Two-loop renormalisation of non-Abelian gauge theories in $4D$ Implicit Regularisation
The data collected at the LHC does not indicate significant deviations from the predictions of the Standard Model (SM). Taking into account that precision observables can be predicted already at two and three loops, it is evident the necessity to develop stringent tests of selfconsistency of the SM. In this work, we compute the 2-loop 𝛽-function of pure Yang-Mills and quantum chromodynamics using the background field method in a fully quadridimensional setup using Implicit Regularisation (IREG). In IREG the renormalisation constants are defined as basic divergent integrals. Finally, an algorithm for the automated calculation of the 𝛽-function was developed in Mathematica.
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