Rational-function interpolation from p-adic evaluations in scattering amplitude calculations

TL;DR

This paper introduces a p-adic evaluation-based interpolation method for rational functions in scattering amplitude calculations, significantly reducing computational probes and producing more compact results.

Contribution

It presents a novel interpolation technique directly in partial-fractioned form using p-adic evaluations, improving efficiency over traditional finite-field methods.

Findings

Requires 25 times fewer numerical probes

Produces results 100 times more compact

Reveals patterns for further optimization

Abstract

Numerical interpolation techniques are widely employed for calculating large rational functions in scattering amplitude computations. It has been observed in recent years that these rational functions greatly simplify upon partial fractioning. In this conference proceedings paper, based on the article [H. A. Chawdhry, Phys. Rev. D 110, 056028 (2024)], a technique is presented to interpolate such rational functions directly in partial-fractioned form, from evaluations at special integer points chosen for their properties under a p-adic absolute value. It is shown that the technique can require 25 times fewer numerical probes than conventional finite-field-based techniques and can produce results that are more compact in size by 2 orders of magnitude. The reconstructed results moreover exhibit additional patterns that could be exploited in future work to further improve the size of the results and the number of required numerical probes.