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
class="interref" data-locatorType="url" data-locatorKey="http://www.fuw.edu.pl/masstomi">www.fuw.edu.pl/masstomi.
Program summary
Manuscript Title:
MassToMI - a Mathematica package for an automatic Mass Insertion expansion
Authors: Janusz Rosiek
Program Title: MassToMI v1.0
Journal Reference:
Catalogue identifier:
Licensing provisions: None
Programming 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
Number of processors used: allocated dynamically by Mathematica
Supplementary material: None
Keywords: Mass Insertion Expansion, Flavor Violation, Mass Eigenstates vs. Interaction Basis
Classification:
class="formula" id="fd000005">
External routines/libraries: Wolfram Mathematica program
Subprograms used: None
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.
Restrictions: None
Unusual features: None
Additional comments: None
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)
class="listitem" id="list_l000005">- class="label">[1]
A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho, K. Tamvakis, Mass Insertions vs. Mass Eigenstates calculations in Flavor Physics, JHEP 1506 (2015) 151 [arXiv:1504.00960 [hep-ph]].
