Speaker
Description
We recently explored methods for 2-loop Feynman integrals in the Euclidean or physical kinematical region, using numerical extrapolation and adaptive iterated integration. Our current goal is to address 3-loop two-point integrals with up to 6 internal lines.
Using double extrapolation, the integral $\mathcal I$ is approximated numerically by the limit of a sequence of integrals $\mathcal I(\varepsilon)$ as $\varepsilon \rightarrow 0,$ where $\varepsilon$ enters in the space-time dimension $\nu = 4-2\varepsilon.$ For a fixed value of $\varepsilon = \varepsilon_\ell,$ the integral $\mathcal I(\varepsilon_\ell)$ is approximated by the limit of a sequence $I(\varepsilon_\ell,\varrho)$ as $\varrho \rightarrow 0.$ Here, $\varrho$ enters in the modification of a factor $V$ to $V-i\varrho$ in the integrand denominator, applied since $V$ may vanish in the integration domain. Alternatively, we can integrate after expanding with respect to $\varepsilon,$ followed by a single extrapolation in $\varrho$ only.
In this work, we will give an analysis with applications to sample diagrams.
References
Paper on 2-loop integrals in ACAT 2022: "Loop integral computation in the Euclidean or physical kinematical region using numerical integration and extrapolation", E. de Doncker, F Yuasa, T. Ishikawa and K. Kato
Significance
Accurate theoretical predictions are needed in view of improvements in the technology of high energy physics experiments. Higher-order corrections are required for accurate theoretical predictions of the cross-section for particle interactions. The Feynman diagrammatic approach is commonly used to address higher-order corrections. We use numerical integration and extrapolation methods to handle integrand singularities in Feynman loop integrals.
