HQET) currents at two loops and leading order in 1/{ital 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 {ital {bar q}}{gamma}{sup [{mu}}{sub 1}...{gamma}{sup {mu}}{sub {ital n}]}{ital q} is obtained, yielding a new result for the tensor current. The dependence of matching coefficients on {gamma}{sub 5} 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 {ital f}{sub {ital B}}{sup *}/{ital f}{sub {ital B}} =1{minus}2{alpha}{sub {ital s}}({ital m}{sub {ital b}})/3{pi}{minus}{ital K}{sub {ital b}}{alpha}{sub {ital s}}{sup 2}/{pi}{sup 2} +{ital O}({alpha}{sub {ital s}}{sup 3},1/{ital m}{sub {ital b}}) is {ital K}{sub {ital b}}=83/12+4/81{pi}{sup 2}+2/27{pi}{sup 2}ln2{minus}1/9{zeta}(3){minus}19/54{ital N}{sub {ital l}} +{Delta}{sub {ital c}}=6.37+{Delta}{sub {ital c}}, with {ital N}{sub {ital l}}=4 light flavors, and a correction {Delta}{sub {ital c}}=0.18{plus_minus}0.01 that takes account of the nonzero ratio {ital m}{sub {ital c}}/{ital m}{sub {ital b}}=0.28{plus_minus}0.03. Convergence of the perturbative series is poor: the fastest apparent convergence would entail {alpha}{sub {ital s}}({mu}) at {mu}=370 MeV. ``Naive non-Abelianization`` of large-{ital N}{sub {ital l}} results, via {ital N}{sub {ital l}}{r_arrow}{ital N}{sub {ital l}}{minus}33/2, gives reasonable approximations to exact two-loop results. All-order results for anomalous dimensions and matching coefficients are obtained at large {beta}{sub 0}=11=2/3{ital N}{sub {ital l}}. Consistent cancellation between infrared- and ultraviolet-renormalon ambiguities is demonstrated.
- OSTI ID:
- 249540
- Journal Information:
- Physical Review, D, Vol. 52, Issue 7; Other Information: PBD: 1 Oct 1995
- Country of Publication:
- United States
- Language:
- English
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