General Mass Insertion Expansion in Flavor Physics

TL;DR

This paper introduces a general algebraic method and a Mathematica package for expanding quantum field theory amplitudes in terms of mass insertions, simplifying flavor physics calculations across various models.

Contribution

A novel, algebraic expansion technique for QFT amplitudes into mass insertions, applicable to all mass matrix types, with an automated Mathematica implementation.

Findings

Method works for Hermitian, complex, and symmetric mass matrices.

Automated in the MassToMI package for practical use.

Illustrated with Higgs decay in MSSM.

Abstract

Calculating amplitudes for the flavor changing transitions in terms of the off-diagonal elements of mass matrices, so called "Mass Insertions" (MI) in the theory defined in "gauge basis" (before mass matrix diagonalization) is the common technique in analyzing the flavor structure of the New Physics models. I present a general method allowing to expand any QFT amplitude calculated in the mass-eigenstates (physical) basis into series in MI's, to any required order. The technique is purely algebraic, translating an amplitude written in the mass eigenbasis into MI series without performing diagrammatic calculations in the gauge basis. It can be applied for all types of mass matrices - either Hermitian (scalar or vector), general complex (Dirac fermions) or complex symmetric (Majorana fermions). Proposed expansion has been also automatized in the form of publicly available specialized Mathematica package, MassToMI, which features I illustrate with the example of the Higgs boson decays in the MSSM.