Interpolating amplitudes

Abstract: While the calculation of scattering amplitudes at higher orders in perturbation theory has reached a high degree of maturity, their usage to produce physical predictions within Monte Carlo programs is often hampered by the slow evaluation of the multi-loop amplitudes, especially so for amplitudes calculated numerically. As a remedy, interpolation frameworks have been successfully used in lower dimensions, but for higher-dimensional problems, such as the five dimensions of a 2 -> 3 phase space, efficient and reliable solutions are sparse. This work aims to fill this gap by reviewing state-of-the-art interpolation methods, and by assessing their performance for concrete examples drawn from particle physics. Specifically, we investigate interpolation methods based on polynomials, splines, spatially adaptive sparse grids, and neural networks (multilayer perceptron and Lorentz-Equivariant Geometric Algebra Transformer). Our additional aim is to motivate further studies of the interpolation of scattering amplitudes among both physicists and mathematicians.