Abstract
Jet calculus offers a unique mathematical technique to bridge the area of QCD resummation with Monte Carlo parton showers. With the ultimate goal of constructing next-to-next-to-leading logarithmic (NNLL) parton showers we study, using the language of generating functionals, the collinear fragmentation of final-state partons. In particular, we focus on the definition and calculation of the Sudakov form factor, which physically describes the no-emission probability in an ordered branching process. We review recent results for quark jets and compute the Sudakov form factor for the collinear fragmentation of gluon jets at NNLL. The NNLL corrections are encoded in a z dependent two-loop anomalous dimension \( \mathcal{B} \)2(z), with z being a suitably defined longitudinal momentum fraction. This is obtained from the integration of the relevant 1 → 3 collinear splitting kernels combined with the one-loop corrections to the 1 → 2 counterpart. This work provides the missing ingredients to extend the methods of jet calculus in the collinear limit to NNLL and gives an important element of the next generation of NNLL parton shower algorithms. As an application we derive new NNLL results for both the fractional moments of energy-energy correlation FCx and the angularities λx measured on mMDT/Soft-Drop (β = 0) groomed jets.
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Acknowledgments
We thank Ludovic Scyboz, Grégory Soyez and Gavin Salam for useful discussions through the course of this work and comments on the manuscript. Furthermore, we are grateful to Gavin Salam for collaboration on the related forthcoming ref. [1]. We would also like to thank other colleagues on the PanScales collaboration whose thoughts and efforts towards pushing forward the logarithmic accuracy of parton showers have directly motivated this work. This work has been partly funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 788223) (MvB, MD, BKE and JH) and by the U.K.’s Science and Technologies Facilities Council under grant ST/T001038 (MD). The work of PM is funded by the European Union (ERC, grant agreement No. 101044599, JANUS). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.
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van Beekveld, M., Dasgupta, M., El-Menoufi, B.K. et al. Collinear fragmentation at NNLL: generating functionals, groomed correlators and angularities. J. High Energ. Phys. 2024, 93 (2024). https://doi.org/10.1007/JHEP05(2024)093
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DOI: https://doi.org/10.1007/JHEP05(2024)093