We show that a master integrand basis exists for all planar, two-loop amplitudes in massless four-dimensional theories which is fully stratified by rigidity -- with each integrand being either pure and strictly polylogarithmic or (pure and) strictly elliptic-polylogarithmic, with each of the later involving a single elliptic curve. Such integrands can be said to have definite rigidity.
@article{arxiv.2207.00596,
title = {The Stratification of Rigidity},
author = {Jacob L. Bourjaily and Nikhil Kalyanapuram},
journal= {arXiv preprint arXiv:2207.00596},
year = {2022}
}
Comments
45 pages; 72 (tikz) figures; ancillary files include explicit details for examples discussed