First subleading power resummation for event shapes

  • Ian Moult
  • Iain W. Stewart
  • Gherardo Vita
  • Hua Xing Zhu
Open Access
Regular Article - Theoretical Physics


We derive and analytically solve renormalization group (RG) equations of gauge invariant non-local Wilson line operators which resum logarithms for event shape observables τ at subleading power in the τ ≪ 1 expansion. These equations involve a class of universal jet and soft functions arising through operator mixing, which we call θ-jet and θ-soft functions. An illustrative example involving these operators is introduced which captures the generic features of subleading power resummation, allowing us to derive the structure of the RG to all orders in αs, and provide field theory definitions of all ingredients. As a simple application, we use this to obtain an analytic leading logarithmic result for the subleading power resummed thrust spectrum for Hgg in pure glue QCD. This resummation determines the nature of the double logarithmic series at subleading power, which we find is still governed by the cusp anomalous dimension. We check our result by performing an analytic calculation up to \( \mathcal{O}\left({\alpha}_s^3\right) \). Consistency of the subleading power RG relates subleading power anomalous dimensions, constrains the form of the θ-soft and θ-jet functions, and implies an exponentiation of higher order loop corrections in the subleading power collinear limit. Our results provide a path for carrying out systematic resummation at subleading power for collider observables.


Effective Field Theories Perturbative QCD Renormalization Group Resummation 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.


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© The Author(s) 2018

Authors and Affiliations

  1. 1.Berkeley Center for Theoretical PhysicsUniversity of CaliforniaBerkeleyU.S.A.
  2. 2.Theoretical Physics GroupLawrence Berkeley National LaboratoryBerkeleyU.S.A.
  3. 3.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  4. 4.Department of PhysicsZhejiang UniversityHangzhouChina

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