Meromorphic modular forms and the three-loop equal-mass banana integral
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Meromorphic modular forms and the three-loop equal-mass banana integral. / Broedel, Johannes; Duhr, Claude; Matthes, Nils.
I: Journal of High Energy Physics, Bind 2022, Nr. 2, 184, 02.2022.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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