Ancillary files for "Graded transcendental functions: an application to four-point amplitudes with one off-shell leg"

We provide ancillary files to "Graded transcendental functions: an application to four-point amplitudes with one off-shell leg".

All attached files are in Mathematica format. See also appendix C of the manuscript for details on the ancillary files. 

Families.zip: For each integral family, we provide in a single file familyname.m the list of propagators, a canonical basis and the corresponding differential equations, and a regularised boundary vector at the point (x, y) = (0, 0). Files contain a list of Mathematica replacement rules in the format {prop["familyname"]-> {...}, basis["familyname"]-> {...}, boundaries["familyname"]-> {....}, DE["familyname"]-> {...}}. 

BoundariesDemo.zip: An executable notebook implementing the fixing of boundary constants using the method for a two-loop example.

TridentFunctions.zip: For each relevant canonical integral and kinematic crossing listed in basis_labels.m, we provide a map to the trident functions in the form of a sparse rational array of size 13812 × 1282 in mapping_positions.m and mapping_values.m. We also provide the UT Laurent expansions of the trident functions in terms of 42258 iterated integrals and transcendental constants in sb_labels.m, again as a sparse array in expansion_positions.m and expansion_values.m.

FormFactor.zip: We provide the three-loop finite remainders R(3) and E(3) of the N = 4 sYM form factor in terms of Chen iterated integrals and MPLs.

Hjet.zip: The three independent helicity coefficients for the decay of a H boson to three partons at three loops are given in terms of iterated integrals and in a manifestly real MPL representation. In particular, we provide the part of the finite remainders containing new letters, with rational coefficients evaluated at x = 3/13, y = 11/17.