Package-X is a Mathematica package for the analytic calculation and symbolic manipulation of one-loop Feynman integrals in relativistic quantum field theory.

Initialize Package-X with `Get`

(`<<`

)

`In[1] := <<X``

Call `LoopIntegrate`

to begin the computation of a one-loop integral:
To compute $\mu^{2\epsilon} \int\frac{d^d k}{(2\pi)^d} \frac{1}{(k^2-m^2 + i\varepsilon) (k+p + i\varepsilon)^2}$,

```
In[2] := LoopIntegrate[1, k, {k, m}, {k + p, 0}]
Out[2] = PVB[0, 0, p.p, m, 0]
```

Apply `LoopRefine`

to convert the Passarino-Veltman function `PVB`

into explicit form:

```
In[3] := % // LoopRefine
1 μ^2 1 m^2
Out[3] = 2 + - + Log[---] - ---(m^2 - p.p) Log[------------]
ϵ m^2 p.p m^2 - p.p
```