Abstract
We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy \( \sqrt{\hat{s}} \), and low-energy matrix elements, which are sensitive to the low scale Q0 ≪ \( \sqrt{\hat{s}} \) characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary 2 → M jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called “super-leading logarithms” discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for pp → 2 jets processes, but suppressed in H/Z and H/Z + jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.
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Acknowledgments
The authors thank Dominik Schwienbacher for discussions and comments on the manuscript. The research of TB was supported by the Swiss National Science Foundation (SNF) under grant 200020_182038. The work of MN and MS was supported by the Cluster of Excellence PRISMA+ (Precision Physics, Fundamental Interactions, and Structure of Matter, EXC 2118/1) funded by the German Research Foundation (DFG) under Germany’s Excellence Strategy (Project ID 390831469). DYS is supported by the National Science Foundations of China under Grant No. 12275052 and No. 12147101 and the Shanghai Natural Science Foundation under Grant No. 21ZR1406100. This research also received funding from the European Research Council (ERC) under the European Union’s Horizon 2022 Research and Innovation Programme (ERC Advanced Grant, Agreement No. 101097780, EFT4jets). TB would like to thank the Pauli Center at ETHZ, the CERN Theory Department and the Munich Institute for Astro-, Particle and BioPhysics (MIAPbP) for hospitality and support. MIAPbP is funded by the German Research Foundation under Germany’s Excellence Strategy (EXC 2094, Project ID 390783311).
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Becher, T., Neubert, M., Shao, D.Y. et al. Factorization of non-global LHC observables and resummation of super-leading logarithms. J. High Energ. Phys. 2023, 116 (2023). https://doi.org/10.1007/JHEP12(2023)116
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DOI: https://doi.org/10.1007/JHEP12(2023)116