Abstract
The emission of collinear radiation off an elementary lepton can be factorised from the hard scattering process by introducing Parton Distribution Functions of a Lepton (LePDF), which, contrary to protons, can be derived from first principles. In case of multi-TeV lepton colliders, such as the muon colliders currently being proposed, the complete structure of Standard Model interactions must be taken into account. In this work we solve numerically the corresponding DGLAP equations at the double-log order and provide public files with LePDFs for both muons and electrons, including polarisation effects. We discuss several interesting aspects of the resulting PDFs and compare them with the Effective Vector Approximation, showing that the latter fails to describe well the vector bosons PDFs at small momentum fractions, unless it is extended to higher orders.
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Acknowledgments
We would like to thank Thomas Gehrmann, Johannes Michel, Luca Vecchi, and Andrea Wulzer for fruitful discussions. DM acknowledges partial support by MIUR grant PRIN 2017L5W2PT and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme, grant agreement 833280 (FLAY). ST is supported by the Swiss National Science Foundation — project n. P500PT_203156, and by the Center of Theoretical Physics at MIT.
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Garosi, F., Marzocca, D. & Trifinopoulos, S. LePDF: Standard Model PDFs for high-energy lepton colliders. J. High Energ. Phys. 2023, 107 (2023). https://doi.org/10.1007/JHEP09(2023)107
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DOI: https://doi.org/10.1007/JHEP09(2023)107