DOI: 10.5281/zenodo.17141554
title: Ancillary Files to "Analytic two-loop amplitudes for di-jet and γ+jet production mediated by a heavy-quark loop"

description: Submission containing ancillary files to the research article "Analytic two-loop amplitudes for di-jet and γ+jet production mediated by a heavy-quark loop" (arXiv: 2509.15315)Preprint Number: TUM-HEP 1570/25If you use the results distributed with this repository in your research work, please cite 2509.15315.

This repository submission contains the following files, all in Mathematica-readable format (most of the expansions are zipped due to size): 

**** README.txt ****

Contains explanations of all the other files.

**** CanonicalBasis.m ****

This file contains the definition of our 220 canonical master integrals.

**** Roots.m ****

This file contains the definitions of the square roots in the form of replacement rules.

**** DiffRelationsEllipticFunctions.m ****

This file contains replacement rules for the differential relations among the elliptic functions.

**** CanonicalDiffEqs.m ****

This file contains the partial differential equations matrices for the canonical basis.

**** Boundary_Constants_Large_Mass_Limit.m ****

This file contains the boundary constants for the canonical basis in the large mass limit.

**** Alphabet.m ****

This file contains the alphabet defining all the dlog-kernels appearing in the canonical differential equations.

**** EllipticKernels.m ****

This file contains all the elliptic kernels appearing in the canonical differential equations.

**** HelCoeffs2lbareII.m ****

In this file, we provide analytic expressions for all the helicity coefficients in terms of a set of independent iterated integrals.

**** HelCoeffs2lbareExpLM.m ****

In this file, we give all the helicity coefficients expanded in the large mass limit.

**** HelCoeffs2lbareExpTt.m ****

In this file, we give all the helicity coefficients expanded in the point (s,t)=(4m2,0) using the original variables.

**** HelCoeffs2lbareExpTtBzu.m ****

In this file, we give all the helicity coefficients expanded in the point (s,t)=(4m2,0) using Bernoulli-like variables, considering physical singularities.

**** HelCoeffs2lbareExpTtBzp.m ****

In this file, we give all the helicity coefficients expanded in the point (s,t)=(4m2,0) using Bernoulli-like variables, considering also pseudo-thresholds.

**** HelCoeffs2lbareExpTu.m ****

In this file, we give all the helicity coefficients expanded in the point (s,u)=(4m2,0) using the original variables.

**** HelCoeffs2lbareExpTuBzt.m ****

In this file, we give all the helicity coefficients expanded in the point (s,u)=(4m2,0) using Bernoulli-like variables, considering physical singularities.

**** HelCoeffs2lbareExpTuBzp.m ****

In this file, we give all the helicity coefficients expanded in the point (s,u)=(4m2,0) using Bernoulli-like variables, considering also pseudo-thresholds.

**** HelCoeffs2lbareExpSM.m ****

In this file, we give all the helicity coefficients expanded in the small mass limit using the original variables.

**** HelCoeffs2lbareExpSMBz.m ****

In this file, we give all the helicity coefficients expanded in the small mass limit using a Bernoulli-like variable.

 

If you require any assistance with any of the material provided, please don't hesitate to contact the authors.

 

Version Documentation:

Version v2 (10.10.2025): Added the boundary constants for the canonical basis in the large mass limit, as well as expressions for all helicity coefficients in terms of a set of independent iterated integrals. Also fixed an issue with the expansion of the gg ->γγ helicity coefficient in the (+++-)-helicity configuration, where the colour factor was not stripped off as per the conventions established in 2502.00118. Further fixed a typo where the δ-helicity coefficient for diphoton production was labeled with "γg" instead of "γγ" in the files with the series expansions.