Tutorial on loop integrals which need regularisation but yield finite results

Understand

In this pedagogical note I will discuss one-loop integrals, where (i) different regions of the integration region lead to divergences and (ii) where these divergences cancel in the sum over all regions.

• These integrals cannot be calculated without regularisation, in spite of the fact that they yield a finite result.
• A typical example where such integrals occur is the decay H --> gamma gamma.