Package-X


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