In the absence of direct observation of Beyond Standard Model physics at the LHC, precise tests of the theory require increasing precision. In many calculations, the limiting factor is our imperfect knowledge of the fundamental parameters of QCD, namely the strong coupling and quark masses. In the case of the $c$ quark mass, a reliable method for its extraction is the use of sum rules to the pseudoscalar correlator, where the theoretical prediction in perturbative QCD is compared to lattice QCD data, which are increasinglyaccurate. At the moment, this determination is limited by the theoretical prediction, since the perturbative series of the pseudoscalar correlator, known up to third order in $\alpha_s$, is quite unstable. The main goal of this research project is to understand in terms of the singularities known as renormalons, the source of this instability in the perturbative series. Thereby, one can find rigorous methods in order to circumvent this instability and be able to fully use lattice QCD data for a precise determination of $m_c$ and contribute to precise tests in the Standard Model.
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