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Non-global Logarithms at 3 Loops, 4 Loops, 5 Loops and Beyond

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arxiv 1403.4949 v2 pith:4GX5A2TU submitted 2014-03-19 hep-ph hep-th

Matthew D. Schwartz , Hua Xing Zhu This is my paper
classification hep-phhep-th
keywords loopsequationcoefficientsdirectionsleadinglogarithmsnon-globalagree
verification ladder T0 review T1 audit T2 compute T3 formal
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We calculate the coefficients of the leading non-global logarithms for the hemisphere mass distribution analytically at 3, 4, and 5 loops at large Nc . We confirm that the integrand derived with the strong-energy-ordering approximation and fixed-order iteration of the Banfi-Marchesini-Syme (BMS) equation agree. Our calculation exploits a hidden PSL(2,R) symmetry associated with the jet directions, apparent in the BMS equation after a stereographic projection to the Poincare disk. The required integrals have an iterated form, leading to functions of uniform transcendentality. This allows us to extract the coefficients, and some functional dependence on the jet directions, by computing the symbols and coproducts of appropriate expressions involving classical and Goncharov polylogarithms. Convergence of the series to a numerical solution of the BMS equation is also discussed.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Precision $e^+e^-$ Hemisphere Masses in the Dijet Region with Power Corrections

    hep-ph 2025-06 conditional novelty 8.0 of 10

    N3LL' resummation for heavy jet and dihemisphere masses in the dijet region, with a new claim that heavy jet mass moments require an extra non-perturbative parameter at order 1/Q.

  2. Extracting Essential Non-perturbative Information in Jet Invariant Mass via the Bayesian Analysis

    hep-ph 2025-07 conditional novelty 7.0 of 10

    A new 3D non-perturbative jet-mass model, fitted to pp data, separates hadronization, ISR, and underlying-event effects and correctly predicts e+e- jet mass data.

  3. $V/H$+Jet Production with the Cambridge/Aachen Algorithm

    hep-ph 2026-07 conditional novelty 6.0 of 10

    C/A clustering reduces non-global and clustering logarithms relative to k_t at three loops and behaves comparably to k_t at all orders in V/H+jet jet-mass predictions.

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