Abstract
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions. Thus it can be systematically applied to problems with arbitrary kinematic configurations. Numerical tests show that our method can not only achieve results with high precision, but also be much faster than the only existing systematic method sector decomposition. As a by product, we find a new strategy to compute scalar one-loop integrals without reducing them to master integrals.
Highlights
We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions
In this Letter, we develop a novel method to compute multi-loop master integrals (MIs) by constructing and solving a system of ordinary differential equations (ODEs)
Our method can be systematically applied to any complicated problem; 2) ODEs can be numerically solved efficiently to high precision, no matter how many mass scales are involved in the problem; 3) Computing MIs with complex kinematic variables is very easy in our method, while it could be hard for other methods
Summary
A Systematic and Efficient Method to Compute Multi-loop Master Integrals We propose a novel method to compute multi-loop master integrals by constructing and numerically solving a system of ordinary differential equations, with almost trivial boundary conditions.
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