Abstract
Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly independent master integrals is reduced to a projection. We present a new method for computing intersection numbers that only uses rational operations and does not require any integral transformation or change of basis. We achieve this by systematically employing the polynomial series expansion, namely the expansion of functions in powers of a polynomial. We also introduce a new prescription for choosing dual integrals, de facto removing the explicit dependence on additional analytic regulators in the computation of intersection numbers. We describe a proof-of-concept implementation of the algorithm over finite fields and its application to the decomposition of Feynman integrals at one and two loops.
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Acknowledgments
We thank Vsevolod Chestnov, Federico Gasparotto and Pierpaolo Mastrolia for many valuable discussions and comments on this work. We also grateful to Thomas Gehrmann and Petr Jakubčík for feedback on the draft. This work was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme grant agreements 101019620 (ERC Advanced Grant TOPUP) and 101040760 (ERC Starting Grant FFHiggsTop).
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Fontana, G., Peraro, T. Reduction to master integrals via intersection numbers and polynomial expansions. J. High Energ. Phys. 2023, 175 (2023). https://doi.org/10.1007/JHEP08(2023)175
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DOI: https://doi.org/10.1007/JHEP08(2023)175