Ancillary Files to "Analytic two-loop amplitudes for q qbar → γγ and gg → γγ mediated by a heavy-quark loop"

Submission containing ancillary files to the research article "Analytic two-loop amplitudes for q qbar → γγ and gg → γγ mediated by a heavy-quark loop" (arXiv: 2502.00118)Preprint Number: TUM-HEP 1554/25If you use the results distributed with this repository in your research work, please cite 2502.00118. This repository submission contains the following files, all in Mathematica-readable format: **** CanonicalBasis.m **** This file contains the definition of our 165 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. **** 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). **** HelCoeffs2lbareExpTu.m **** In this file, we give all the helicity coefficients expanded in the point (s,u)=(4m2,0). **** README.txt **** For more details, see the README.txt file. Version Documentation: Version v3 (17.03.2025): fixes an issue with the expansions in "HelCoeffs2lbareExpLM.m" not being properly truncated. Updated "README.txt" with comments on the analytic continuation of logarithms and square roots of the expansion variables. Version v2 (06.02.2025): added the two files "CanonicalDiffEqs.m" and "HelCoeffs2lbareExpTu.m" missing in version v1.本提交为研究论文《基于重夸克圈传播的$qar{q} o gammagamma$与$gg o gammagamma$解析两圈振幅》（arXiv: 2502.00118）的配套辅助文件，预印本编号：TUM-HEP 1554/25。若您在研究工作中使用本仓库分发的研究结果，请引用该预印本（2502.00118）。 本仓库提交包含以下所有采用Mathematica可读格式的文件： - **CanonicalBasis.m**：本文件包含165个正则主积分（canonical master integrals）的定义。 - **Roots.m**：本文件以替换规则的形式定义了各类平方根。 - **DiffRelationsEllipticFunctions.m**：本文件包含椭圆函数（elliptic functions）间微分关系的替换规则。 - **CanonicalDiffEqs.m**：本文件包含正则基的偏微分方程（partial differential equations）矩阵。 - **HelCoeffs2lbareExpLM.m**：本文件给出了所有在大质量极限下展开的螺旋度系数（helicity coefficients）。 - **HelCoeffs2lbareExpTt.m**：本文件给出了所有在点$(s,t)=(4m^2,0)$处展开的螺旋度系数。 - **HelCoeffs2lbareExpTu.m**：本文件给出了所有在点$(s,u)=(4m^2,0)$处展开的螺旋度系数。 - **README.txt**： 详细说明请参阅README.txt文件。 版本说明： v3版（2025年3月17日）：修复了**HelCoeffs2lbareExpLM.m**中展开式未正确截断的问题；更新了README.txt，补充了关于展开变量的对数与平方根解析延拓的相关注释。 v2版（2025年2月6日）：新增了v1版中缺失的两个文件**CanonicalDiffEqs.m**与**HelCoeffs2lbareExpTu.m**。