Demonstration of the Equivalence of Soft and Zero-Bin Subtractions

Abstract

Calculations of collinear correlation functions in perturbative QCD and Soft-Collinear Effective Theory (SCET) 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 $\lambda$, where $\lambda$ is the SCET 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 provide strong support for the equivalence, which can be used to give a nonperturbative definition of the zero-bin subtraction at lowest order in $\lambda$.

14 pages, 3 figures

References in corpus (4)

• The Zero-Bin and Mode Factorization in Quantum Field Theory
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• On The Equivalence of Soft and Zero-Bin Subtractions
• QCD Factorization for Deep-Inelastic Scattering At Large Bjorken $x_B\sim 1-\mathcal{O}({\Lambda }_{\mathrm{QCD}}/Q$

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