Meromorphic modular forms and the three-loop equal-mass banana integral

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Standard

Meromorphic modular forms and the three-loop equal-mass banana integral. / Broedel, Johannes; Duhr, Claude; Matthes, Nils.

In: Journal of High Energy Physics, Vol. 2022, No. 2, 184, 02.2022.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Broedel, J, Duhr, C & Matthes, N 2022, 'Meromorphic modular forms and the three-loop equal-mass banana integral', Journal of High Energy Physics, vol. 2022, no. 2, 184. https://doi.org/10.1007/JHEP02(2022)184

APA

Broedel, J., Duhr, C., & Matthes, N. (2022). Meromorphic modular forms and the three-loop equal-mass banana integral. Journal of High Energy Physics, 2022(2), [184]. https://doi.org/10.1007/JHEP02(2022)184

Vancouver

Broedel J, Duhr C, Matthes N. Meromorphic modular forms and the three-loop equal-mass banana integral. Journal of High Energy Physics. 2022 Feb;2022(2). 184. https://doi.org/10.1007/JHEP02(2022)184

Author

Broedel, Johannes ; Duhr, Claude ; Matthes, Nils. / Meromorphic modular forms and the three-loop equal-mass banana integral. In: Journal of High Energy Physics. 2022 ; Vol. 2022, No. 2.

Bibtex

@article{8e6920bbf9ee4b3db17d4099eba6a8fb,
title = "Meromorphic modular forms and the three-loop equal-mass banana integral",
abstract = "We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup under which the modular forms transform can naturally be identified with the monodromy group of a certain second-order differential operator. We provide an explicit decomposition of the spaces of modular forms into a direct sum of total derivatives and a basis of modular forms that cannot be written as derivatives of other functions, thereby generalising a result by one of the authors form the full modular group to arbitrary finite-index subgroups of genus zero. Finally, we apply our results to the two- and three-loop equal-mass banana integrals, and we obtain in particular for the first time complete analytic results for the higher orders in dimensional regularisation for the three-loop case, which involves iterated integrals of meromorphic modular forms.",
keywords = "Differential and Algebraic Geometry, Scattering Amplitudes",
author = "Johannes Broedel and Claude Duhr and Nils Matthes",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s).",
year = "2022",
month = feb,
doi = "10.1007/JHEP02(2022)184",
language = "English",
volume = "2022",
journal = "Journal of High Energy Physics (Online)",
issn = "1126-6708",
publisher = "Springer",
number = "2",

}

RIS

TY - JOUR

T1 - Meromorphic modular forms and the three-loop equal-mass banana integral

AU - Broedel, Johannes

AU - Duhr, Claude

AU - Matthes, Nils

N1 - Publisher Copyright: © 2022, The Author(s).

PY - 2022/2

Y1 - 2022/2

N2 - We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup under which the modular forms transform can naturally be identified with the monodromy group of a certain second-order differential operator. We provide an explicit decomposition of the spaces of modular forms into a direct sum of total derivatives and a basis of modular forms that cannot be written as derivatives of other functions, thereby generalising a result by one of the authors form the full modular group to arbitrary finite-index subgroups of genus zero. Finally, we apply our results to the two- and three-loop equal-mass banana integrals, and we obtain in particular for the first time complete analytic results for the higher orders in dimensional regularisation for the three-loop case, which involves iterated integrals of meromorphic modular forms.

AB - We consider a class of differential equations for multi-loop Feynman integrals which can be solved to all orders in dimensional regularisation in terms of iterated integrals of meromorphic modular forms. We show that the subgroup under which the modular forms transform can naturally be identified with the monodromy group of a certain second-order differential operator. We provide an explicit decomposition of the spaces of modular forms into a direct sum of total derivatives and a basis of modular forms that cannot be written as derivatives of other functions, thereby generalising a result by one of the authors form the full modular group to arbitrary finite-index subgroups of genus zero. Finally, we apply our results to the two- and three-loop equal-mass banana integrals, and we obtain in particular for the first time complete analytic results for the higher orders in dimensional regularisation for the three-loop case, which involves iterated integrals of meromorphic modular forms.

KW - Differential and Algebraic Geometry

KW - Scattering Amplitudes

UR - http://www.scopus.com/inward/record.url?scp=85125470244&partnerID=8YFLogxK

U2 - 10.1007/JHEP02(2022)184

DO - 10.1007/JHEP02(2022)184

M3 - Journal article

AN - SCOPUS:85125470244

VL - 2022

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 2

M1 - 184

ER -

ID: 314452208