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Journal of High Energy Physics

, 2018:75 | Cite as

Resumming double non-global logarithms in the evolution of a jet

  • Y. Hatta
  • E. Iancu
  • A. H. Mueller
  • D. N. Triantafyllopoulos
Open Access
Regular Article - Theoretical Physics

Abstract

We consider the Banfi-Marchesini-Smye (BMS) equation which resums ‘non-global’ energy logarithms in the QCD evolution of the energy lost by a pair of jets via soft radiation at large angles. We identify a new physical regime where, besides the energy logarithms, one has to also resum (anti)collinear logarithms. Such a regime occurs when the jets are highly collimated (boosted) and the relative angles between successive soft gluon emissions are strongly increasing. These anti-collinear emissions can violate the correct time-ordering for time-like cascades and result in large radiative corrections enhanced by double collinear logs, making the BMS evolution unstable beyond leading order. We isolate the first such a correction in a recent calculation of the BMS equation to next-to-leading order by Caron-Huot. To overcome this difficulty, we construct a ‘collinearly-improved’ version of the leading-order BMS equation which resums the double collinear logarithms to all orders. Our construction is inspired by a recent treatment of the Balitsky-Kovchegov (BK) equation for the high-energy evolution of a space-like wavefunction, where similar time-ordering issues occur. We show that the conformal mapping relating the leading-order BMS and BK equations correctly predicts the physical time-ordering, but it fails to predict the detailed structure of the collinear improvement.

Keywords

Perturbative QCD Resummation 

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) 2018

Authors and Affiliations

  • Y. Hatta
    • 1
  • E. Iancu
    • 2
  • A. H. Mueller
    • 3
  • D. N. Triantafyllopoulos
    • 4
  1. 1.Yukawa Institute for Theoretical PhysicsKyoto UniversityKyotoJapan
  2. 2.Institut de physique théoriqueUniversité Paris Saclay, CNRS, CEAGif-sur-YvetteFrance
  3. 3.Department of PhysicsColumbia UniversityNew YorkU.S.A.
  4. 4.European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno KesslerVillazzano (TN)Italy

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