Equivalence of soft and zero-bin subtractions at two loops
Calculations of collinear correlation functions in perturbative QCD and soft-collinear effective theory require a prescription for subtracting soft or zero-bin contributions in order to avoid double counting the contributions from soft modes. At leading order in λ, where λ is the soft-collinear effective theory expansion parameter, the zero-bin subtractions have been argued to be equivalent to convolution with soft Wilson lines. We give a proof of the factorization of naive collinear Wilson lines that is crucial for the derivation of the equivalence. We then check the equivalence by computing the non-Abelian two-loop mixed collinear-soft contribution to the jet function in the quark form factor. These results demonstrate the equivalence, which can be used to give a nonperturbative definition of the zero-bin subtraction at lowest order in λ. © 2007 The American Physical Society.
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