Calabi-Yau periods for black hole scattering in classical general relativity

Abstract

The high-precision description of black hole scattering in classical general relativity using the post-Minkowskian (PM) expansion requires the evaluation of single-scale Feynman integrals at increasing loop orders. Up to 4PM, the scattering angle and the impulse are expressible in terms of polylogarithmic functions and Calabi-Yau (CY) two-fold periods. As in QFT, periods of higher dimensional CY n-folds are expected at higher PM order. We find at 5PM in the dissipative leading order self-force sector (5PM-1SF) that the only non-polylogarithmic functions are the K3 periods encountered before and the ones of a new hypergeometric CY three-fold. In the 5PM-2SF sector further CY two- and three-fold periods appear. Griffiths transversality of the CY period motives allows to transform the differential equations for the master integrals into $\epsilon$-factorized form and to solve them in terms of a well controlled function space, as we demonstrate in the 5PM-1SF sector.