# Purpose

The calculation of loop decays is a tedious work, which can rarely be performed in a reasonable time by calculating all arising diagrams by hand. The Mathematica package MasterTwoallows the automated calculation of all one- and two-loop Feynman integrals reducable to scalar integrals independent of external momenta and depending on up to two different masses. In contrast to other programmes like Reduceand Form it works completely inside Mathematica. Compared to other programmes like HIP, Tracer and FeynArts , MasterTwo is much smaller.

It consists of two subpackages, Fermions and Integrals. Fermions covers the standard Dirac Algebra allowing the transformation of the integrals in scalar integrals. Integrals perform the subsequent Taylor expansion, partial fraction, tensor reduction and the integration of the thus achieved scalar integrals.

# Structure

The main programme MasterTwo.m calls these two subpackages

• Fermions.m:  containing functions for standard Dirac algebra allowing the transformation of the integrals in scalar integrals.

• Integrals.m: containing functions for Taylor expansion, partial fraction, tensor reduction and the integration of the thus achieved scalar integrals.

# Help

The package is equipped with an online help to each command. MasterTwoInfo[] produces a list with all the available commands and  ?commandprints a short information on syntax and effect of command. A detailed description of all functionalities is given in the manual being part of this distribution.

# Installation under Linux

The installer MasterTwoInstall copies the files into the correct path, updates the init.m file in the .Mathematica/Autoload/directory in the home directory, To install the package,

• copy the zip file MasterTwo-1.0.zipto your disk,
• unpack it with unzip MasterTwo-1.0.zip.
• Change directory to MasterTwo-1.0
• Change the permission of the installation script:   chmod +x MasterTwoInstall
• Execute it: ./MasterTwoInstall Follow the instructions.

# Uninstallation under Linux

Run the program ./MasterTwoUninstall in the installation directory of MasterTwo.

# Installation under MACOS and Windows

To install the package

• Quit Mathematica . Eventually uninstall older version of MasterTwo.
• Start Mathematica
• Type \$Path: Lists the path(s) of the Autoload directories of your Mathematica distribution
• Copy the files
• Fermions.m
• Integrals.m
• MasterTwo.m in one of the Autoload directories.
• Close Mathematica.
• In your next Mathematica session you can start the package by typing in <<MasterTwo`

Submitted June 6, 2020 Feynman diagrams scalar two loop integration Dirac algebra tensor reduction heavy mass expansion published