Renormalons, correccions de potències, sumes de borel i hiperasintoticitat

Résumé

Perturbative series in QCD are expected to be divergent asymptotic expansions, and therefore, there is an intrincic fuzzyness to the information that can be extracted from them. Consequently, many summation schemes can be defined to assign them a reasonable finite number, each with its advantages and disadvantages. This discussion is particularly relevant when one considers OPEs, where non-perturbative corrections are considered on top of a perturbative expansion. These non-perturbative corrections will intimately depend on how the divergent perturbative expansion is regulated. In this dissertation, one summation scheme to regulate divergent series is explored: Borel summation with the PV prescription. Two different avenues to estimate the Borel sum from truncated versions of the perturbative expansions are presented. These methods are then applied to obtain the gluon condensate from the OPE of the plaquette, and the HQET power correction Lambda bar, both from the lattice and B physics. We also obtain a value for the QCD strong coupling from lattice data of the singlet static quark-antiquark energy making use of PV Borel sums.