Demonstration of the Equivalence of Soft and Zero-Bin Subtractions
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 $$\lambda$$.
- Research Organization:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Sponsoring Organization:
- USDOE - Office of Energy Research (ER)
- DOE Contract Number:
- AC05-06OR23177
- OSTI ID:
- 909831
- Report Number(s):
- JLAB-THY-07-676; DOE/OR/23177-0084; arXiv:0707.1101; TRN: US0703980
- Journal Information:
- Phys.Rev.D, Vol. 76
- Country of Publication:
- United States
- Language:
- English
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On The Equivalence of Soft and Zero-Bin Subtractions
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