Discussion on Renormalons

Perturbative series of some quantities in quantum field theories, such as the pole mass of a quark, suffer from a kind of divergence called renormalon divergence. In this paper, the leading renormalon in the pole mass is investigated, and a map is introduced to suppress this renormalon. The inverse of the map is then used to generate the leading renormalon and obtain an explicit expression to calculate its overall normalization. It is also briefly discussed how to apply the method for higher order renormalons, and investigate the asymptotic behavior of other quantities. Finally, the overall normalization of the leading renormalon of the pole mass is calculated for several values of quark flavors.