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Journal of High Energy Physics

, Volume 2015, Issue 12, pp 1–36 | Cite as

Hard matching for boosted tops at two loops

  • André H. Hoang
  • Aditya PathakEmail author
  • Piotr Pietrulewicz
  • Iain W. Stewart
Open Access
Regular Article - Theoretical Physics

Abstract

Cross sections for top quarks provide very interesting physics opportunities, being both sensitive to new physics and also perturbatively tractable due to the large top quark mass. Rigorous factorization theorems for top cross sections can be derived in several kinematic scenarios, including the boosted regime in the peak region that we consider here. In the context of the corresponding factorization theorem for e + e collisions we extract the last missing ingredient that is needed to evaluate the cross section differential in the jet-mass at two-loop order, namely the matching coefficient at the scale μm t . Our extraction also yields the final ingredients needed to carry out logarithmic re-summation at next-to-next-to-leading logarithmic order (or N3LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at \( \mathcal{O}\left({\alpha}_s^2\right) \) due to virtual top quark loops, which we treat using rapidity renormalization group (RG) evolution. Interestingly, this rapidity RG evolution appears in the matching coefficient between two effective theories around the heavy quark mass scale μm t .

Keywords

QCD Phenomenology NLO Computations 

Notes

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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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • André H. Hoang
    • 1
    • 2
  • Aditya Pathak
    • 3
    Email author
  • Piotr Pietrulewicz
    • 4
  • Iain W. Stewart
    • 3
  1. 1.University of Vienna, Faculty of PhysicsWienAustria
  2. 2.Erwin Schrödinger International Institute for Mathematical PhysicsUniversity of ViennaViennaAustria
  3. 3.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  4. 4.Theory Group, Deutsches Elektronen-Synchrotron (DESY)HamburgGermany

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