MassToMI—A Mathematica package for an automatic Mass Insertion expansion

Abstract

We present a Mathematica package designed to automatize the expansion of 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 Dedes et al. (2015). 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. Program summaryProgram title: MassToMI v1.0Catalogue identifier: AEZF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 4061No. of bytes in distributed program, including test data, etc.: 23755Distribution format: tar.gzProgramming language: Mathematica 10.2 (earlier versions should work as well).Computer: Any running Mathematica.Operating system: Any running Mathematica.RAM: Allocated dynamically by Mathematica, at least 4GB total RAM suggested.Classification: 11.1, 5.Nature of problem: Automatized expansion of QFT transition amplitude calculated in mass eigenstates basis into power series of off-diagonal elements of mass matrices of the interaction basis Lagrangian.Solution method: Implementation (as the Mathematica package) of the algebraic algorithm “Flavor Expansion Theorem”, formulated and proven in Ref. [1] given below.Running time: Depending on complexity of the analyzed expression, from seconds for simple problems to hours for complicated amplitudes expanded to high order (using Mathematica 10.2 running on a personal computer)