Methods of calculation of higher power corrections in QCD

Abstract

Although the methods of calculation of power corrections in QCD sum rules are well known, algebraic complexity rapidly grows with the increase of vacuum condensates' dimensions. Currently, state-of-the-art calculations include dimension 7 and 8 condensates. I summarize and extend algorithms of such calculations. First, I present all the formulae necessary for application of the systematic classification of bilinear quark condensates proposed earlier, and extend this method to the case of gluon condensates. Then I apply these systematic procedures to expansions of bilinear and noncollinear quark and gluon condensates in local ones, and of noncollinear condensates in bilocal ones. The formulae obtained can be used for calculation of correlators involving nonlocal condensates, and for inventing consistent anzatzs for these condensates. Finally, I briefly summarize the methods of calculation of heavy- and light-quark currents' correlators. This paper is aimed both to present new results on gluon and nonlocal condensates and to be a self-contained handbook of formulae necessary for calculation of power corrections in QCD sum rules.