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


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.


Perturbative QCD Resummation 


Open Access

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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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