ON-SHELL2: FORM based package for the calculation of two-loop self-energy single scale Feynman diagrams occurring in the Standard Model

TL;DR

ON-SHELL2 is a FORM-based computational package designed to efficiently evaluate two-loop self-energy Feynman diagrams with specific mass and momentum conditions in the Standard Model, utilizing recurrence relations and master integrals.

Contribution

It introduces a new FORM-based package that automates the reduction and calculation of complex two-loop self-energy diagrams with one nonzero internal mass.

Findings

Automates reduction of diagrams to master integrals.

Provides analytical results for key master integrals.

Enables calculations relevant to Standard Model precision tests.

Abstract

A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations obtained from the integration-by-parts method, allows us to reduce diagrams with arbitrary indices (powers of scalar propagators) to a set of master integrals. The SHELL2 package is used for the calculation of special types of diagrams. Analytical results for master integrals are collected.