MassToMI

A Mathematica package for an automatic Mass Insertion expansion.
Program maintainer: Janusz Rosiek

News

December 18, 2015:

MassToMI v1.02 available. Two minor problems corrected (see changelog below).

Manual included in the updated version accepted for publication in Computer Physics Communications.

November 11, 2015:

MassToMI v1.01 available. Functions expanding summation convention (FetSumParticle and FetSumFactor) now work correctly also for c.c. of objects with repeating indices.

September 15, 2015: MassToMI v1.00 available.

Program description has been published as Comput.Phys.Commun. 201 (2016) 144-158 (arXiv:1509.05030 [hep-ph]).

Program purpose and content

MassToMI is a Mathematica package designed to automatize an expansion of the 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 general the ``Flavor Expansion Theorem'' proven in Ref. [1] cited below. 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 and vector particle (Hermitian) and Dirac or Majorana fermion (general complex) mass matrices.

Package provides also several auxiliary functions for simplifying and expanding expressions containing objects with repeating arguments ("indices"), assumed to be implicitely summed over.

Papers to be cited in connection with MassToMI

  1. Mass Insertions vs. Mass Eigenstates calculations in Flavour Physics A. Dedes, M. Paraskevas, J. Rosiek, K. Suxho, K. Tamvakis, JHEP 1506 (2015) 151, arXiv:1504.00960 [hep-ph].
  2. MassToMI - a Mathematica package for an automatic Mass Insertion expansion, J. Rosiek, Comput.Phys.Commun. 201 (2016) 144-158, arXiv:1509.05030 [hep-ph].

Download

Download v1.02 (released 18.12.2015): MassToMI v1.02

Installation

The MassToMI package does not require any special installation procedures. It should be unpacked to the directory accessible to Mathematica, or installed system-wide using Install command from the Mathematica menu. Then the package can be loaded using the commands

Needs["MassToMI`"]

or

<< MassToMI.m

Changelog

Version 1.02 (18 December 2015)

Two problems corrected:

1. Internal package notation for c.c. of Majorana fermion mixing matrices was in some cases used also in the program output, for example Conjugate[NMIX[A,i,j]]^2 was displayed as NMIX[A,i,j,MassToMI`Private`C]^2. Not really a bug, but potentially confusing.

2. Products of fermion mixing matrices and fermion mass factor (like V_Q^{ij*} m_Q^j U_Q^{kj} etc,) were not correctly evaluated in the case they were not multiplied by any loop function depending on fermion mass m_j. For example, V_Q^{ij*} m_Q^j U_Q^{kj} was evaluated as KroneckerDelta[i,k] instead of MF[Q,i,k] as it should be. Corrected.

Version 1.01 (15 November 2015)

Functions expanding summation convention (FetSumParticle and FetSumFactor) now work correctly also for c.c. of objects with repeating indices.

Version 1.00 (15 September 2015)

MassToMI v1.00 published.