MassToMI - a Mathematica package for an automatic Mass Insertion expansion

TL;DR

MassToMI is a Mathematica package that automates the expansion of quantum field theory amplitudes from mass eigenstates into series of mass insertions, facilitating calculations involving off-diagonal mass matrix elements.

Contribution

It introduces an algorithm based on the Flavor Expansion Theorem to automatically analyze and expand amplitudes in terms of mass insertions for various particle types.

Findings

Automates the expansion process for complex amplitudes.

Handles scalar, vector, Dirac, and Majorana fermion mass matrices.

Provides a downloadable tool for researchers in quantum field theory.

Abstract

We present a Mathematica package designed to automatize the expansion of QFT transition amplitudes calculated in the mass eigenstates basis (i.e. expressed in terms of physical masses and mixing matrices) into series of "mass insertions", defined as off-diagonal entries of mass matrices in Lagrangian before diagonalization and identification of the physical states. The algorithm implemented in this package is based on the general "Flavor Expansion Theorem" proven in Ref.~\cite{FET}. The supplied routines are able to automatically analyze the structure of the amplitude, identify the parts which could be expanded and expand them to any required order. They are capable of dealing with amplitudes depending on both scalar or vector (Hermitian) and Dirac or Majorana fermion (complex) mass matrices. The package can be downloaded from the address www.fuw.edu.pl/masstomi.