On The Equivalence of Soft and Zero-Bin Subtractions

Abstract

Zero-bin subtractions are required to avoid double counting soft contributions in collinear loop integrals in Soft-Collinear Effective Theory (SCET). In traditional approaches to factorization, double counting is avoided by dividing jet functions by matrix elements of soft Wilson lines. In this paper, we compare the two approaches to double counting, studying the quark form factor and deep inelastic scattering (DIS) as x_B \to 1 as examples. We explain how the zero-bin subtractions in SCET are required to reproduce the well-established factorization theorem for DIS as x_B \to 1. We study one-loop virtual contributions to the quark form factor and real gluon emission diagrams in DIS. The two approaches to double counting are equivalent if dimensional regularization (DR) is used to regulate infrared (IR) divergences. We discuss in detail ambiguities in the calculation of one-loop scaleless integrals in DR in SCET and perturbative QCD. We also demonstrate a nontrivial check of the equivalence of the zero-bin subtraction and the soft Wilson line subtraction in the virtual two-loop Abelian contributions to the quark form factor.

24 pages, 6 figures

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• Designing Gapped Soft Functions for Jet Production
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• Parton Fragmentation within an Identified Jet at NNLL
• Electroweak Corrections using Effective Field Theory: Applications to the LHC
• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• Angular correlations in multi-jet final states from kt-dependent parton showers
• Transverse Momentum Distributions from Effective Field Theory with Numerical Results
• Demonstration of the Equivalence of Soft and Zero-Bin Subtractions
• Transverse Momentum Distributions in the Non-Perturbative Region
• Infrared Safety in Factorized Hard Scattering Cross-Sections
• Factorization theorem for high-energy scattering near the endpoint
• Piecewise Linear Wilson lines
• Endpoint behavior of high-energy scattering cross sections
• Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)