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Comparing and Counting Logs in Direct and Effective Methods of Resummation

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arxiv 1401.4460 v3 pith:65KDOLYJ submitted 2014-01-17 hep-ph

classification hep-ph
keywords accuracytheyeffectiveformulaespacecorrespondingcrossdirectly
verification ladder T0 review T1 audit T2 compute T3 formal
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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$'$ accuracy.

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Cited by 4 Pith papers

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  4. Heavy Jet Mass in Hadronic Higgs Decays

    hep-ph 2026-07 conditional novelty 6.0 of 10

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