Cuts and isogenies
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Cuts and isogenies. / Frellesvig, Hjalte; Vergu, Cristian; Volk, Matthias; von Hippel, Matt.
In: Journal of High Energy Physics, Vol. 2021, No. 5, 064, 10.05.2021.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Cuts and isogenies
AU - Frellesvig, Hjalte
AU - Vergu, Cristian
AU - Volk, Matthias
AU - von Hippel, Matt
PY - 2021/5/10
Y1 - 2021/5/10
N2 - We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in full and loop-by-loop variants). We find that the same geometry for the genus-one curves arises in all cases, which lends support to the idea that there exists an invariant notion of genus-one geometry, independent on the way it is computed. We further indicate how to interpret some previous results which found that these curves are related by isogenies instead.
AB - We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a number of ways, including Feynman parametrization, lightcone and Baikov (in full and loop-by-loop variants). We find that the same geometry for the genus-one curves arises in all cases, which lends support to the idea that there exists an invariant notion of genus-one geometry, independent on the way it is computed. We further indicate how to interpret some previous results which found that these curves are related by isogenies instead.
KW - Scattering Amplitudes
KW - Differential and Algebraic Geometry
KW - 2-LOOP SELF-ENERGIES
KW - DIFFERENTIAL-EQUATIONS
KW - FEYNMAN-INTEGRALS
KW - ELLIPTIC POLYLOGARITHMS
KW - ITERATED INTEGRALS
KW - SUNRISE
KW - DIAGRAMS
KW - SPACE
KW - SERIES
KW - GRAPH
U2 - 10.1007/JHEP05(2021)064
DO - 10.1007/JHEP05(2021)064
M3 - Journal article
VL - 2021
JO - Journal of High Energy Physics (Online)
JF - Journal of High Energy Physics (Online)
SN - 1126-6708
IS - 5
M1 - 064
ER -
ID: 272415779