Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
Reducing differential equations for multiloop master integrals
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abstract
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\epsilon$. We consider linear transformations of the functions column which are rational in the variable and in $\epsilon$. Apart from some degenerate cases described below, the algorithm allows one to obtain the required transformation or to ascertain irreducibility to the form required. Degenerate cases are quite anticipated and likely to correspond to irreducible systems.
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A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.
citing papers explorer
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The gravitational Compton amplitude at third post-Minkowskian order
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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Recurrence Relations and Dispersive Techniques for Precision Multi-Loop Calculations
Connects recurrence techniques and dispersive methods with dimension shifts to reduce multi-point functions to two-point basis, minimizing dispersive integrals for one- and two-loop calculations.