Quark Effects in the Gluon Condensate Contribution to the Scalar Glueball Correlation Function

Abstract

One-loop quark contributions to the dimension-four gluon condensate term in the operator product expansion (OPE) of the scalar glueball correlation function are calculated in the MS scheme in the chiral limit of n f quark flavours. The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluonic condensate term represents the leading power corrections to the scalar glueball correlator and, therein, the one-loop logarithmic contributions provide the most important condensate contribution to those QCD sum-rules independent of the low-energy theorem (the subtracted sum-rules).The QCD correlation function of scalar gluonic currentsis used to study the properties of scalar gluonium via QCD sum-rule techniques [1,2]. The current J(x) is the lowest-order version of the operator β(α)G 2 (x), which is renormalization-group invariant for chiral quarks [3,4]. As first noted in [5,6], the one-loop gluon condensate contribution to (1)where {a 0 , b 0 , b 1 } are numerical coefficients (see (26)- (28) below), represents the leading condensate contribution to those sum-rules independent of the low-energy theorem [7], and so provide important nonperturbative effects within sum-rule analyses of scalar glueballs. The one-loop coefficients b 0 and b 1 were evaluated in [5] in the absence of quark effects (i.e. the n f = 0 limit). As these n f = 0 gluon condensate effects have been used in a number of sum-rule analyses where the effects of three quark flavours have been included in the perturbative part [2], it is necessary to extend the results of [5] to enable self-consistent sum-rule analyses in the presence of n f chiral quarks. *

OPE of the energy-momentum tensor correlator in massless QCD

“…The tree and one-loop contributions in (4.24) are in agreement with [8] and [30,31] correspondingly. The two-loop part is new and has a feature that did not occur in lower orders, namely, a divergent contact term.…”

OPE of the energy-momentum tensor correlator and the gluon condensate operator in massless QCD to three-loop order

“…The tree-level, one-loop and two-loop terms in (2.17) have been computed in [9], [37,38] and [1] correspondingly.…”