Comparing and Counting Logs in Direct and Effective Methods of Resummation

Abstract

We compare methods to resum logarithms in event shape distributions as they have been used in perturbative QCD directly and in effective field theory. We demonstrate that they are equivalent. In showing this equivalence, we are able to put standard soft-collinear effective theory (SCET) formulae for cross sections in momentum space into a novel form more directly comparable with standard QCD formulae, and endow the QCD formulae with dependence on separated hard, jet, and soft scales, providing potential ways to improve estimates of theoretical uncertainty. We show how to compute cross sections in momentum space to keep them as accurate as the corresponding expressions in Laplace space. In particular, we point out that that care is required in truncating differential distributions at N${}^k$LL accuracy to ensure they match the accuracy of the corresponding cumulant or Laplace transform. We explain how to avoid such mismatches at N${}^k$LL accuracy, and observe why they can also be avoided by working to N${}^k$LL${}^{\prime }$ accuracy.

65 pages plus Appendices, 8 figures, uses JHEP style. v2: improved clarity, added references, clarified that potential mismatches in accuracy of distribution vs. cumulant/Laplace transform exist at unprimed but not primed orders. v3: added references, footnote in Sec. 3.5 on earlier related results, minor corrections, version published in JHEP

References in corpus (22)

• Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly
• Boosted objects: a probe of beyond the Standard Model physics
• Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Treating the b quark distribution function with reliable uncertainties
• Threshold Resummation in Momentum Space from Effective Field Theory
• Boosted objects and jet substructure at the LHC
• Jet Shapes with the Broadening Axis
• Momentum Flow Correlations from Event Shapes: Factorized Soft Gluons and Soft-Collinear Effective Theory
• Toward a NNLO calculation of the B-->X_s+gamma decay rate with a cut on photon energy: II. Two-loop result for the jet function
• Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
• Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production
• Resummation of heavy jet mass and comparison to LEP data
• Resummation and NLO Matching of Event Shapes with Effective Field Theory
• Designing Gapped Soft Functions for Jet Production
• Electroweak Corrections in High Energy Processes using Effective Field Theory
• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• On The Equivalence of Soft and Zero-Bin Subtractions
• Demonstration of the Equivalence of Soft and Zero-Bin Subtractions
• Subleading Corrections To Thrust Using Effective Field Theory
• Infrared Safety in Factorized Hard Scattering Cross-Sections

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