Calculations in external fields in quantum chromodynamics. Technical review

Abstract

We review the technique of calculation of operator expansion coefficients. The main emphasis is put on gluon operators which appear in expansion of n‐point functions induced by colourless quark currents. Two convenient schemes are discussed in detail: the abstract operator method and the method based on the Fock‐Schwinger gauge for the vacuum gluon field. We consider a large number of instructive examples important from the point of view of physical applications.

Improved determination of the mass of the1−+light hybrid meson from QCD sum rules

“…[13]. Because we will use a slightly modified version of the external field method, we give a brief introduction to this method before carrying out our calculations.…”

“…Then, with the aid of the technique proposed in [13], the gluon propagator in the presence of the external field can be obtained straightforwardly. For instance, up to the term O(q −4 ) the gluon propagator is given by…”

“…One can convert the 4-dimensional quark propagator given in [13] to the D-dimensional quark propagator…”

Ultraviolet-Renormalon Calculus

“…Here we find coefficients c i in the tree approximation using the Schwinger background field technique [16] (for a review, see Ref. [17]). In this technique, the lines in the graph of Fig.…”

Light-cone sum rules for theNγΔtransitions for real photons

“…(8) in powers of the background field and taking only the terms linear in F µν corresponds to the single photon emission, also described by Eq.(3). We will refrain from a more detailed presentation of this expansion, but instead would like to refer to [40] for a review on the background field method and to Chapter 2 in Ref. [27], which is dedicated to the expansion of correlation functions in an electromagnetic background field.…”