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Untangling the IBP Equations

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If you have a question about this talk, please contact Terry Generet .

In this talk, I will present a general strategy for solving integration-by-parts (IBP) identities—a class of multivariable linear homogeneous relations that connect different Feynman integrals. Our approach is based on the diagonalisation of the IBP system, which effectively reduces it to single-variable recurrence relations. To the best of our knowledge, this is achieved here for the first time in over forty years of its use. Moreover, I will demonstrate that the diagonal IBP system takes the form V[n-1] = A(n+B)V[n], where A and B are non-commuting operators. We show that such systems can be solved analytically for complex values of n using GKZ -type differential equations, thereby providing a direct route to closed-form solutions. I will also briefly present a modified version of the method tailored to QCD multi-loop reductions, which leads to improved computational efficiency.

This talk is part of the HEP phenomenology joint Cavendish-DAMTP seminar series.

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