# Linking FeynCalc to *Package*-X

FeynCalc is a *Mathematica* package consisting of a wide array of tools to assist with high energy physics computations. Since the tensor algebraic capabilities of FeynCalc are more comprehensive than those of *Package*-X, it is expedient to carry out the bulk of your calculations with FeynCalc, and only use *Package*-X's OneLoop.m file as a library of analytic one-loop integrals. The add-on FeynHelpers to FeynCalc provides this interface. This tutorial illustrates how you can analytically evaluate one loop integrals in FeynCalc using FeynHelpers.

## Loading FeynHelpers

After installing FeynCalc 9.2 or later together with FeynHelpers 1.1, initialize them from a fresh kernel:

In[2]:= |

In[8]:= |

Once initialized, FeynHelpers provides the function PaXEvaluate, which interfaces with *Package*-X to insert the analytic forms of one loop integrals.

PaXEvaluate[expr,q] | evaluates scalar 1-loop integrals (up to 4-point functions) in expr that depend on the loop momentum q in D dimensions. |

Substitute analytic forms of 1-loop integrals with *Package*-X.

## Example

In this tutorial, we will calculate the one loop gluon self energy in QCD in covariant ξ-gauges. Omitting the quarks, there are three contributing diagrams:

This example uses FeynCalc's library of Feynman rules, and its ability to carry out color algebra. *Package*-X will be used in the end to supply the analytic expressions.