The three-loop nonmixing contributions to the anomalous dimension of the leading order quark pair production current in nonrelativistic QCD are computed. It is demonstrated that the renormalization procedure can only be carried out consistently if the dynamics of both soft and ultrasoft degrees of freedom is present for all scales below the heavy quark mass and if the soft and ultrasoft renormalization scales are always correlated.
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Univ Liverpool, Dept Math Sci, Div Theoret Phys, Liverpool L69 7ZF, Merseyside, EnglandUniv Liverpool, Dept Math Sci, Div Theoret Phys, Liverpool L69 7ZF, Merseyside, England
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Michigan State Univ, Dept Phys & Astron, E Lansing, MI 48824 USAUniv Oxford, Rudolf Peierls Ctr Theoret Phys, Clarendon Lab, Parks Rd, Oxford OX1 3PU, England
Chakraborty, Amlan
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Gambuti, Giulio
von Manteuffel, Andreas
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Michigan State Univ, Dept Phys & Astron, E Lansing, MI 48824 USAUniv Oxford, Rudolf Peierls Ctr Theoret Phys, Clarendon Lab, Parks Rd, Oxford OX1 3PU, England
von Manteuffel, Andreas
Tancredi, Lorenzo
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Univ Oxford, Rudolf Peierls Ctr Theoret Phys, Clarendon Lab, Parks Rd, Oxford OX1 3PU, EnglandUniv Oxford, Rudolf Peierls Ctr Theoret Phys, Clarendon Lab, Parks Rd, Oxford OX1 3PU, England