Integration-by-parts identities in FDR

Abstract

Four-dimensional renormalized (FDR) integrals play an increasingly important role in perturbative loop calculations. Thanks to them, loop computations can be performed directly in four dimensions and with no ultraviolet (UV) counterterms. In this paper I prove that integration-by-parts (IBP) identities can be used to find relations among multi-loop FDR integrals. Since algorithms based on IBP are widely applied beyond one loop, this result represents a decisive step forward towards the use of FDR in multi-loop calculations.

13 pages

References in corpus (9)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Feynman Diagrams and Differential Equations
• Magnus and Dyson Series for Master Integrals
• Three-loop master integrals for ladder-box diagrams with one massive leg
• A four-dimensional approach to quantum field theories
• Simplified differential equations approach for Master Integrals
• FDR, an easier way to NNLO calculations: a two-loop case study
• Two-loop off-shell QCD amplitudes in FDR
• Tutorial on loop integrals which need regularisation but yield finite results

Cited by in corpus (4)

• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Two-loop off-shell QCD amplitudes in FDR
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Numerical Evaluation of Two-Loop Integrals in FDR